Which one of the following sets of ions represents a collections of isoelectronic species

Complete answer:
Isoelectronic species or ions are the ions of different elements that have the same number of electrons but differ in the magnitude of the nuclear charge.
Besides ions, a neutral atom may also the same number of electrons hence it is also isoelectronic species.
Example, sulphide ion (${{S}^{2-}}$ ), chloride ion ($C{{l}^{-}}$), argon (Ar), and potassium ion (${{K}^{+}}$ ) are isoelectronic species.
Variation of size among isoelectronic species: As the nuclear charge increases, the force of attraction by the nucleus on the electrons also increases. As a result, the ionic radius decreases.
Let us observe all the options one by one:
(a)- $N{{a}^{+}},M{{g}^{2+}}A{{l}^{3+}},C{{l}^{-}}$
Sodium ion has 10 electrons
Magnesium ion has 10 electrons
Aluminum ion has 10 electrons
Chlorine ion has 18 electrons

(b)- $N{{a}^{+}},C{{a}^{2+}}S{{c}^{3+}},{{F}^{-}}$
Sodium ion has 10 electrons
Calcium has 18 electrons
Scandium ion has 18 electrons
Fluorine ion has 10 electrons

(c)- ${{K}^{+}},C{{l}^{-}},C{{a}^{2+}}S{{c}^{3+}}$
Potassium ion has 18 electrons
Chlorine ion has 18 electrons
Calcium ion has 18 electrons
Scandium ion has 18 electrons

(d)- ${{K}^{+}},C{{a}^{2+}},S{{c}^{3+}},{{F}^{-}}$
Potassium ion has 18 electrons
Calcium ion has 18 electrons
Scandium ion has 18 electrons
Fluorine ions have 10 electrons.
Hence, only option (c) has all the ions containing 18 electrons, therefore, ${{K}^{+}},C{{l}^{-}},C{{a}^{2+}}S{{c}^{3+}}$ are isoelectronic species.
So, the correct answer is “Option C”.

Note: The nuclear charge is calculated by the number of electrons + charge on the ion.
For example, In Ar,${{K}^{+}}$ and$C{{a}^{2+}}$ the number of electrons is 18.
The nuclear charge of Ar is 18 because there is no charge on the ion.
The nuclear charge of the ${{K}^{+}}$ ion is 19 because potassium ion has a +1 charge.
The nuclear charge of the $C{{a}^{2+}}$ ion is 20 because calcium ion has a +2 charge.

1. A

   Li+,Na+,Mg2+,Ca2+

2. B

   K+,Cl−,Ca2+,Sc3+

3. C

   Ba2+,Sr2+,K+,Ca2+

4. D

   N3−,O2−,F−,S2−

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Solution:

 19K+,17Cl−,20Ca2+ and  21Sc3+ have the same number of 18 electrons.

Thus option B represents a collection of isoelectronic species.

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`K^(+),Cl^(-),Mg^(2+),Sc^(3+)``Na^(+),Ca^(2+),SC^(3+),F^(-)``K^(+),Ca^(2+),Sc^(3+),Cl^(-)``Na^(+), Mg^(2+),Al^(3+), Cl^(-)`

Solution : Iso- electronic species are those which have same number of electrons `K^(+), Ca^(2+), Sc^(3+)` and `Cl^(-)` have 18 electrons each.

`K^(+),Cl^(-),Mg^(2+),Si^(3+)``Na^(+),Ca^(2+),Si^(3+),F^(-)``K^(+),Ca^(2+),Si^(3+),Cl^(-)``Na^(+),Mg^(2+),Al^(3+),Cl^(-)`

Solution : `K^(+) (19-1=18) , Cl^(-) (17+1-18) , Ca^(2+) (20-2=18) Se^(3+) (21-3=18) `represents a collections of isoelectronic species.

`K^(+),Ca^(2+),Sc^(3+),Cl^(-)``Na^(+),Mg^(2+),Al^(3+),Cl^(-)``K^(+),Cl^(-),Mg^(2+),Sc^(3+)Na^(+),Ca^(2+),Sc^(3+),F^(-)`

Solution : `K^(+)` (Z=9), `Ca^(2+)` (Z=20) , `Sc^(3+)` (Z=21) and `Cl^(-)` (Z=17) , all have 18 electrons each and as such are isoelectronic.

`K^(+) ,C1^(-) ,Mg^(2+) , Sc^(3+)``Na^(+) , Ca^(2+) , Sc^(3+) , F^(-)``K^(+) , Ca^(2+) , Sc^(3+) , C1^(-)``Na^(+) , Mg^(2+) ,A1^(3+) ,C1^(-)`

Solution : `K^(+) (19 - 1= 18 ) . C1^(-) (17 + 1= 18) .`
`Ca^(2+) (20- 2 =18) , Sc^(3+) (21 = 3=18)` represent a collection of isoelectronic species.

The two-dimensional (2D) magnet, a long-standing missing member in the family of 2D functional materials, is promising for next-generation information technology. The recent experimental discovery of 2D magnetic ordering in CrI3, Cr2Ge2Te6, VSe2, and Fe3GeTe2 has stimulated intense research activities to expand the scope of 2D magnets. This review covers the essential progress on 2D magnets, with an emphasis on the current understanding of the magnetic exchange interaction, the databases of 2D magnets, and the modification strategies for modulation of magnetism. We will address a large number of 2D intrinsic magnetic materials, including binary transition metal halogenides; chalogenides; carbides; nitrides; oxides; borides; silicides; MXene; ternary transition metal compounds CrXTe3, MPX3, Fe-Ge-Te, MBi2Te4, and MXY (M = transition metal; X = O, S, Se, Te, N; Y = Cl, Br, I); f-state magnets; p-state magnets; and organic magnets. Their electronic structure, magnetic moment, Curie temperature, and magnetic anisotropy energy will be presented. According to the specific 2D magnets, the underlying direct, superexchange, double exchange, super-superexchange, extended superexchange, and multi-intermediate double exchange interactions will be described. In addition, we will also highlight the effective strategies to manipulate the interatomic exchange mechanism to improve the Curie temperature of 2D magnets, such as chemical functionalization, isoelectronic substitution, alloying, strain engineering, defect engineering, applying electronic/magnetic field, interlayer coupling, carrier doping, optical controlling, and intercalation. We hope this review will contribute to understanding the magnetic exchange interaction of existing 2D magnets, developing unprecedented 2D magnets with desired properties, and offering new perspectives in this rapidly expanding field.

I. INTRODUCTION

Section:

Since the discovery of magnetic phenomena in ancient times, magnetism has attracted vast research interest due to its technological importance and theoretical complexity. From the technique point of view, permanent magnets, which are required for high coercivity and large energy product, are widely used in loudspeakers, earphones, electric meters, small motors, and wind power generation. The more esoteric applications of magnetism are in magnetic recording and storage devices of computers, as well as in audio and video systems. Only ten years after the discovery of interlayer exchange coupling and related giant magnetoresistance (GMR) effect in the magnetic multilayers, GMR devices were routinely used in the hard disk drives of computers.11. M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61(21), 2472 (1988). https://doi.org/10.1103/PhysRevLett.61.2472 They are also crucial for the emerging field of spintronics, which is regarded as the core of the next-generation information technology. By using electron spin rather than charge as the information carrier, spintronics possesses prominent advantages of speeding up data processing, high circuit integration density, and low energy consumption.2,32. X. Li and J. Yang, Natl. Sci. Rev. 3(3), 365 (2016). https://doi.org/10.1093/nsr/nww0263. N. Mason and M. Stehno, Nat. Phys. 9(2), 67 (2013). https://doi.org/10.1038/nphys2529

From the theoretical point of view, two fundamental concepts have been proposed to explain the fascinating magnetic phenomenon, namely, exchange interaction and spin-orbit coupling (SOC). The interplay between exchange interaction, spin-orbit coupling, and Zeeman effect is the essence of magnetism research. Together, they explain the origin of spin arrangement, orbital moment, and magnetocrystalline anisotropy, and the effect of external field on these quantities.44. J. Stöhr and H. C. Siegmann, Magnetism: From Fundamentals to Nanoscale Dynamics ( Springer, 2006). Among them, the interatomic/interelectronic exchange interactions are at the heart of the phenomenon of long-range magnetic ordering. Parallel and antiparallel arrangements of spins constitute long-range ferromagnetic (FM) and antiferromagnetic (AFM) orderings. As the dimensionality decreases, the net magnetic moment per atom generally increases. This might be ascribed to lower coordination number, quantum confinement effect, less quenching of orbital magnetic moment, and so on. Meanwhile, in two-dimensional (2D) lattices, exchange interactions would be stronger along one or two spatial directions than others, showing large anisotropy. Depending on the type of magnetic ions and the electronic band structures, the traditional exchange mechanisms, including direct exchange interaction,5–75. Q. Liu, J. Xing, Z. Jiang, X. Jiang, Y. Wang, and J. Zhao, Nanoscale 12(12), 6776 (2020). https://doi.org/10.1039/D0NR00092B6. Z. Liu, J. Liu, and J. Zhao, Nano Res. 10(6), 1972 (2017). https://doi.org/10.1007/s12274-016-1384-37. X. Li and J. Yang, J. Phys. Chem. Lett. 10(10), 2439 (2019). https://doi.org/10.1021/acs.jpclett.9b00769 superexchange interaction,8–148. H. Wang, F. Fan, S. Zhu, and H. Wu, Europhys. Lett. 114(4), 47001 (2016). https://doi.org/10.1209/0295-5075/114/470019. K. Yang, F. Fan, H. Wang, D. I. Khomskii, and H. Wu, Phys. Rev. B 101(10), 100402 (2020). https://doi.org/10.1103/PhysRevB.101.10040210. H. L. Zhuang and R. G. Hennig, Phys. Rev. B 93(5), 054429 (2016). https://doi.org/10.1103/PhysRevB.93.05442911. Y. Sun, R. C. Xiao, G. T. Lin, R. R. Zhang, L. S. Ling, Z. W. Ma, X. Luo, W. J. Lu, Y. P. Sun, and Z. G. Sheng, Appl. Phys. Lett. 112(7), 072409 (2018). https://doi.org/10.1063/1.501656812. H. Kumar, N. C. Frey, L. Dong, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 11(8), 7648 (2017). https://doi.org/10.1021/acsnano.7b0257813. J. He, P. Lyu, and P. Nachtigall, J. Mater. Chem. C 4(47), 11143 (2016). https://doi.org/10.1039/C6TC03917K14. J. Li, Y. Li, S. Du, Z. Wang, B.-L. Gu, S.-C. Zhang, K. He, W. Duan, and Y. Xu, Sci. Adv. 5(6), eaaw5685 (2019). https://doi.org/10.1126/sciadv.aaw5685 double exchange interaction,1515. X. Zhang, B. Wang, Y. Guo, Y. Zhang, Y. Chen, and J. Wang, Nanoscale Horiz. 4(4), 859 (2019). https://doi.org/10.1039/C9NH00038K itinerant electrons,16–2116. H. L. Zhuang, P. R. C. Kent, and R. G. Hennig, Phys. Rev. B 93(13), 134407 (2016). https://doi.org/10.1103/PhysRevB.93.13440717. Y. Ma, Y. Dai, M. Guo, C. Niu, Y. Zhu, and B. Huang, ACS Nano 6(2), 1695 (2012). https://doi.org/10.1021/nn204667z18. F. Li, K. Tu, and Z. Chen, J. Phys. Chem. C 118(36), 21264 (2014). https://doi.org/10.1021/jp507093t19. J.-J. Zhang, L. Lin, Y. Zhang, M. Wu, B. I. Yakobson, and S. Dong, J. Am. Chem. Soc. 140(30), 9768 (2018). https://doi.org/10.1021/jacs.8b0647520. G. V. Pushkarev, V. G. Mazurenko, V. V. Mazurenko, and D. W. Boukhvalov, Phys. Chem. Chem. Phys. 21(40), 22647 (2019). https://doi.org/10.1039/C9CP03726H21. Y. Wen, Z. Liu, Y. Zhang, C. Xia, B. Zhai, X. Zhang, G. Zhai, C. Shen, P. He, R. Cheng, L. Yin, Y. Yao, M. Getaye Sendeku, Z. Wang, X. Ye, C. Liu, C. Jiang, C. Shan, Y. Long, and J. He, Nano Lett. 20(5), 3130 (2020). https://doi.org/10.1021/acs.nanolett.9b05128 and Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanisms,2222. D. Zhang, A. Rahman, W. Qin, X. Li, P. Cui, Z. Zhang, and Z. Zhang, Phys. Rev. B 101(20), 205119 (2020). https://doi.org/10.1103/PhysRevB.101.205119 are all found in various 2D systems, as well as three new interesting exchange interaction mechanisms, known as super-superexchange,23,2423. N. Sivadas, S. Okamoto, X. Xu, C. J. Fennie, and D. Xiao, Nano Lett. 18(12), 7658 (2018). https://doi.org/10.1021/acs.nanolett.8b0332124. J. Xiao and B. Yan, 2D Mater. 7(4), 045010 (2020). https://doi.org/10.1088/2053-1583/ab9ea4 extended superexchange,25,2625. F. Zhang, Y.-C. Kong, R. Pang, L. Hu, P.-L. Gong, X.-Q. Shi, and Z.-K. Tang, New J. Phys. 21(5), 053033 (2019). https://doi.org/10.1088/1367-2630/ab1ee426. C. Wang, X. Zhou, L. Zhou, N.-H. Tong, Z.-Y. Lu, and W. Ji, Sci. Bull. 64(5), 293 (2019). https://doi.org/10.1016/j.scib.2019.02.011 and multi-intermediate double exchange interactions.2727. C. Wang, X. Zhou, L. Zhou, Y. Pan, Z.-Y. Lu, X. Wan, X. Wang, and W. Ji, Phys. Rev. B 102(2), 020402 (2020). https://doi.org/10.1103/PhysRevB.102.020402 These magnetic spin coupling mechanisms will be discussed in Sec. II.

The magnetism in 2D materials has been an emerging and rapidly growing research field. Much on-going progress on 2D magnets has been made mainly in the following three aspects. First, the experimentally unprecedented realizations of high quality 2D magnetic monolayer/multilayer materials using micromechanical cleavage, chemical vapor deposition (CVD), and molecular beam epitaxy (MBE) methods, including CrI3,2828. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391 VI3,2929. S. Tian, J.-F. Zhang, C. Li, T. Ying, S. Li, X. Zhang, K. Liu, and H. Lei, J. Am. Chem. Soc. 141(13), 5326 (2019). https://doi.org/10.1021/jacs.8b13584 CrCl3,3030. X. Cai, T. Song, N. P. Wilson, G. Clark, M. He, X. Zhang, T. Taniguchi, K. Watanabe, W. Yao, D. Xiao, M. A. McGuire, D. H. Cobden, and X. Xu, Nano Lett. 19(6), 3993 (2019). https://doi.org/10.1021/acs.nanolett.9b01317 CrBr3,3131. Z. Zhang, J. Shang, C. Jiang, A. Rasmita, W. Gao, and T. Yu, Nano Lett. 19(5), 3138 (2019). https://doi.org/10.1021/acs.nanolett.9b00553 α-RuCl3,32,3332. A. Banerjee, J. Yan, J. Knolle, C. A. Bridges, M. B. Stone, M. D. Lumsden, D. G. Mandrus, D. A. Tennant, R. Moessner, and S. E. Nagler, Science 356(6342), 1055 (2017). https://doi.org/10.1126/science.aah601533. B. Zhou, Y. Wang, G. B. Osterhoudt, P. Lampen-Kelley, D. Mandrus, R. He, K. S. Burch, and E. A. Henriksen, J. Phys. Chem. Solids 128, 291 (2019). https://doi.org/10.1016/j.jpcs.2018.01.026 VSe2,3434. M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan, and M. Batzill, Nature Nanotechnol. 13(4), 289 (2018). https://doi.org/10.1038/s41565-018-0063-9 VTe2,3535. J. Li, B. Zhao, P. Chen, R. Wu, B. Li, Q. Xia, G. Guo, J. Luo, K. Zang, Z. Zhang, H. Ma, G. Sun, X. Duan, and X. Duan, Adv. Mater. 30(36), 1801043 (2018). https://doi.org/10.1002/adma.201801043 NbTe2,3535. J. Li, B. Zhao, P. Chen, R. Wu, B. Li, Q. Xia, G. Guo, J. Luo, K. Zang, Z. Zhang, H. Ma, G. Sun, X. Duan, and X. Duan, Adv. Mater. 30(36), 1801043 (2018). https://doi.org/10.1002/adma.201801043 MnSex,3636. D. J. O'Hara, T. Zhu, A. H. Trout, A. S. Ahmed, Y. K. Luo, C. H. Lee, M. R. Brenner, S. Rajan, J. A. Gupta, D. W. McComb, and R. K. Kawakami, Nano Lett. 18(5), 3125 (2018). https://doi.org/10.1021/acs.nanolett.8b00683 CrGeTe3,3737. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature 546(7657), 265 (2017). https://doi.org/10.1038/nature22060 MPS3 (M = Fe, Mn, Ni),38–4038. X. Wang, K. Du, Y. Y. F. Liu, P. Hu, J. Zhang, Q. Zhang, M. H. S. Owen, X. Lu, C. K. Gan, P. Sengupta, C. Kloc, and Q. Xiong, 2D Mater. 3(3), 031009 (2016). https://doi.org/10.1088/2053-1583/3/3/03100939. K. Kim, S. Y. Lim, J. Kim, J.-U. Lee, S. Lee, P. Kim, K. Park, S. Son, C.-H. Park, J.-G. Park, and H. Cheong, 2D Mater. 6(4), 041001 (2019). https://doi.org/10.1088/2053-1583/ab27d540. G. Le Flem, R. Brec, G. Ouvard, A. Louisy, and P. Segransan, J. Phys. Chem. Solids 43(5), 455 (1982). https://doi.org/10.1016/0022-3697(82)90156-1 Fe3,5GeTe2,41,4241. Z. Fei, B. Huang, P. Malinowski, W. Wang, T. Song, J. Sanchez, W. Yao, D. Xiao, X. Zhu, A. F. May, W. Wu, D. H. Cobden, J. H. Chu, and X. Xu, Nat. Mater. 17(9), 778 (2018). https://doi.org/10.1038/s41563-018-0149-742. A. F. May, D. Ovchinnikov, Q. Zheng, R. Hermann, S. Calder, B. Huang, Z. Fei, Y. Liu, X. Xu, and M. A. McGuire, ACS Nano 13(4), 4436 (2019). https://doi.org/10.1021/acsnano.8b09660 and MnBi2Te4.4343. Y. Deng, Y. Yu, M. Z. Shi, Z. Guo, Z. Xu, J. Wang, X. H. Chen, and Y. Zhang, Science 367(6480), 895 (2020). https://doi.org/10.1126/science.aax8156 These exciting experiments not only bring about the missing magnetic member in the family of 2D materials but also solve a long-standing controversy about the existence of magnetism in low-dimensional systems. Based on Mermin-Wagner theorem,4444. N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17(22), 1133 (1966). https://doi.org/10.1103/PhysRevLett.17.1133 2D magnetic systems cannot have any long-range FM or AFM ordering at T > 0 for isotropic Heisenberg model. The main reason for the existence of magnetism is the magnetocrystalline anisotropy and the dipolar interaction. Although the strength of these interactions is of order of magnitude of ∼1 meV, they will have a crucial impact on the 2D materials by breaking the conditions of Mermin-Wagner theorem.

Second, optical and electronic means have also been widely developed to characterize the 2D magnets.4545. K. S. Burch, D. Mandrus, and J.-G. Park, Nature 563(7729), 47 (2018). https://doi.org/10.1038/s41586-018-0631-z Spin-polarized scanning tunneling microscope (SP-STM), and x-ray magnetic circular dichroism (XMCD) are the standard experimental techniques. They are highlighted in the recently developed 2D van der Waals magnets. SP-STM can provide valuable and precise information about the magnetic ordering and differentiate magnetic structures as well as exchange interactions. Based on excitation of spin polarized carriers from core levels to Fermi levels via circularly polarized x rays, XMCD is an efficient photocurrent technique used to obtain the local electronic configuration of the valence states. Moreover, due to the theoretical development of the sum rules, the element-specific spin and orbital moments can be obtained separately.4646. W. Liu, Y. Xu, S. Hassan, J. Weaver, and G. van der Laan, in Handbook of Spintronics, edited by Y. Xu , D. D. Awschalom , and J. Nitta ( Springer, Dordrecht, Netherlands, 2016), pp. 709–756. XMCD can also yield the orbital moment anisotropy, which is related to the magnetocrystalline anisotropy energy (MAE) via perturbation model. X-ray magnetic linear dichroism (XMLD) has been proposed as a mean of measuring the anisotropy in the spin orbit interaction, which can be related to the MAE using a straight forward sum rule.4747. G. van der Laan, Phys. Rev. Lett. 82(3), 640 (1999). https://doi.org/10.1103/PhysRevLett.82.640 Inelastic light scattering provides access to the energy, symmetry, and statistics of lattice, electronic, and magnetic excitations in nanomaterials. In addition, Raman spectroscopy can also provide indirect evidence of magnetism, based on either spin-phonon coupling or magnons. Raman scattering from spin-phonon excitations yields incisive information on magnetic materials, which can be used to reveal magnetic ordering and phase transitions. For example, the studies of Kerr rotation versus the applied magnetic field (MOKE) produced the first indirect evidence of magnetic ordering in ultrathin films of Cr2Ge2Te63737. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature 546(7657), 265 (2017). https://doi.org/10.1038/nature22060 and CrI3.2828. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391 Specifically, single-layer FePS34848. J.-U. Lee, S. Lee, J. H. Ryoo, S. Kang, T. Y. Kim, P. Kim, C.-H. Park, J.-G. Park, and H. Cheong, Nano Lett. 16(12), 7433 (2016). https://doi.org/10.1021/acs.nanolett.6b03052 and Cr2Ge2Te64949. Y. Tian, M. J. Gray, H. Ji, R. J. Cava, and K. S. Burch, 2D Mater. 3(2), 025035 (2016). https://doi.org/10.1088/2053-1583/3/2/025035 at high temperatures showed a broad feature above the Curie temperature (TC), which resulted from thermal magnetic fluctuations. In addition to the optical probes, the magnetic state of 2D itinerant magnets with conduction electrons can be detected by the anomalous Hall effect (AHE). So far, AHE has been applied to explore the magnetic ordering of layered Fe3GeTe2 down to the monolayer limit5050. Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen, and Y. Zhang, Nature 563(7729), 94 (2018). https://doi.org/10.1038/s41586-018-0626-9 and few-layer antiferromagnetic MnBi2Te4.4343. Y. Deng, Y. Yu, M. Z. Shi, Z. Guo, Z. Xu, J. Wang, X. H. Chen, and Y. Zhang, Science 367(6480), 895 (2020). https://doi.org/10.1126/science.aax8156

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The powerful DFT tool and high-throughput computations would efficiently accelerate the screening of 2D magnetic candidate materials without having to synthesize them first.65–6865. Z. Jiang, P. Wang, J. Xing, X. Jiang, and J. Zhao, ACS Appl. Mater. Inter. 10(45), 39032 (2018). https://doi.org/10.1021/acsami.8b1403766. H. Liu, J.-T. Sun, M. Liu, and S. Meng, J. Phys. Chem. Lett. 9(23), 6709 (2018). https://doi.org/10.1021/acs.jpclett.8b0278367. N. Mounet, M. Gibertini, P. Schwaller, D. Campi, A. Merkys, A. Marrazzo, T. Sohier, I. E. Castelli, A. Cepellotti, G. Pizzi, and N. Marzari, Nat. Nanotechnol. 13(3), 246 (2018). https://doi.org/10.1038/s41565-017-0035-568. Y. Zhu, X. Kong, T. D. Rhone, and H. Guo, Phys. Rev. Mater. 2(8), 081001 (2018). https://doi.org/10.1103/PhysRevMaterials.2.081001 Starting from the existing database of inorganic compounds, Mounet et al.6767. N. Mounet, M. Gibertini, P. Schwaller, D. Campi, A. Merkys, A. Marrazzo, T. Sohier, I. E. Castelli, A. Cepellotti, G. Pizzi, and N. Marzari, Nat. Nanotechnol. 13(3), 246 (2018). https://doi.org/10.1038/s41565-017-0035-5 performed comprehensive DFT calculations to explore these 3D parent materials for possible exfoliation and finally identified 2662 prospective layered structures with weak interlayer binding energy. Among them, 36 ferromagnetic systems with relatively simple unit cells (less than six atoms) were identified with long-range magnetic order. After a further screening, monolayer materials of LaCl, YCl, ScCl, LaBr2, and CrSBr have been identified as robust ferromagnets with TC > 200 K.6565. Z. Jiang, P. Wang, J. Xing, X. Jiang, and J. Zhao, ACS Appl. Mater. Inter. 10(45), 39032 (2018). https://doi.org/10.1021/acsami.8b14037 Very recently, the ferromagnetic ordering of 2D CrSBr has been confirmed by experimental evidence, and the predicted TC is very likely beyond 132 K.6969. E. J. Telford, A. H. Dismukes, K. Lee, M. Cheng, A. W. A. K. Bartholomew, Y.-S. Chen, X. Xu, A. N. Pasupathy, X. Zhu, C. R. Dean, and X. Roy, arXiv:2005.06110 (2020). In another study, a larger set of a 2D materials database (∼65 000) has been screened by high-throughput DFT calculations, yielding a total of 89 magnetic monolayer systems.6666. H. Liu, J.-T. Sun, M. Liu, and S. Meng, J. Phys. Chem. Lett. 9(23), 6709 (2018). https://doi.org/10.1021/acs.jpclett.8b02783 Among them, 56 showed FM ordering, while 33 prefer antiferromagnetic behavior. Furthermore, 24 FM monolayers were promising candidates possessing TC higher than that of CrI3.

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Driven by all these three aspects, the research of 2D magnets has boomed in the last few years. In recent years, a great deal of new 2D magnetic materials have been experimentally discovered and theoretically predicted. In this review, however, we restricted the term to the 2D intrinsic magnets. The 2D intrinsic nonmagnetic materials, which have already been concluded in the previous review,8383. X. Shi, Z. Huang, M. Huttula, T. Li, S. Li, X. Wang, Y. Luo, M. Zhang, and W. Cao, Crystals 8(1), 24 (2018). https://doi.org/10.3390/cryst8010024 will not be covered here. In this review, we classified these emerging 2D intrinsic magnets into binary transition metal halogenides; chalogenides; carbides; nitrides; oxides; borides; silicides; ternary transition metal compounds CrXTe3, MPX3, Fe-Ge-Te, MBi2Te4, and MXY (M = transition metal; X = O, S, Se, Te, N; Y = Cl, Br, I); f-state magnets; p-state magnets; and organic magnets such as metal organic framework (MOF) and covalent organic framework (COF). The most common prototypes of 2D inorganic magnetic materials are shown in Fig. 1. Their key magnetic properties, especially the magnetic ground state, magnetic moment, TC, and MAE will be comprehensively described in Sec. III.

FIG. 1. The most common 2D inorganic magnetic materials. The representative crystal lattices are included, such as Binary transition metal halides (CrI3, CrI2, Nb3Cl8, and ScCl), binary transition metal (BTM) chalcogenides (Cr3Se4 and VSe2), MXenes (MnB and Cr2CT2), other binary transition metal compounds (Co2P, CrB2, MnO2, and FeSi2), Ternary transition metal compounds (CrSiTe3, CrSBr, FePS3, MnBi2Te4, Fe3GeTe2, and Fe5GeTe2), and p/f magnets (GdI2 and K2N). They have been either experimentally realized or theoretically proposed for each type of magnetic lattice.

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For 2D layered materials, their magnetic properties can be readily modulated by chemical compositions, functional groups, intercalation, and substrates. Moreover, the spin coupling to external perturbations like strain, electronic/magnetic fields, and carrier doping could be the other critical factors for tailoring the strength of exchange interactions or magnetic anisotropy. These modulation methods could be utilized on 2D intrinsic magnets to further enhance Curie temperature. The corresponding mechanisms for modulating the charge distributions, energy level, orbital occupation, symmetry, and hopping paths will be discussed in Sec. IV.

In the final Sec. V, we will conclude with a discussion about future challenges and opportunities of 2D magnets. Four potential future directions regarding the practical applications have been proposed. In addition, this review article mainly focuses on the underlying mechanisms of exchange interaction, which not only determine the Curie temperature of 2D intrinsic magnets but also shed light on the strategies to manipulate the magnetic coupling. Therefore, this discussion is complementary to the other recent review articles on 2D magnets, which have discussed the history,8484. D. L. Cortie, G. L. Causer, K. C. Rule, H. Fritzsche, W. Kreuzpaintner, and F. Klose, Adv. Funct. Mater. 30(18), 1901414 (2020). https://doi.org/10.1002/adfm.201901414 representative 2D magnets,45,85,8645. K. S. Burch, D. Mandrus, and J.-G. Park, Nature 563(7729), 47 (2018). https://doi.org/10.1038/s41586-018-0631-z85. N. Sethulakshmi, A. Mishra, P. M. Ajayan, Y. Kawazoe, A. K. Roy, A. K. Singh, and C. S. Tiwary, Mater. Today 27, 107 (2019). https://doi.org/10.1016/j.mattod.2019.03.01586. D. L. Duong, S. J. Yun, and Y. H. Lee, ACS Nano 11(12), 11803 (2017). https://doi.org/10.1021/acsnano.7b07436 experimental synthesis,8787. P. Huang, P. Zhang, S. Xu, H. Wang, X. Zhang, and H. Zhang, Nanoscale 12(4), 2309 (2020). https://doi.org/10.1039/C9NR08890C probing techniques,8888. K. F. Mak, J. Shan, and D. C. Ralph, Nat. Rev. Phys. 1(11), 646 (2019). https://doi.org/10.1038/s42254-019-0110-y magnetic anisotropy,8989. J. Hu, P. Wang, J. Zhao, and R. Wu, Adv. Phys.: X 3(1), 1432415 (2018). https://doi.org/10.1080/23746149.2018.1432415 device applications,84,90–9284. D. L. Cortie, G. L. Causer, K. C. Rule, H. Fritzsche, W. Kreuzpaintner, and F. Klose, Adv. Funct. Mater. 30(18), 1901414 (2020). https://doi.org/10.1002/adfm.20190141490. W. Zhang, P. K. J. Wong, R. Zhu, and A. T. S. Wee, InfoMat 1(4), 479 (2019). https://doi.org/10.1002/inf2.1204891. I. Choudhuri, P. Bhauriyal, and B. Pathak, Chem. Mater. 31(20), 8260 (2019). https://doi.org/10.1021/acs.chemmater.9b0224392. X. Zhang and C. Gong, Science 363(6428), 4450 (2019). https://doi.org/10.1126/science.aav4450 and their emergent phenomena.9393. T. Cai, X. Li, F. Wang, S. Ju, J. Feng, and C. D. Gong, Nano Lett. 15(10), 6434 (2015). https://doi.org/10.1021/acs.nanolett.5b01791

II. THE ORIGIN OF MAGNETISM IN 2D MATERIALS

Section:

A. The magnetic moment of free atoms

To start discussing the magnetic properties of 2D materials, we should first know the magnetic ground state of a multi-electron atom, which is mainly determined by Hund's rules. Generally speaking, Hund's rules refer to a set of rules that describe spin-spin coupling, orbital-orbital coupling, and spin-orbit coupling, respectively. The first rule about the spin-spin coupling in a multi-electron atom, whose strength is at the order of c.a. 2 eV is especially important. Hence, the magnetic moment is mainly determined by the intra-atomic exchange interaction. The spin-orbit interaction describing the coupling between spin and orbital angular momentum further produces the energy level splitting with the order of several to hundreds mega-electron volts. We can estimate the moment per atom from this rule by maximizing spin (S), orbital momentum (L), and angular moment (J).

In a solid, exchange interaction and SOC are two most important concepts for magnetism. First of all, without interatomic exchange, there would be no spontaneous magnetization. Interatomic exchange interaction determines the long-range spin ordering, i.e., parallel or antiparallel spin alignment in a magnetic material. Meanwhile, spin-orbit interaction creates orbital magnetism and couples the spin to the lattice. Through the SOC interaction, spin and charge can talk to each other via exchanging energy and angular momentum, thereby establishing magnetic anisotropy. In addition, the other competition interactions have also been investigated to determine the size of the moment, including crystal fields, Hund's rule coupling, and onsite Coulomb repulsion.9494. J. M. Coey, Magnetism and Magnetic Materials ( Cambridge University Press, Cambridge, 2010). These factors will be discussed in a following paper.

B. Ligand field theory

When a free ion is placed in a lattice and subjected to the interaction with its surrounding atoms, another key interaction arises, termed a ligand (crystal) field. The ligand effect on the central atom is entirely determined by symmetry and strength of field produced by these surrounding atoms. The symmetry and degenerate states of typical 2D magnets with 3d transition metals are summarized in Table I. It should be noted that the amplitude of splitting energy due to ligand field is comparable to the intra-atomic Coulomb and exchange interactions. Thus, the final ground state depends on the relative amplitude of them. For example, the d4-d7 configurations would show either low-spin or high-spin states in an octahedral ligand field.

TABLE I. The types of crystal field point group symmetry, and orbital splitting of central transition metals ions in some typical 2D magnets.

Crystal fieldPoint groupOrbitals2D magnetsOctahedralOht2g (dxy, dxz, dyz), eg (dx2-y2, dz2)MX3 (X = F, Cl, Br, I);53,10453. W.-B. Zhang, Q. Qu, P. Zhu, and C.-H. Lam, J. Mater. Chem. C 3(48), 12457 (2015). https://doi.org/10.1039/C5TC02840J104. L. Webster and J.-A. Yan, Phys. Rev. B 98(14), 144411 (2018). https://doi.org/10.1103/PhysRevB.98.144411 MX2 (X= Cl, Br, I);100100. V. V. Kulish and W. Huang, J. Mater. Chem. C 5(34), 8734 (2017). https://doi.org/10.1039/C7TC02664A 1T-MX2 (X = S, Se, Te);105105. E. Bruyer, D. Di Sante, P. Barone, A. Stroppa, M.-H. Whangbo, and S. Picozzi, Phys. Rev. B 94(19), 195402 (2016). https://doi.org/10.1103/PhysRevB.94.195402 MPS4;9595. Q. Chen, Q. Ding, Y. Wang, Y. Xu, and J. Wang, J. Phys. Chem. C 124(22), 12075 (2020). https://doi.org/10.1021/acs.jpcc.0c02432 CoGaX4 (X = S, Se, Te)9696. S. Zhang, R. Xu, W. Duan, and X. Zou, Adv. Funct. Mater. 29(14), 1808380 (2019). https://doi.org/10.1002/adfm.201808380 MGe(Si)X3 (X = Se, Te)99,29199. W. Xing, Y. Chen, P. M. Odenthal, X. Zhang, W. Yuan, T. Su, Q. Song, T. Wang, J. Zhong, S. Jia, X. C. Xie, Y. Li, and W. Han, 2D Mater. 4(2), 024009 (2017). https://doi.org/10.1088/2053-1583/aa7034291. J.-Y. You, Z. Zhang, X.-J. Dong, B. Gu, and G. Su, Phys. Rev. Res. 2(1), 013002 (2020). https://doi.org/10.1103/PhysRevResearch.2.013002Distorted octahedralD4ha1 (dz2), b1 (dx2-y2), b2 (dxy), e (dxz, dyz)Mn-Pc,101101. J. Zhou and Q. Sun, J. Am. Chem. Soc. 133(38), 15113 (2011). https://doi.org/10.1021/ja204990j Mn-TCNB102102. M. Mabrouk and R. Hayn, Phys. Rev. B 92(18), 184424 (2015). https://doi.org/10.1103/PhysRevB.92.184424Trigonal prismaticD3he1 (dxz, dyz); e2 (dx2-y2, dxy); a1 (dz2)2H-MX2 (X = S, Se, Te, F, Cl, Br, I, H)10,27,103,28310. H. L. Zhuang and R. G. Hennig, Phys. Rev. B 93(5), 054429 (2016). https://doi.org/10.1103/PhysRevB.93.05442927. C. Wang, X. Zhou, L. Zhou, Y. Pan, Z.-Y. Lu, X. Wan, X. Wang, and W. Ji, Phys. Rev. B 102(2), 020402 (2020). https://doi.org/10.1103/PhysRevB.102.020402103. X. Li, Z. Zhang, and H. Zhang, Nanoscale Adv. 2(1), 495 (2020). https://doi.org/10.1039/C9NA00588A283. Q. Wu, Y. Zhang, Q. Zhou, J. Wang, and X. C. Zeng, J. Phys. Chem. Lett. 9(15), 4260 (2018). https://doi.org/10.1021/acs.jpclett.8b01976Triangular prismC3va1 (dz2); e′ (dxz, dyz) e (dx2-y2, dxy)Fe2C;9797. Y. Yue, J. Magn. Magn. Mater. 434, 164 (2017). https://doi.org/10.1016/j.jmmm.2017.03.058 M2XTx MXene1212. H. Kumar, N. C. Frey, L. Dong, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 11(8), 7648 (2017). https://doi.org/10.1021/acsnano.7b02578HexagonalC6Ve1 (dxz, dyz); e2 (dx2-y2, dxy); a1 (dz2)MN (M = Cr, V, Mn)264–266264. A. V. Kuklin, A. A. Kuzubov, E. A. Kovaleva, N. S. Mikhaleva, F. N. Tomilin, H. Lee, and P. V. Avramov, Nanoscale 9(2), 621 (2017). https://doi.org/10.1039/C6NR07790K265. A. V. Kuklin, S. A. Shostak, and A. A. Kuzubov, J. Phys. Chem. Lett. 9(6), 1422 (2018). https://doi.org/10.1021/acs.jpclett.7b03276266. Z. Xu and H. Zhu, J. Phys. Chem. C 122(26), 14918 (2018). https://doi.org/10.1021/acs.jpcc.8b02323

In fact, ligand field theory provides a simple model to predict the magnetic behavior of 2D transition metal compounds, which is strongly influenced by the coordination environment and the number of d electrons. For example, the configurations of M2NT2 MXene are shown in Figs. 2(a) and 2(b).1212. H. Kumar, N. C. Frey, L. Dong, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 11(8), 7648 (2017). https://doi.org/10.1021/acsnano.7b02578 For a transition metal ion located in an octahedral crystal field, its d orbitals split into the lower-energy t2g states and higher-energy eg orbitals. Similar to the transition metal dichalcogenides (TMDs), these nonbonding t2g and eg states of the MXenes are positioned between the bonding and antibonding states (σ and σ*) of M–X and M–T bonds [Fig. 2(c)]. We assume a perfect bonding case as follows: (1) the nonmetal elements are in their nominal oxidation state, i.e., C4–, N3–, O2–, F−, and OH−; (2) the M–X and M–T bonding states are filled; (3) the M–X and M–T antibonding states are empty. Therefore, only the electrons occupying the nonbonding d orbitals will contribute to the magnetism. For example, the nominal oxidation state of Cr ion in Cr2CF2 is +3. Based on Hund's rules, the remaining 3 electrons on Cr ion will occupy the t2g band half filled, thereby giving a local magnetic moment of 3 μB. Similarly, the local magnetic moments of Mn2CO2, Mn2CF2, and Mn2C(OH)2 are 3 μB, 4 μB, and 4 μB, respectively. The electron spin arrangements on the transition metals in the nitride MXene are shown in the Fig. 2(d).1212. H. Kumar, N. C. Frey, L. Dong, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 11(8), 7648 (2017). https://doi.org/10.1021/acsnano.7b02578 Similar analyses based on symmetry have also been used to identify the magnetic properties of binary transition metal halides, carbides, nitrides, oxides, borides, phosphides, silicides, arsenides, hydrides, and ternary transition metal compounds. The representative examples are shown in Table I. All these results are consistent with the results from DFT calculations.10,12,45,65,93,95–10510. H. L. Zhuang and R. G. Hennig, Phys. Rev. B 93(5), 054429 (2016). https://doi.org/10.1103/PhysRevB.93.05442912. H. Kumar, N. C. Frey, L. Dong, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 11(8), 7648 (2017). https://doi.org/10.1021/acsnano.7b0257845. K. S. Burch, D. Mandrus, and J.-G. Park, Nature 563(7729), 47 (2018). https://doi.org/10.1038/s41586-018-0631-z65. Z. Jiang, P. Wang, J. Xing, X. Jiang, and J. Zhao, ACS Appl. Mater. Inter. 10(45), 39032 (2018). https://doi.org/10.1021/acsami.8b1403793. T. Cai, X. Li, F. Wang, S. Ju, J. Feng, and C. D. Gong, Nano Lett. 15(10), 6434 (2015). https://doi.org/10.1021/acs.nanolett.5b0179195. Q. Chen, Q. Ding, Y. Wang, Y. Xu, and J. Wang, J. Phys. Chem. C 124(22), 12075 (2020). https://doi.org/10.1021/acs.jpcc.0c0243296. S. Zhang, R. Xu, W. Duan, and X. Zou, Adv. Funct. Mater. 29(14), 1808380 (2019). https://doi.org/10.1002/adfm.20180838097. Y. Yue, J. Magn. Magn. Mater. 434, 164 (2017). https://doi.org/10.1016/j.jmmm.2017.03.05898. M. A. U. Absor and F. Ishii, Phys. Rev. B 100(11), 115104 (2019). https://doi.org/10.1103/PhysRevB.100.11510499. W. Xing, Y. Chen, P. M. Odenthal, X. Zhang, W. Yuan, T. Su, Q. Song, T. Wang, J. Zhong, S. Jia, X. C. Xie, Y. Li, and W. Han, 2D Mater. 4(2), 024009 (2017). https://doi.org/10.1088/2053-1583/aa7034100. V. V. Kulish and W. Huang, J. Mater. Chem. C 5(34), 8734 (2017). https://doi.org/10.1039/C7TC02664A101. J. Zhou and Q. Sun, J. Am. Chem. Soc. 133(38), 15113 (2011). https://doi.org/10.1021/ja204990j102. M. Mabrouk and R. Hayn, Phys. Rev. B 92(18), 184424 (2015). https://doi.org/10.1103/PhysRevB.92.184424103. X. Li, Z. Zhang, and H. Zhang, Nanoscale Adv. 2(1), 495 (2020). https://doi.org/10.1039/C9NA00588A104. L. Webster and J.-A. Yan, Phys. Rev. B 98(14), 144411 (2018). https://doi.org/10.1103/PhysRevB.98.144411105. E. Bruyer, D. Di Sante, P. Barone, A. Stroppa, M.-H. Whangbo, and S. Picozzi, Phys. Rev. B 94(19), 195402 (2016). https://doi.org/10.1103/PhysRevB.94.195402

FIG. 2. Schematic diagram to explain the local magnetic moment of M2NT2 MXene (M = Ti, V, Cr, Mn; T = F, OH, O) with different transition metal groups. (a–b) The local coordination of transition metals, each transition-metal ion is subjected to an octahedral crystal field. (c) The simplified density of states, the nonbonding d-orbitals of the MXenes are positioned between bonding (σ) and antibonding (σ*) states of M−X and M−T bonds. (d) Occupation of the electrons on the transition metal centers. Dotted spin indicates electron occupation is equally probable in the states corresponding to either the top (T) or the bottom (B) layer. Each N atom gains three electrons either by accepting two electrons from M atom in the top layer and one electron from the bottom layer M atom or vice versa, which leads to the coexistence of two different oxidation states for the two M atoms. Reproduced with permission from Kumar et al., ACS Nano 11, 7648 (2017). Copyright 2017 American Chemical Society.1212. H. Kumar, N. C. Frey, L. Dong, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 11(8), 7648 (2017). https://doi.org/10.1021/acsnano.7b02578

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C. The importance of exchange interaction

Heisenberg model is a simple theoretical model to describe the physical effects of magnetic systems. Due to the strong local magnetic moment, the leading term is symmetric exchange interaction in Heisenberg model, which has the formĤex=−∑i≠jJijŜi⋅Ŝj,(1)where i and j denote the lattice sites bearing a localized magnetic moment, and Ŝi or Ŝj is a quantum mechanical spin operator. Jij is the exchange constant, which is the basis of most studies of magnetism. Evidently, Jij will decrease rapidly with the distance between lattice i and j. The positive Jij favors parallel spin alignment (i.e., FM), while the negative Jij favors antiparallel spin alignment (i.e., AFM). Theoretically, the values of Jij can be obtained from first-principles calculations. The simplest way is to calculate from the total energy difference between different spin orderings. In experiment, Jij can be determined by fitting the inelastic neutron scattering data to the Heisenberg Hamiltonian.

Generally speaking, these microscopic parameters of Jij define most of macroscopic magnetic properties, especially the Curie temperature and the magnetic response function to an external field. For example, one can estimate magnetic transition temperatures via mean field theory (MFT)106106. N. W. Ashcroft and N. D. Mermin, Solid State Physics ( Holt, Rinehart and Winston, 1976). as follows:TC=J0S(S+1)3kB,(2)where S is the atomic spin, J0 is the sum of exchange interactions, and kB is the Boltzmann constant. For 2D magnets, MFT usually overestimates the transition temperature by around 20% or even more, which is dependent on the coordination number.106106. N. W. Ashcroft and N. D. Mermin, Solid State Physics ( Holt, Rinehart and Winston, 1976). Monte Carlo (MC) method gives a numerical solution to the Heisenberg model with reasonable accuracy. Therefore, it becomes the most commonly used method to predict the critical temperature in 2D magnets. However, MFT is still meaningful in establishing an upper limit of TC at much less computational cost, which can be compared to MC results.

To explain the origin of spontaneous magnetization in metallic magnets with itinerant/localized electrons, such as single layer of Fe3GeTe2, T phase of TMDs, Cr2C, and Fe2C MXenes, another two models—Stoner model and RKKY model—have also been proposed, which will be discussed in Secs. II F and II G, respectively.

D. Spin orbital coupling in 2D magnets

The exchange term is isotropic in the sense that the scalar product Ŝi·Ŝj in Eq. (1) does not change under any rotation applied to every spin in the system. Based on Mermin-Wagner theorem,4444. N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17(22), 1133 (1966). https://doi.org/10.1103/PhysRevLett.17.1133 2D materials can be neither FM nor AFM at nonzero temperature due to thermal fluctuations under isotropic Heisenberg model. However, considering the spin-orbit interaction, this symmetry is broken. Besides the symmetric exchange term Hex discussed in Sec. II C, the spin orbital coupling gives rise to the antisymmetric anisotropic exchange terms. Generally, the strength of antisymmetric anisotropic exchange terms are far less than Hex. However, they become crucial for the magnetic ground state of 2D systems.

So far, many simple anisotropic spin models have been proposed to interpret the emerging magnetism in 2D materials. A typical 2D magnet possesses easy-plane magnetic anisotropy, uniaxial anisotropy, and isotropic anisotropy, which can be described in 2D XY, Ising, and Heisenberg models (XXZ), respectively. Specifically, 2D XY-like behavior has been observed in Cr2Ge2Te6,3737. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature 546(7657), 265 (2017). https://doi.org/10.1038/nature22060 MnPS3,107107. A. Hashemi, H.-P. Komsa, M. Puska, and A. V. Krasheninnikov, J. Phys. Chem. C 121(48), 27207 (2017). https://doi.org/10.1021/acs.jpcc.7b09634 CoGa2X4,9696. S. Zhang, R. Xu, W. Duan, and X. Zou, Adv. Funct. Mater. 29(14), 1808380 (2019). https://doi.org/10.1002/adfm.201808380 CaI2,108108. G. Bhattacharyya, P. Garg, P. Bhauriyal, and B. Pathak, ACS Appl. Nano Mater. 2(10), 6152 (2019). https://doi.org/10.1021/acsanm.9b00967 and so on; 2D Ising FM behavior was also demonstrated in plenty of 2D magnets, such as Cr2Si2Te6,109109. V. Carteaux, F. Moussa, and M. Spiesser, Europhys. Lett. 29(3), 251 (1995). https://doi.org/10.1209/0295-5075/29/3/011 CrI3,88. H. Wang, F. Fan, S. Zhu, and H. Wu, Europhys. Lett. 114(4), 47001 (2016). https://doi.org/10.1209/0295-5075/114/47001 VI3,2929. S. Tian, J.-F. Zhang, C. Li, T. Ying, S. Li, X. Zhang, K. Liu, and H. Lei, J. Am. Chem. Soc. 141(13), 5326 (2019). https://doi.org/10.1021/jacs.8b13584 NiCl3,110110. J. He, X. Li, P. Lyu, and P. Nachtigall, Nanoscale 9(6), 2246 (2017). https://doi.org/10.1039/C6NR08522A NiCl2,111111. E. A. Kovaleva, I. Melchakova, N. S. Mikhaleva, F. N. Tomilin, S. G. Ovchinnikov, W. Baek, V. A. Pomogaev, P. Avramov, and A. A. Kuzubov, J. Phys. Chem. Solids 134, 324 (2019). https://doi.org/10.1016/j.jpcs.2019.05.036 H-VTe2,5757. W. Chen, J.-m. Zhang, Y.-z. Nie, Q.-l. Xia, and G.-h. Guo, J. Magn. Magn. Mater. 508, 166878 (2020). https://doi.org/10.1016/j.jmmm.2020.166878 T-VTe2,5757. W. Chen, J.-m. Zhang, Y.-z. Nie, Q.-l. Xia, and G.-h. Guo, J. Magn. Magn. Mater. 508, 166878 (2020). https://doi.org/10.1016/j.jmmm.2020.166878 T-MnTe2,5757. W. Chen, J.-m. Zhang, Y.-z. Nie, Q.-l. Xia, and G.-h. Guo, J. Magn. Magn. Mater. 508, 166878 (2020). https://doi.org/10.1016/j.jmmm.2020.166878 H-FeTe2,5757. W. Chen, J.-m. Zhang, Y.-z. Nie, Q.-l. Xia, and G.-h. Guo, J. Magn. Magn. Mater. 508, 166878 (2020). https://doi.org/10.1016/j.jmmm.2020.166878 and NiPS3.112112. D. Lançon, R. A. Ewings, T. Guidi, F. Formisano, and A. R. Wildes, Phys. Rev. B 98(13), 134414 (2018). https://doi.org/10.1103/PhysRevB.98.134414

The antisymmetric anisotropic exchange terms contain various generic forms, for example, Dzyaloshinski-Moriya (DM) interaction term and single ion magnetocrystalline anisotropy term.113,114113. I. Dzyaloshinsky, J. Phys. Chem. Solids 4(4), 241 (1958). https://doi.org/10.1016/0022-3697(58)90076-3114. T. Moriya, Phys. Rev. Lett. 4(5), 228 (1960). https://doi.org/10.1103/PhysRevLett.4.228 As stated above, both of them were determined by spin-orbit interaction. They have the following forms:ĤDM=∑i≠jD→ij⋅(Ŝi×Ŝj),(3)Ĥan=∑iAi(Ŝi)2.(4)

In 2D materials, the spin orbital interaction plays a similar role with non-metal atoms in superexchange interaction. As shown in Eq. (3), the DM interaction is characterized by the vector D→ij, which is proportional to spin orbit coupling constant. It is also dependent on the position of the non-metal atom between the two magnetic atoms. Clearly, DM interaction favors an orthogonal alignment between spins.

In Eq. (4), Ai is the easy-axis single ion anisotropy factor. The magnetic anisotropy energy (MAE) is defined as the largest possible energy difference between two different magnetization directions. Within DFT framework, it can be easily obtained by performing total energy calculations including SOC.5151. D. Hobbs, G. Kresse, and J. Hafner, Phys. Rev. B 62(17), 11556 (2000). https://doi.org/10.1103/PhysRevB.62.11556 To clarify the origin of MAEs, the torque method115115. X. D. Wang, R. Q. Wu, D. S. Wang, and A. J. Freeman, Phys. Rev. B 54(1), 61 (1996). https://doi.org/10.1103/PhysRevB.54.61 was implemented in either all-electron full potential linearized augmented plane wave (FPLAPW) or Vienna Ab-initio Simulation Package (VASP) with plane wave basis sets.116,117116. D.-s. Wang, R. Wu, and A. J. Freeman, Phys. Rev. B 47(22), 14932 (1993). https://doi.org/10.1103/PhysRevB.47.14932117. M. Weinert, E. Wimmer, and A. J. Freeman, Phys. Rev. B 26(8), 4571 (1982). https://doi.org/10.1103/PhysRevB.26.4571 To evaluate the contribution of SOC to the magnetic anisotropy, second-order perturbation theory has also been introduced.116116. D.-s. Wang, R. Wu, and A. J. Freeman, Phys. Rev. B 47(22), 14932 (1993). https://doi.org/10.1103/PhysRevB.47.14932

The DM interaction and single ion magnetocrystalline anisotropy term are typically a few percent of the isotropic term, producing a modest canting to symmetric exchange interactions. Nevertheless, the DM and single ion magnetocrystalline anisotropy terms are the good supplement to the 2D materials. A spontaneous rearrangement of atoms to favor the DM interaction can produce a large electric polarization in magnetoelectric materials. Meanwhile, the competition of spin-spin directions would be helpful to understand complicated magnetic behavior, such as magnetic skyrmions, and quantum spin liquid. The magnetic anisotropy is a prerequisite to realize FM or AFM states at the 2D limit.

A much-studied spin model (Kitaev model) is developed to describe the anisotropic spin exchange coupling for honeycomb spin lattice.118118. A. Kitaev, Ann. Phys. 321(1), 2 (2006). https://doi.org/10.1016/j.aop.2005.10.005 It has the formHK=∑⟨i,j⟩γKγSiγSjγ.(5)

Neighboring spins couple depending on the direction of their bond γ with SxSx, SySy, or SzSz. This exchange term and the symmetric Heisenberg term (Kitaev-Heisenberg model) together serve as a putative minima model for several materials, including α-RuCl3119119. K. W. Plumb, J. P. Clancy, L. J. Sandilands, V. V. Shankar, Y. F. Hu, K. S. Burch, H.-Y. Kee, and Y.-J. Kim, Phys. Rev. B 90(4), 041112 (2014). https://doi.org/10.1103/PhysRevB.90.041112 and Li(Na)2IrO3.120120. J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 110(9), 097204 (2013). https://doi.org/10.1103/PhysRevLett.110.097204

Beyond these terms, one should also note that the real materials may have additional exchange couplings other than these couplings, including dipolar term, biquadratic interaction, and Zeeman coupling to the external magnetic field.121121. S. Baierl, M. Hohenleutner, T. Kampfrath, A. K. Zvezdin, A. V. Kimel, R. Huber, and R. V. Mikhaylovskiy, Nat. Photon. 10(11), 715 (2016). https://doi.org/10.1038/nphoton.2016.181 The strength of these exchange interactions is also much lower than that of symmetric exchange interaction. Therefore, to simplify, only the dominated spin models are investigated and discussed in this review, which are roughly enough to describe the critical parameters of 2D magnets.

E. The known exchange interaction

In this section, we discuss the identified exchange mechanisms in the real 2D magnets based on the abovementioned three models, including direct exchange, superexchange, double exchange, super-superexchange, extended superexchange, multi-intermediate double exchange interaction, itinerant electrons, and RKKY (Fig. 3). Their regimes of applicability depend on the electronic band structures and the types of magnetic ions, i.e., metal or insulator, and localized or delocalized. However, it is really difficult to distinguish them completely. For example, 3d electrons are partially localized on the atomic sites and also partially delocalized in the crystal. In each exchange interaction, the magnetic ground state and Curie temperature will be further discussed, which are determined from the competition between the kinetic exchange energy and the Coulomb repulsion. It is worth noting that magnetic exchange interactions in the 2D magnets are rather complicated; thus, they are unable to be generalized under a one-theory umbrella. Although these types of exchange mechanism have been utilized to explain different materials appropriately, there are no clear borderlines between them. Moreover, several exchange interactions may possibly coexist in one real material. To understand the magnetic ordering and magnetic coupling strength, we always need to ask which one is dominant.

FIG. 3. Schematic diagram of the representative exchange interaction mechanisms. Several kinds of magnetic interaction between localized moments have been included, such as the conventional direct exchange, superexchange, double exchange, indirect exchange, and RKKY. The exchange interaction between itinerant electrons have also been covered. In addition, the small blue circle in superexchange region is super-superexchange interaction (SSE). The small grey circle in double exchange region is multi-intermediate double exchange interaction (MDE). The overlap region of double exchange and superexchange—the blue part—is the extended superexchange (ESE) interaction.

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1. Direct exchange interaction

Direct exchange interaction is based on the overlap of electronic wavefunctions and is therefore very short ranged.122122. A. J. Freeman and R. E. Watson, Phys. Rev. 124(5), 1439 (1961). https://doi.org/10.1103/PhysRev.124.1439 It is always confined to electrons in the orbitals from the nearest neighboring atoms. Considering the distance of the magnetic atoms, the strength of direct exchange interaction is always very weak. As a consequence, the direct exchange interaction is neither the main source of magnetism nor can it appropriately describe the magnetic behavior in most of the reported 2D magnets. Even so, direct exchange interaction between the neighboring sites is still dominant in the magnetic materials with peculiar d-d, d-p, and p-p hybridizations. With sufficiently large overlap, the exchange integral Jij tends to be antiferromagnetic, ferromagnetic, or ferrimagnetic, depending on symmetry relationship and occupation number of the orbitals.

As a specific example, Liu et al.55. Q. Liu, J. Xing, Z. Jiang, X. Jiang, Y. Wang, and J. Zhao, Nanoscale 12(12), 6776 (2020). https://doi.org/10.1039/D0NR00092B proposed a novel class of 2D magnetic metal-shrouded materials, namely tetragonal transition metal phosphides (TM2P), which showed peculiar coexistence of in-plane TM–P covalent bonds and interlayer TM–TM metallic bonds. For Co2P, the spin-up dz2 orbital contributes to the total on-site moment of ∼1 μB. The electrons can hop from the occupied dz2 orbital to the empty dz2 orbital via Co–Co metallic bonds; thus, the d-d exchange between the neighboring sites is ferromagnetic. However, the more active dxz/dyz orbitals dominate the AFM ground states in Fe2P. There is overlap between dxz/dyz orbitals at two neighboring metal sites, and electrons would hop between these two active orbitals of Fe atoms. The resulting exchange interaction is antiferromagnetic and strong. Consequently, Fe2P behaves as an antiferromagnetic material with TN = 23 K, while Co2P is a ferromagnetic material with TC = 580 K. The corresponding AFM and FM direct interaction mechanisms are shown in Fig. 4(a).

FIG. 4. (a) Direct FM (AFM) exchange interactions between dz2-dz2 (dyz/dxz-dyz/dxz) orbitals. (b) Schematic diagram of the possible paths for magnetic exchange interaction in MPS3 (M = Ni, Mn, Fe) monolayer. (c) Schematic diagram of the FM coupling mechanism: p-p direct exchange interaction in TaN2 monolayer. (d) Schematic diagram of the FM coupling mechanism: d-p direct exchange interaction in 2D organometallic lattices. Panel (a) reproduced with permission from Liu et al., Nanoscale 12, 6776 (2020). Copyright 2020, Royal Society of Chemistry.55. Q. Liu, J. Xing, Z. Jiang, X. Jiang, Y. Wang, and J. Zhao, Nanoscale 12(12), 6776 (2020). https://doi.org/10.1039/D0NR00092B Panel (b) reproduced with permission from Lançon et al., Phys. Rev. B 98, 134414 (2018). Copyright 2018 American Physical Society.112112. D. Lançon, R. A. Ewings, T. Guidi, F. Formisano, and A. R. Wildes, Phys. Rev. B 98(13), 134414 (2018). https://doi.org/10.1103/PhysRevB.98.134414 Panel (c) reproduced with permission from Liu et al., J. Mater. Chem. C 5, 727 (2017). Copyright 2017 Royal Society of Chemistry.124124. J. Liu, Z. Liu, T. Song, and X. Cui, J. Mater. Chem. C 5(3), 727 (2017). https://doi.org/10.1039/C6TC04490E Panel (d) reproduced with permission from Li et al., J. Phys. Chem. Lett. 10, 2439 (2019). Copyright 2019 American Chemical Society.77. X. Li and J. Yang, J. Phys. Chem. Lett. 10(10), 2439 (2019). https://doi.org/10.1021/acs.jpclett.9b00769

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To clarify the novel AFM ground state of ternary MPS3 monolayer, the dominant electron hopping paths were analyzed. As a representative case, the first neighboring-to-neighboring interaction for MnPSe3 monolayer is shown in Fig. 4(b).123123. Q. Pei, X.-C. Wang, J.-J. Zou, and W.-B. Mi, Front. Phys. 13(4), 137105 (2018). https://doi.org/10.1007/s11467-018-0796-9 Electrons hopping from two paths has been discussed—one is short-range direct interaction between the two neighboring Mn ions, and the other one is long-range Mn–Se–Mn superexchange with an angle of 84.1°. Owing to the strong interaction between neighboring Mn2+ cations and the large electron excitation energy from Se p orbital to Mn d orbital, direct AFM exchange interaction prevails over FM superexchange interaction.

Moreover, robust FM coupling with high Curie temperature was also observed in 1T-TaN2124124. J. Liu, Z. Liu, T. Song, and X. Cui, J. Mater. Chem. C 5(3), 727 (2017). https://doi.org/10.1039/C6TC04490E and 1T-YN2 monolayers.66. Z. Liu, J. Liu, and J. Zhao, Nano Res. 10(6), 1972 (2017). https://doi.org/10.1007/s12274-016-1384-3 In these systems, the N–N distances (∼1.74 Å) are short enough to generate the strong direct exchange interaction. In TaN2, the magnetic moment arises mainly from the fully filled spin-up pz orbitals and nearly unfilled spin-down pz orbitals. Benefiting from the delocalized feature of p orbitals of N atoms, p-p direct exchange interaction [see Fig.4(c)] leads to strong long-range FM coupling. In 1T-YN2, the J1 parameter is 11.3 meV, confirming again that the direct interaction is FM coupling.

Robust ferrimagnetic ordering was proposed in 2D metal organic frameworks with conjugated electron acceptors diketopyrrolopyrrole (DPP) as organic linkers and transition metal Cr as nodes, namely, Cr-DPP [Fig. 4(d)].77. X. Li and J. Yang, J. Phys. Chem. Lett. 10(10), 2439 (2019). https://doi.org/10.1021/acs.jpclett.9b00769 In 2D Cr-DPP, each Cr atom possesses a spin magnetic moment of around 4 μB, and each DPP unit has a spin magnetic moment of about 1 μB. Considering the symmetry matching rule, the majority of magnetic coupling between Cr and DPP can be ascribed to direct exchange interaction between dxy↑ orbital of Cr and p↓ orbital (px or py) of the adjacent N atoms. Meanwhile, direct exchange between dxz/dyz↑ orbital of Cr and pz↓ orbital of N contributes to the minority part due to the comparatively big energy gap between the two orbitals. The strong d-p direct exchange coupling of 2D Cr-DPP yields a Curie temperature of 316 K. Robust d-p direct exchange coupling was also found in 2D ferrimagnetic V-DPP77. X. Li and J. Yang, J. Phys. Chem. Lett. 10(10), 2439 (2019). https://doi.org/10.1021/acs.jpclett.9b00769 and Cr-pentalene MOF,125125. X. Li and J. Yang, J. Am. Chem. Soc. 141(1), 109 (2019). https://doi.org/10.1021/jacs.8b11346 and the corresponding TC was 406 and 560 K, respectively.

2. Superexchange interaction

Among the reported 2D magnets, there is a large number of transition metal compounds, such as binary/ternary transition metal halides, chalcogenides, borides, carbides, nitrides, oxides, hydrides, and silicides. Their detailed magnetic properties will be discussed in Sec. III. As we stated above, the direct overlap between d orbitals in these transition metal compounds is generally too small due to the large distance. Thus, d electrons can only move through hybridization with the ligand atoms between them, like 2p orbitals of B, C, N, O, H, and F. Such p-d hybridization provides a common type of exchange mechanism, known as superexchange interaction. That is to say, superexchange interaction arises from the non-neighboring magnetic ions mediated by the neighboring non-magnetic ions. Empirically, the magnetic ground state is determined by Goodenough-Kanamori-Anderson (GKA) rules,126–128126. J. B. Goodenough, Phys. Rev. 100(2), 564 (1955). https://doi.org/10.1103/PhysRev.100.564127. J. Kanamori, J. Appl. Phys. 31(5), S14 (1960). https://doi.org/10.1063/1.1984590128. P. W. Anderson, Phys. Rev. 115(1), 2 (1959). https://doi.org/10.1103/PhysRev.115.2 which are based on the symmetry relationships and electron occupancy of the overlapping atomic orbitals. According to these rules: (1) A 180° superexchange interaction of two magnetic ions with partially filled d shells is AFM if virtual electron transfer occurs between the overlapping orbitals that are each half filled. (2) A 180° superexchange interaction of two magnetic ions with partially filled d shells is FM if virtual electron transfer occurs from a half-filled to an empty orbital or from a filled to a half-filled orbital. (3) A 90° superexchange interaction where the occupied d orbitals of metal atom overlap with different orthogonal p orbitals of the ligands results in weak ferromagnetism. In addition, the strength of superexchange coupling is also sensitive to two factors, i.e., (1) the degree of p-d hopping process and (2) the strength of SOC.

Based on the superexchange mechanism and GKA rules, the magnetic behavior of a variety of 2D magnets has been successfully explained, including the recently highlighted CrI3,88. H. Wang, F. Fan, S. Zhu, and H. Wu, Europhys. Lett. 114(4), 47001 (2016). https://doi.org/10.1209/0295-5075/114/47001 VI3,99. K. Yang, F. Fan, H. Wang, D. I. Khomskii, and H. Wu, Phys. Rev. B 101(10), 100402 (2020). https://doi.org/10.1103/PhysRevB.101.100402 VS2,1010. H. L. Zhuang and R. G. Hennig, Phys. Rev. B 93(5), 054429 (2016). https://doi.org/10.1103/PhysRevB.93.054429 Cr2Ge2Te3,1111. Y. Sun, R. C. Xiao, G. T. Lin, R. R. Zhang, L. S. Ling, Z. W. Ma, X. Luo, W. J. Lu, Y. P. Sun, and Z. G. Sheng, Appl. Phys. Lett. 112(7), 072409 (2018). https://doi.org/10.1063/1.5016568 MXenes,12,1312. H. Kumar, N. C. Frey, L. Dong, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 11(8), 7648 (2017). https://doi.org/10.1021/acsnano.7b0257813. J. He, P. Lyu, and P. Nachtigall, J. Mater. Chem. C 4(47), 11143 (2016). https://doi.org/10.1039/C6TC03917K MnBi2Te4,1414. J. Li, Y. Li, S. Du, Z. Wang, B.-L. Gu, S.-C. Zhang, K. He, W. Duan, and Y. Xu, Sci. Adv. 5(6), eaaw5685 (2019). https://doi.org/10.1126/sciadv.aaw5685 GdI2,129129. B. Wang, X. Zhang, Y. Zhang, S. Yuan, Y. Guo, S. Dong, and J. Wang, Mater. Horiz. 7, 1623 (2020). https://doi.org/10.1039/D0MH00183J and so on. For instance, 2D CrI3 is an insulator [Fig. 5(a)] with local spin of S = 3/2.88. H. Wang, F. Fan, S. Zhu, and H. Wu, Europhys. Lett. 114(4), 47001 (2016). https://doi.org/10.1209/0295-5075/114/47001 Considering the local octahedral coordination field [Fig. 5(b)], the valence bands and the conduction bands consist of t2g states and eg states, respectively. The closed t2g3 configuration indicates the formal Cr3+ charge state. The exchange splitting in 2D CrI3 is about 3 eV, which is larger than the t2g-eg crystal field splitting. For the corner sharing I atoms, their in-plane px/py orbitals couple to the Cr dx2-y2 orbital, and the out-of-plane I pz to Cr dxz/yz [Fig. 5(c)]. Owing to the closed t2g3 subshell, the direct exchange interaction between two neighboring Cr3+ ions is AFM, which is associated with Pauli exclusion principle in the virtually excited t2g2-t2g4 state. However, the Cr–Cr distance is as large as 3.95 Å; thus the AFM exchange should be weak. As a consequence, the two nearly 90° Cr–I–Cr superexchange mechanisms dominate in 2D CrI3. One originates from the stronger p-d hybridization via the orthogonal orbitals [Figs. 5(d) and 5(f)], and the other involves the relatively weak p-d hybridization via the same px orbital [Figs. 5(d) and 5(e)]. Both of them give an effective Cr–Cr FM coupling. According to the weak 90° d-p-d superexchange interaction, the Curie temperature of CrI3 monolayer is 45 K.2828. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391 In fact, the weak superexchange interaction also results in low Curie temperatures for the experimentally reported 2D magnets, such as 30 K for Cr2Ge2Te63737. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature 546(7657), 265 (2017). https://doi.org/10.1038/nature22060 and 34 K for CrBr3.3131. Z. Zhang, J. Shang, C. Jiang, A. Rasmita, W. Gao, and T. Yu, Nano Lett. 19(5), 3138 (2019). https://doi.org/10.1021/acs.nanolett.9b00553

FIG. 5. (a) Honeycomb lattice of CrI3 monolayer. Three magnetic pair interactions are marked with J1, J2, and J3. (b) Edge-sharing CrI6 octahedra. (c) Partial density of states (DOS) for Cr 3d and I 5p orbitals, and the Fermi level is set to zero. (d)–(f) Schematic structures of FM superexchange interactions in CrI3 monolayer. (g) Illustrations of the Cr–Cr direct exchange, Cr–X–Cr superexchange, and Cr–X–Cr double exchange interactions in Cr3X4 (X = S, Se, Te) monolayers. Panels (a)–(f) reproduced with permission from Wang et al., Europhys. Lett. 114, 47001 (2016). Copyright 2016 IOP.88. H. Wang, F. Fan, S. Zhu, and H. Wu, Europhys. Lett. 114(4), 47001 (2016). https://doi.org/10.1209/0295-5075/114/47001 Panel (g) reproduced with permission from Zhang et al., Nanoscale Horiz. 4, 859 (2019). Copyright 2019 Royal Society of Chemistry.1515. X. Zhang, B. Wang, Y. Guo, Y. Zhang, Y. Chen, and J. Wang, Nanoscale Horiz. 4(4), 859 (2019). https://doi.org/10.1039/C9NH00038K

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3. Double exchange interaction

Besides direct exchange and superexchange, double exchange interaction always exists in the 2D magnets with high-spin states. It arises between the ions in different oxidation states. In double exchange pictures, the interaction occurs when one atom has an extra electron compared to the other one. The electron transfer from the neighboring sites should have the same direction of spin. Therefore, the magnetic coupling is ferromagnetic.130130. P. G. De Gennes, Phys. Rev. 118(1), 141 (1960). https://doi.org/10.1103/PhysRev.118.141 For example, Zhang et al.1515. X. Zhang, B. Wang, Y. Guo, Y. Zhang, Y. Chen, and J. Wang, Nanoscale Horiz. 4(4), 859 (2019). https://doi.org/10.1039/C9NH00038K provided a double exchange model [Fig. 5(g)] in Cr3X4 monolayers (X = S, Se, Te), where seven hexagonal atomic layers are stacked in the sequence of X1–Cr1–X2–Cr2–X2–Cr1–X1 along the z direction. The Cr1 and Cr2 atoms have different local coordination environments and show different valence states as Cr13+ and Cr22+, respectively. The X atom connects the nearest-neighboring Cr13+ and Cr22+ ions and gives up its spin-up or spin-down electron to Cr13+. Then its vacant orbital could be filled by an electron from Cr22+. Mediated by the X atom, double exchange process is revealed by the electron hopping from one Cr ion to the other neighboring Cr ion of different oxidation state. Such mechanism dominates in Cr3Se4 and Cr3Te4 monolayers, and strengthens the FM coupling. Consequently, high Curie temperatures of 370 and 460 K were reported for Cr3Se4 and Cr3Te4 monolayers, respectively.

4. Extended superexchange theory

The above three fundamental magnetic interactions have already explained the origin of most 2D magnetic insulators. However, the magnetic ground state of some complicated 2D materials are still too difficult to be determined from these theories. In such situations, a few new theories, i.e., extended superexchange interaction, super-superexchange interaction, and multi-intermediate double exchange interactions, have been proposed recently.

For the 2D materials containing anions with different valence states, an extended superexchange theory was further proposed.2525. F. Zhang, Y.-C. Kong, R. Pang, L. Hu, P.-L. Gong, X.-Q. Shi, and Z.-K. Tang, New J. Phys. 21(5), 053033 (2019). https://doi.org/10.1088/1367-2630/ab1ee4 It has been validated in the representative CrOCl and FeOCl monolayers. Four possible superexchange paths (P1–P4) in CrOCl are displayed in Fig. 6(a). Similar to 2D CrI3, the Cr atoms in 2D CrOCl are still located in a distorted octahedral crystal field. The d3 state (Cr3+) in CrI3 can be written as t2g3eg,0 while the d3 state (Cr3+) and d4 state (Cr2+) in CrOCl is t2g3eg0 and t2g3eg1, respectively. The extended superexchange theory indicates that (1) a 180° bond angle in the interaction path Cr–O–Cr (P4) favors strongly FM configuration through the dominated pσ-pσ bond; (2) a 180° bond angle in the P3 path corresponds to strong AFM, where the interaction is conducted through pσ-pσ bond; (3) For Cr–O–Cr path (P2) with 90° bond angle, the d3 state has a crucial unfilled eg orbital; thus, the interaction is FM with weak coupling strength, owing to the competition of the two pσ-pπ bonds; (4) For a 90° bond angle in the interaction path of Cr-Cl-Cr (P1), the d4 states interact through two pσ-pπ bonds with moderate strength of AFM coupling. Based on first-principles calculations, they further clarified that monolayer CrOCl exhibited antiferromagnetic ordering.2525. F. Zhang, Y.-C. Kong, R. Pang, L. Hu, P.-L. Gong, X.-Q. Shi, and Z.-K. Tang, New J. Phys. 21(5), 053033 (2019). https://doi.org/10.1088/1367-2630/ab1ee4 On all accounts, this extended superexchange theory supports the strongly FM/AFM configurations, which are highly anticipated to design robust 2D magnetic materials with polyvalent anions. Based on this theory, the high Curie/Néel temperatures in 2D MXY (M = metal; X = S, Se, Te; Y = F, Cl, Br, I) compounds could be explained.26,65,70,131–13326. C. Wang, X. Zhou, L. Zhou, N.-H. Tong, Z.-Y. Lu, and W. Ji, Sci. Bull. 64(5), 293 (2019). https://doi.org/10.1016/j.scib.2019.02.01165. Z. Jiang, P. Wang, J. Xing, X. Jiang, and J. Zhao, ACS Appl. Mater. Inter. 10(45), 39032 (2018). https://doi.org/10.1021/acsami.8b1403770. R. Han, Z. Jiang, and Y. Yan, J. Phys. Chem. C 124(14), 7956 (2020). https://doi.org/10.1021/acs.jpcc.0c01307131. Y. Guo, Y. Zhang, S. Yuan, B. Wang, and J. Wang, Nanoscale 10(37), 18036 (2018). https://doi.org/10.1039/C8NR06368K132. J. Pan, J. Yu, Y.-F. Zhang, S. Du, A. Janotti, C.-X. Liu, and Q. Yan, npj Computat. Mater. 6, 152 (2020). https://doi.org/10.1038/s41524-020-00419-y133. S. Wang, J. Wang, and M. Khazaei, Phys. Chem. Chem. Phys. 22(20), 11731 (2020). https://doi.org/10.1039/D0CP01767A According to above discussions, the extended superexchange theory may be regarded as a combination of superexchange and double exchange. Similar mechanism has also been proposed by Wang et al.2626. C. Wang, X. Zhou, L. Zhou, N.-H. Tong, Z.-Y. Lu, and W. Ji, Sci. Bull. 64(5), 293 (2019). https://doi.org/10.1016/j.scib.2019.02.011

FIG. 6. (a) Four possible superexchange paths in CrOCl monolayer. Electrons can only hop between orbitals that are connected by dashed blue and red lines. (b) Hopping of t2g−t2g and t2g-eg orbitals in the FM/AFM alignment. (c) Interlayer Cr nearest-neighboring J1, the second-nearest-neighboring J2 in AB-stacking, and the nearest-neighboring J′1 in AB′-stacking CrI3. (d) Schematic diagrams for the AFM/FM super-superexchange interaction involving different orbital hybridizations. (e) Electronic structure, FM-AFM, and FM-FM interlayer double superexchange mechanism of bilayer CrSe2. The up and down solid arrows represent the electron with different spin components and the hollow arrows display different magnetic moments of the Cr atoms. The interlayer sharing electrons are surrounded by dashed green circles. The length of the arrow qualitatively shows the amounts of electrons with given spin component. Panel (a) reproduced with permission from Zhang et al., New J. Phys. 21, 053033 (2019). Licensed under a Creative Commons Attribution (CC-BY-3.0).2525. F. Zhang, Y.-C. Kong, R. Pang, L. Hu, P.-L. Gong, X.-Q. Shi, and Z.-K. Tang, New J. Phys. 21(5), 053033 (2019). https://doi.org/10.1088/1367-2630/ab1ee4 Panels (b)–(d) reproduced with permission from Sivadas et al., Nano Lett. 18, 7658 (2018). Copyright 2018 American Chemical Society.2323. N. Sivadas, S. Okamoto, X. Xu, C. J. Fennie, and D. Xiao, Nano Lett. 18(12), 7658 (2018). https://doi.org/10.1021/acs.nanolett.8b03321 Panel (e) reproduced with permission from Wang et al., Phys. Rev. B 102, 020402 (2020). Copyright 2020 American Physical Society.2727. C. Wang, X. Zhou, L. Zhou, Y. Pan, Z.-Y. Lu, X. Wan, X. Wang, and W. Ji, Phys. Rev. B 102(2), 020402 (2020). https://doi.org/10.1103/PhysRevB.102.020402

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5. Super-superexchange interaction

The super-superexchange interaction is different from the typical superexchange interactions by the mediated ligands.23,2423. N. Sivadas, S. Okamoto, X. Xu, C. J. Fennie, and D. Xiao, Nano Lett. 18(12), 7658 (2018). https://doi.org/10.1021/acs.nanolett.8b0332124. J. Xiao and B. Yan, 2D Mater. 7(4), 045010 (2020). https://doi.org/10.1088/2053-1583/ab9ea4 As we stated above, single anion serves as an intermediate to bridge two magnetic cations in the superexchange interaction (M–X–M). In contrast, the super-superexchange interaction involves longer M–X⋯X–M hopping paths. According to the distance between magnetic ions, the strength of super-superexchange interaction is generally much weaker than those of direct interaction and superexchange interaction. Taking single layer CrAsS4 as a representative, the exchange interaction parameter contributed by both short-range Cr–Cr direct exchange interaction and Cr–S–Cr superexchange interaction is 3.03 meV, while the value for long-range Cr–S–As–S–Cr super-superexchange interaction is –0.49 meV. Therefore, the super-superexchange interaction is usually neglected in most investigations. However, it could become stronger than superexchange interaction in some few-layer magnetic systems with non-covalent van der Waals (vdW) gaps. The importance of super-superexchange interaction is highlighted in the well-known bilayer CrI3.23,28,13423. N. Sivadas, S. Okamoto, X. Xu, C. J. Fennie, and D. Xiao, Nano Lett. 18(12), 7658 (2018). https://doi.org/10.1021/acs.nanolett.8b0332128. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391134. P. Jiang, C. Wang, D. Chen, Z. Zhong, Z. Yuan, Z.-Y. Lu, and W. Ji, Phys. Rev. B 99(14), 144401 (2019). https://doi.org/10.1103/PhysRevB.99.144401 For bilayer CrI3, the local magnetic moments form intralayer FM ordering below 45 K.2828. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391 However, its interlayer magnetic coupling varies between FM and AFM, depending on local stacking geometry.2323. N. Sivadas, S. Okamoto, X. Xu, C. J. Fennie, and D. Xiao, Nano Lett. 18(12), 7658 (2018). https://doi.org/10.1021/acs.nanolett.8b03321 These significant results reveal that even weak overlap has a large impact on the interlayer magnetic coupling through exchange between two adjacent interlayer I atoms, which signifies a new exchange interaction mechanism, i.e., super-superexchange. It also means that the super-superexchange is basically the coupling between next-next nearest neighbor.

Sivadas et al.2323. N. Sivadas, S. Okamoto, X. Xu, C. J. Fennie, and D. Xiao, Nano Lett. 18(12), 7658 (2018). https://doi.org/10.1021/acs.nanolett.8b03321 carefully investigated the details of stacking-dependent interlayer exchange interaction for bilayer CrI3 systems. The AB stacking (S6 point group) from the low-temperature bulk structure and the AB′ stacking (C2h point group) from the high-temperature bulk structure were considered. Figure 6(b) schematically shows different exchange interactions between Cr atoms in different layers. One can see that hopping from a t2g to t2g orbital is prohibited for FM alignment, while this is allowed for AFM alignment. Therefore, t2g to t2g hybridization leads to AFM ordering. On the other hand, hopping from t2g-eg leads to an exchange coupling that is predominantly FM because of the local Hund coupling. All these interlayer Cr−Cr exchange interactions are mediated by the hybridization between I pz orbitals in different layers, which is the nature of super-superexchange interaction.

The stacking-dependent magnetism originates from a competition between different interlayer orbital hybridizations. Interlayer Cr−Cr nearest neighboring interaction J1 and the second neighboring one J2 in AB-stacking are shown in Fig. 6(c). One can see that J1 is dominated by the virtual excitations between the half-filled t2g orbitals of Cr and induces an AFM coupling, while J2 is dominated by a virtual excitation from the half-filled t2g orbitals of Cr to the empty eg orbitals, resulting in a FM coupling [Fig. 6(c)]. Clearly, the second neighboring FM interlayer super-superexchange prevails as the AFM nearest neighboring interlayer exchange, making AB-stacking system ferromagnetic. A lateral shift of one layer to AB′-stacking of the bilayer system breaks the interlayer hybridization between I p states and generates a new type of hybridization, which in turn would reduce the strength of FM exchange interactions and result in an AFM ground state for AB′-stacking [Fig. 6(d)].

6. Multi-intermediate double exchange interaction

Compared to bilayer CrI3 with the same Cr3+ ions, a mixture of Cr4+ and Cr3+ was found in bilayer CrS2 due to the charge transfer from eg to t2g orbitals. This mixed valance state, together with delocalized S p orbitals and their resulting strongly interlayered S-S hopping, favor the double exchange interaction mechanism.135135. C. Wang, X. Zhou, Y. Pan, J. Qiao, X. Kong, C.-C. Kaun, and W. Ji, Phys. Rev. B 97(24), 245409 (2018). https://doi.org/10.1103/PhysRevB.97.245409 With further increase of the strength of interlayer coupling, a novel multi-intermediate double exchange interaction has been revealed by extensively investigating nine TMD bilayers MX2 (M = V, Cr, Mn; X = S, Se, Te).2727. C. Wang, X. Zhou, L. Zhou, Y. Pan, Z.-Y. Lu, X. Wan, X. Wang, and W. Ji, Phys. Rev. B 102(2), 020402 (2020). https://doi.org/10.1103/PhysRevB.102.020402 Taking 2D CrSe2 as a prototype, one can see a distinct overlapped region (OR) at the interlayer area, as displayed in Fig. 6(e). In other words, OR could be effectively considered as an area accumulating an appreciable shared charge from the two adjacent interfacial Se sublayers. The OR can be regarded as a real atomic site and plays an important role in determining the interlayer magnetic coupling. In the interlayer FM configuration, the transferred spin-up charge of Se pz to Cr leaves the spin-down component predominated at the OR [Fig. 6(e)]. Hence, the spin-up electrons of the bottom Cr atom could hop into the top Cr atom through 4pz orbital of Se_ib atom [defined in Fig. 6(e)], and then through OR upon excitation, and further through Se_it 4pz, as denoted by the wave-like red-dotted arrow [Fig. 6(e)]. Such electron hopping process largely reduces the kinetic energy of spin-up electron across the bilayer. The process in CrSe2 is similar to double exchange interaction of CrS2135135. C. Wang, X. Zhou, Y. Pan, J. Qiao, X. Kong, C.-C. Kaun, and W. Ji, Phys. Rev. B 97(24), 245409 (2018). https://doi.org/10.1103/PhysRevB.97.245409 but is mediated by multiple sites, which is termed as a new multi-intermediate double exchange interaction. Similarly, the interlayer AFM bilayer also has stacking-induced charge transfer and the interfacial Se pz overlapping area. As displayed in Fig. 6(e), the spin-up electron of bottom Cr could still hop into the Se_ib 4pz orbital and reach the OR. However, the next hopping step from OR to the Se_it 4pz orbital is forbidden since the spin-up component is fully occupied. This appreciably lifts up the kinetic energy. Based on the modified interlayer Hubbard model, the competition between the interlayer hopping across the bilayer and the Pauli and Coulomb repulsions at OR will determine the MX2 bilayers to have FM or AFM magnetic ground state.

F. Stoner model

In the above discussions, we mainly focus on 2D FM/AFM insulators. Their magnetism originates from local magnetic moments with exchange interactions that can be interpreted by the Heisenberg exchange mode. For 2D magnetic metals, a simplified model called Stoner model,1616. H. L. Zhuang, P. R. C. Kent, and R. G. Hennig, Phys. Rev. B 93(13), 134407 (2016). https://doi.org/10.1103/PhysRevB.93.134407 can be formulated in terms of dispersion relations for the spin-up and spin-down electrons. In the Stoner model, there is a competition between kinetic energy and exchange energy due to Coulomb repulsion. In ferromagnetic metals, the exchange interaction will split the energy of states with different spins. This restructuring of the spins leads to a change in the energy of the system. The up spins occupying higher energy states would cost the kinetic energy. At the same time, the potential energy would decrease due to spin-spin exchange interaction. These changes in total energy provide the Stoner criterion for itinerant ferromagnetism. The Stoner criterion for itinerant ferromagnetic ordering is D(EF)×I > 1, where D(EF) is the total density of states at the Fermi level (EF), and the Stoner parameter I can be estimated from dividing the exchange splitting of spin-up and spin-down bands by the corresponding magnetic moments. These two parameters reflect the competition between the exchange energy and kinetic energy. The former parameter D(EF) is inversely proportional to the kinetic energy of electrons, whereas the latter one, I, describes the strength of electron exchange. Owing to the nature of itinerant electrons, Stoner model is applicable to illustrate the origin of the spontaneous magnetization in plenty of 2D metallic magnets, such as Fe3GeTe2,1616. H. L. Zhuang, P. R. C. Kent, and R. G. Hennig, Phys. Rev. B 93(13), 134407 (2016). https://doi.org/10.1103/PhysRevB.93.134407 TMDs,17,18,20,2117. Y. Ma, Y. Dai, M. Guo, C. Niu, Y. Zhu, and B. Huang, ACS Nano 6(2), 1695 (2012). https://doi.org/10.1021/nn204667z18. F. Li, K. Tu, and Z. Chen, J. Phys. Chem. C 118(36), 21264 (2014). https://doi.org/10.1021/jp507093t20. G. V. Pushkarev, V. G. Mazurenko, V. V. Mazurenko, and D. W. Boukhvalov, Phys. Chem. Chem. Phys. 21(40), 22647 (2019). https://doi.org/10.1039/C9CP03726H21. Y. Wen, Z. Liu, Y. Zhang, C. Xia, B. Zhai, X. Zhang, G. Zhai, C. Shen, P. He, R. Cheng, L. Yin, Y. Yao, M. Getaye Sendeku, Z. Wang, X. Ye, C. Liu, C. Jiang, C. Shan, Y. Long, and J. He, Nano Lett. 20(5), 3130 (2020). https://doi.org/10.1021/acs.nanolett.9b05128 MXene,19,97,13619. J.-J. Zhang, L. Lin, Y. Zhang, M. Wu, B. I. Yakobson, and S. Dong, J. Am. Chem. Soc. 140(30), 9768 (2018). https://doi.org/10.1021/jacs.8b0647597. Y. Yue, J. Magn. Magn. Mater. 434, 164 (2017). https://doi.org/10.1016/j.jmmm.2017.03.058136. C. Si, J. Zhou, and Z. Sun, ACS Appl. Mater. Inter. 7(31), 17510 (2015). https://doi.org/10.1021/acsami.5b05401 as well as a variety of charge doped 2D materials.137–142137. T. Cao, Z. Li, and S. G. Louie, Phys. Rev. Lett. 114(23), 236602 (2015). https://doi.org/10.1103/PhysRevLett.114.236602138. S.-H. Zhang and B.-G. Liu, J. Mater. Chem. C 6(25), 6792 (2018). https://doi.org/10.1039/C8TC01450G139. S. Gong, W. Wan, S. Guan, B. Tai, C. Liu, B. Fu, S. A. Yang, and Y. Yao, J. Mater. Chem. C 5(33), 8424 (2017). https://doi.org/10.1039/C7TC01399J140. H. Xiang, B. Xu, Y. Xia, J. Yin, and Z. Liu, Sci. Rep. 6(1), 39218 (2016). https://doi.org/10.1038/srep39218141. Y. Nie, M. Rahman, P. Liu, A. Sidike, Q. Xia, and G.-h. Guo, Phys. Rev. B 96(7), 075401 (2017). https://doi.org/10.1103/PhysRevB.96.075401142. H. Y. Lv, W. J. Lu, X. Luo, X. B. Zhu, and Y. P. Sun, Phys. Rev. B 99(13), 134416 (2019). https://doi.org/10.1103/PhysRevB.99.134416 Most of these reported 2D magnetic metals have excitingly high Curie temperatures.

The electronic and magnetic properties of 2D Fe3GeTe2 have been investigated by Zhuang et al.1616. H. L. Zhuang, P. R. C. Kent, and R. G. Hennig, Phys. Rev. B 93(13), 134407 (2016). https://doi.org/10.1103/PhysRevB.93.134407 The spin orbital projected band structures [Fig. 7(a)] show its metallic behavior. Several partially occupied d bands crossing the Fermi level contribute to the noninteger magnetic moment of Fe (1.484 μB). Both characters indicate the itinerant ferromagnetism in Fe3GeTe2. The two important parameters of Stoner model, i.e., D(EF) and I, were determined from DOS as 1.56 states/eV per Fe atom and 0.71 eV, respectively. Therefore, Stoner's criterion of I×D(EF) > 1 is satisfied, giving rise to the itinerant ferromagnetic ordering in monolayer Fe3GeTe2. The validity of Stoner model was also extended to the successively reported 2D Fe5GeTe2,143143. M. Joe, U. Yang, and C. Lee, Nano Mater. Sci. 1(4), 299 (2019). https://doi.org/10.1016/j.nanoms.2019.09.009 which has a Curie temperature of 270 K.4242. A. F. May, D. Ovchinnikov, Q. Zheng, R. Hermann, S. Calder, B. Huang, Z. Fei, Y. Liu, X. Xu, and M. A. McGuire, ACS Nano 13(4), 4436 (2019). https://doi.org/10.1021/acsnano.8b09660

FIG. 7. (a) Orbital-resolved spin-up and spin-down band structures of single-layer Fe3GeTe2. (b) A summary of four types of known room-temperature vdW ferromagnets and their unit cell. (c) Hopping paths of the nearest, next-nearest, and next-next-nearest interactions in a MnSiTe3 monolayer. (d) RKKY interaction strength as a function of Mn–Mn distance and first-principles results for (JMnSiTe3–JCrSiTe3). The yellow triangle, blue circle, and green square denote the first-principles results for the difference between JMnSiTe3 and JCrSiTe3 for the N, NN, and NNN neighbors, respectively. The red solid line denotes the interaction strength calculated within RKKY model with kF = 0.47 Å−1. Panel (a) reproduced with permission from Zhuang et al., Phys. Rev. B 93, 134407 (2016). Copyright 2016 American Physical Society.1616. H. L. Zhuang, P. R. C. Kent, and R. G. Hennig, Phys. Rev. B 93(13), 134407 (2016). https://doi.org/10.1103/PhysRevB.93.134407 Panel (b) reproduced with permission from Sun et al., Nano Res. 13, 3358 (2020). Copyright 2020 Springer Nature.147147. X. Sun, W. Li, X. Wang, Q. Sui, T. Zhang, Z. Wang, L. Liu, D. L. Li, S. Feng, S. Zhong, H. Wang, V. Bouchiat, M. N. Regueiro, N. Rougemaille, J. Coraux, Z. Wang, B. Dong, X. Wu, T. Yang, G. Yu, B. Wang, Z. V. Han, X. Han, and Z. Zhang, Nano Res. 13, 3358 (2020). https://doi.org/10.1007/s12274-020-3021-4 Panels (c) and (d) reproduced with permission from Zhang et al., Phys. Rev. B 101, 205119 (2020). Copyright 2020 American Physical Society.2222. D. Zhang, A. Rahman, W. Qin, X. Li, P. Cui, Z. Zhang, and Z. Zhang, Phys. Rev. B 101(20), 205119 (2020). https://doi.org/10.1103/PhysRevB.101.205119

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Intrinsic vdW ferromagnets with TC above 300 K have been experimentally reported in some binary transitional metal dichalcogenides (MX2) with structural phases containing the octahedral units [Fig. 7(b)], including 1T-MnSex,144144. I. Eren, F. Iyikanat, and H. Sahin, Phys. Chem. Chem. Phys. 21(30), 16718 (2019). https://doi.org/10.1039/C9CP03112J 1T-VSe2,34,14534. M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan, and M. Batzill, Nature Nanotechnol. 13(4), 289 (2018). https://doi.org/10.1038/s41565-018-0063-9145. P. K. J. Wong, W. Zhang, F. Bussolotti, X. Yin, T. S. Herng, L. Zhang, Y. L. Huang, G. Vinai, S. Krishnamurthi, D. W. Bukhvalov, Y. J. Zheng, R. Chua, A. T. N'Diaye, S. A. Morton, C.-Y. Yang, K.-H. O. Yang, P. Torelli, W. Chen, K. E. J. Goh, J. Ding, M.-T. Lin, G. Brocks, M. P. de Jong, A. H. C. Neto, and A. T. S. Wee, Adv. Mater. 31(23), 1901185 (2019). https://doi.org/10.1002/adma.201901185 1T-VTe2,146146. E. Vatansever, S. Sarikurt, and R. F. L. Evans, Mater. Res. Express 5(4), 046108 (2018). https://doi.org/10.1088/2053-1591/aabca6 and 1T-CrTe2.147147. X. Sun, W. Li, X. Wang, Q. Sui, T. Zhang, Z. Wang, L. Liu, D. L. Li, S. Feng, S. Zhong, H. Wang, V. Bouchiat, M. N. Regueiro, N. Rougemaille, J. Coraux, Z. Wang, B. Dong, X. Wu, T. Yang, G. Yu, B. Wang, Z. V. Han, X. Han, and Z. Zhang, Nano Res. 13, 3358 (2020). https://doi.org/10.1007/s12274-020-3021-4 Both theoretical and experimental results suggested that exchange coupling due to the enhancement of itinerant type is responsible for their room-temperature ferromagnetism. The above four 2D room-temperature ferromagnets are compared to the corresponding elemental metals and some ferromagnetic elemental metals like Fe, Co, and Ni. As expected, only Fe, Co, and Ni among all the considered elemental metals meet the Stoner criterion to exhibit band ferromagnetism. In contrast, 2D VSe2, CrTe2, MnTe2, and MnSe2 sheets have much higher I×D(EF) values than those of the corresponding elementary metals; thus the Stoner criterion is met for a band ferromagnetism in these 2D materials.147147. X. Sun, W. Li, X. Wang, Q. Sui, T. Zhang, Z. Wang, L. Liu, D. L. Li, S. Feng, S. Zhong, H. Wang, V. Bouchiat, M. N. Regueiro, N. Rougemaille, J. Coraux, Z. Wang, B. Dong, X. Wu, T. Yang, G. Yu, B. Wang, Z. V. Han, X. Han, and Z. Zhang, Nano Res. 13, 3358 (2020). https://doi.org/10.1007/s12274-020-3021-4

G. RKKY mechanism

RKKY is a particular form of magnetic interaction that occurs in metals with localized magnetic moments. In the RKKY picture, the magnetic moments interact effectively through an indirect exchange process mediated by the conduction electrons. A localized magnetic moment induces spin polarization to the surrounding conduction electrons, and such polarization in turn couples to another neighboring localized moment. The coupling strength takes the form of distance-dependent exchange interaction given byJij(r)∝ sin [(k→F↑+k→F↓)·R→ijRij3],(6)where kF is the Fermi wave vector for two spin channels, and Rij is the distance between the two magnetic atoms i and j. First, this interaction is of the long-range type. Second, FM or AFM ground states depend on the interatomic distance. Third, its strength oscillates with the distance. Similar to the Heisenberg model, the strength of exchange coupling is related to the magnetic transition temperature, but is not rooted in the symmetry. RKKY interaction is well understood in conventional 3D intermetallic compounds, which is the dominant coupling mechanism between rare earth ions. In 2D materials, however, only a few theoretical studies have directly discussed the existence of RKKY-type interaction.2222. D. Zhang, A. Rahman, W. Qin, X. Li, P. Cui, Z. Zhang, and Z. Zhang, Phys. Rev. B 101(20), 205119 (2020). https://doi.org/10.1103/PhysRevB.101.205119 In this regard, Zhang et al.2222. D. Zhang, A. Rahman, W. Qin, X. Li, P. Cui, Z. Zhang, and Z. Zhang, Phys. Rev. B 101(20), 205119 (2020). https://doi.org/10.1103/PhysRevB.101.205119 inferred that ferromagnetic interaction between Mn ions in MnSiTe3 monolayer possibly originated from the RKKY coupling. Figure 7(c) displays the possible electron hopping paths between Mn ions of the nearest (N), next-nearest (NN), and next-next-nearest (NNN) interactions (JN, JNN, JNNN). Unlike CrSiTe3 and CrGeTe3, the theoretical results showed that MnSiTe3 monolayer is a half metal with the largest positive JNNN, which is inconsistent with superexchange model. Benefiting from the half metallic nature, the mediation carriers between Mn ions are 100% spin-polarized free carriers. Figure 7(d) presents the RKKY interaction as a function of Mn–Mn distance. The RKKY contributions to the interaction for the N, NN, NNN neighbors in the model show good agreement with the results from first-principles calculations.2222. D. Zhang, A. Rahman, W. Qin, X. Li, P. Cui, Z. Zhang, and Z. Zhang, Phys. Rev. B 101(20), 205119 (2020). https://doi.org/10.1103/PhysRevB.101.205119 Nevertheless, further theoretical and experimental efforts are still needed to exploit the RKKY mechanism in other 2D magnets.

III. THE 2D VDW MAGNETS DATABASE

Section:

Two-dimensional vdW magnets are defined as the layered materials that adopt ferromagnetic/antiferromagnetic ground states at finite temperature. The theoretical concept was first established 150 years ago.148148. L. Onsager, Phys. Rev. 65(3–4), 117 (1944). https://doi.org/10.1103/PhysRev.65.117 Since 2004, many efforts have been devoted to searching for new 2D magnetic materials with spontaneous magnetization.8484. D. L. Cortie, G. L. Causer, K. C. Rule, H. Fritzsche, W. Kreuzpaintner, and F. Klose, Adv. Funct. Mater. 30(18), 1901414 (2020). https://doi.org/10.1002/adfm.201901414 In 2017, for the first time, the intrinsic 2D ferromagnetism in atomically thin CrI3 and Cr2Ge2Te6 was demonstrated in an experiment.28,3728. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature2239137. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature 546(7657), 265 (2017). https://doi.org/10.1038/nature22060 Nowadays, finding 2D ferromagnets with high Curie temperatures remains an important issue for spintronics, and many promising 2D materials have been attained theoretically and experimentally over the past five years.

A. Binary transition metal halides

1. MX3

The first class of widely investigated 2D vdW magnets is binary transition metal halides. During the past 150 years, many bulk crystals of transition metal halides have been synthesized in the laboratory.149149. A. M. McGuire, Crystals 7(5), 121 (2017). https://doi.org/10.3390/cryst7050121 These bulk materials adopted simple AA or ABC layered stacking geometry with weak interlayer vdW interaction; thus, they can be mechanically exfoliated to fabricate 2D monolayer or few-layered sheets.54,14954. J. Liu, Q. Sun, Y. Kawazoe, and P. Jena, Phys. Chem. Chem. Phys. 18(13), 8777 (2016). https://doi.org/10.1039/C5CP04835D149. A. M. McGuire, Crystals 7(5), 121 (2017). https://doi.org/10.3390/cryst7050121 The compounds composed of transition metals with partially filled d shell are commonly observed, since they are easy to host local magnetic moments and produce ordered magnetism. Most of transition metal trihalides (MX3), transition metal dihalides (MX2), transition metal monohalides (MX), and other stoichiometric M-X monolayers reported to date are listed in Table II and categorized by their compositions as well as magnetic properties for discussion.

TABLE II. A list of 2D magnets in binary transition metal halides family with their compositions and key electronic and magnetic properties, including magnetic ground state (GS), values of Hubbard U term, energy gap (Eg), magnetic moment on per transition metal atom (Ms), Curie temperature (TC), and magnetic anisotropy energy per unit cell (MAE). The experimental result is indicated by the superscript i. Positive/negative MAE value corresponds to the out-of-plane/in-plane easy magnetization direction.

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The successful exfoliation of bulk CrI3 crystal into atomic monolayers opened a new era of 2D magnetism.2828. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391 Using scanning magneto-optic Kerr microscopy, neutron scattering, and NMR spectroscopy, pristine monolayer CrI3 has been proven to be an Ising ferromagnetic semiconductor with a bandgap of 1.2 eV,150150. J. F. Dillon, Jr. and C. E. Olson, J. Appl. Phys. 36(3), 1259 (1965). https://doi.org/10.1063/1.1714194 a Curie temperature of 45 K,2828. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391 and an out-plane MAE of 0.69 meV [Figs. 8(a)–(e)].5353. W.-B. Zhang, Q. Qu, P. Zhu, and C.-H. Lam, J. Mater. Chem. C 3(48), 12457 (2015). https://doi.org/10.1039/C5TC02840J In fact, the study of magnetism of layered CrI3 began even before that. In prior experiments, several theoretical groups already predicted robust long-range ferromagnetic ordering in the monolayer limit of CrI3.8,53,548. H. Wang, F. Fan, S. Zhu, and H. Wu, Europhys. Lett. 114(4), 47001 (2016). https://doi.org/10.1209/0295-5075/114/4700153. W.-B. Zhang, Q. Qu, P. Zhu, and C.-H. Lam, J. Mater. Chem. C 3(48), 12457 (2015). https://doi.org/10.1039/C5TC02840J54. J. Liu, Q. Sun, Y. Kawazoe, and P. Jena, Phys. Chem. Chem. Phys. 18(13), 8777 (2016). https://doi.org/10.1039/C5CP04835D The reported magnetic moment, magnetic anisotropy energy, and Curie temperature of 2D CrI3 were 3∼3.44 μB per formula unit, 0.65∼0.686 meV, and 61∼107 K, respectively.8,53,548. H. Wang, F. Fan, S. Zhu, and H. Wu, Europhys. Lett. 114(4), 47001 (2016). https://doi.org/10.1209/0295-5075/114/4700153. W.-B. Zhang, Q. Qu, P. Zhu, and C.-H. Lam, J. Mater. Chem. C 3(48), 12457 (2015). https://doi.org/10.1039/C5TC02840J54. J. Liu, Q. Sun, Y. Kawazoe, and P. Jena, Phys. Chem. Chem. Phys. 18(13), 8777 (2016). https://doi.org/10.1039/C5CP04835D The magnetic moment in monolayer CrI3 with honeycomb lattice is contributed by the Cr3+ ions with electronic configuration of 3s03d3 under edge sharing octahedral crystal field coordinated by six nonmagnetic I¯ ions. In the octahedral crystal field, Cr3+ ions prefer S = 3/2 with three d electrons occupying the lower-energy t2g triplet state via splitting. The long-range FM ordering is driven by the competition between direct antiferromagnetic exchange interaction of Cr–Cr sites and the superexchange interaction in the near 90° Cr–I–Cr bonds.88. H. Wang, F. Fan, S. Zhu, and H. Wu, Europhys. Lett. 114(4), 47001 (2016). https://doi.org/10.1209/0295-5075/114/47001 The large magnetic anisotropy is attributed to the spin-orbit coupling of the intermediate I atom along the superexchange path.151151. J. L. Lado and J. Fernández-Rossier, 2D Mater. 4(3), 035002 (2017). https://doi.org/10.1088/2053-1583/aa75ed Using magneto-Raman spectroscopy, Xu et al.152152. J. Cenker, B. Huang, N. Suri, P. Thijssen, A. Miller, T. Song, T. Taniguchi, K. Watanabe, M. McGuire, X. Di, and X. Xu, arXiv:2001.07025 (2020). directly observed 2D magnons with acoustic magnon mode of 0.3 meV in monolayer CrI3. Moreover, the magnetism in CrI3 is layer dependent, that is, monolayer, trilayer, bulk CrI3 systems are ferromagnetic, whereas the weak magnetic coupling between the individual FM monolayer leads to the AFM ground state in bilayer CrI3 [Figs. 8(f)–8(h)].2828. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391 An exfoliated thin film of CrI3 sandwiched between graphene contacts acts as a spin-filter tunnel barrier, showing a record high tunneling magnetoresistance of 190 000%.153,154153. Z. Wang, I. Gutierrez-Lezama, N. Ubrig, M. Kroner, M. Gibertini, T. Taniguchi, K. Watanabe, A. Imamoglu, E. Giannini, and A. F. Morpurgo, Nat. Commun. 9(1), 2516 (2018). https://doi.org/10.1038/s41467-018-04953-8154. T. Song, X. Cai, M. W.-Y. Tu, X. Zhang, B. Huang, N. P. Wilson, K. L. Seyler, L. Zhu, T. Taniguchi, K. Watanabe, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao, and X. Xu, Science 360(6394), 1214 (2018). https://doi.org/10.1126/science.aar4851

FIG. 8. Magneto-optical Kerr effect (MOKE) measurements of monolayer CrI3. (a) Polar MOKE signal for a CrI3 monolayer. (b) Power dependence of the MOKE signal taken at three different incident powers (3, 10, and 30 μW). (c) MOKE maps at μoH = 0 T, 0.15 T, and 0.3 T. (d) Temperature dependence of MOKE signal. (e) The relationship between θK abd μ0H marked by dots in (c). (f)–(h) Layer-dependent magnetic ordering in atomically thin CrI3. MOKE signal on a monolayer, bilayer, and trilayer flakes. They show ferromagnetic, antiferromagnetic, and ferromagnetic behavior, respectively. Reproduced with permission from Huang et al., Nature 546, 270 (2017). Copyright 2017 Springer Nature.2828. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391

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Motivated by the discovery of CrI3, its sister transition metal compounds, i.e., chromium trihalides CrX3 (X= F, Cl, Br) monolayers have been explored as potential 2D intrinsic magnetic semiconductors by many groups.30,53,54,104,155,15630. X. Cai, T. Song, N. P. Wilson, G. Clark, M. He, X. Zhang, T. Taniguchi, K. Watanabe, W. Yao, D. Xiao, M. A. McGuire, D. H. Cobden, and X. Xu, Nano Lett. 19(6), 3993 (2019). https://doi.org/10.1021/acs.nanolett.9b0131753. W.-B. Zhang, Q. Qu, P. Zhu, and C.-H. Lam, J. Mater. Chem. C 3(48), 12457 (2015). https://doi.org/10.1039/C5TC02840J54. J. Liu, Q. Sun, Y. Kawazoe, and P. Jena, Phys. Chem. Chem. Phys. 18(13), 8777 (2016). https://doi.org/10.1039/C5CP04835D104. L. Webster and J.-A. Yan, Phys. Rev. B 98(14), 144411 (2018). https://doi.org/10.1103/PhysRevB.98.144411155. M. Moaied, J. Lee, and J. Hong, Phys. Chem. Chem. Phys. 20(33), 21755 (2018). https://doi.org/10.1039/C8CP03489C156. F. Iyikanat, M. Yagmurcukardes, R. T. Senger, and H. Sahin, J. Mater. Chem. C 6(8), 2019 (2018). https://doi.org/10.1039/C7TC05266A Owing to the structural similarity with CrI3, FM is also the ground state for monolayer CrX3 (X= F, Cl, and Br), and the magnetic moment of each Cr3+ ion in these systems is about 3 μB. However, with the increase in the atomic radius of halogen, the theoretical bandgap reduces from 4.68 eV for CrF3, to 3.44 eV for CrCl3, to 2.54 eV for CrBr3, and finally to 1.53 eV for CrI3 at HSE06 level of theory.5353. W.-B. Zhang, Q. Qu, P. Zhu, and C.-H. Lam, J. Mater. Chem. C 3(48), 12457 (2015). https://doi.org/10.1039/C5TC02840J Considering the microscopic origin of long-range FM ordering, a strongly increased hybridization between X-p and Cr-3d states will strengthen the Cr–X–Cr FM exchange interactions as X goes from F to I. However, direct AFM exchange interaction is expected to be weakened with increasing Cr–Cr distance along this series. Indeed, MC simulations based on classical Heisenberg model predicted Curie temperatures of CrF3, CrCl3, CrBr3, and CrI3 monolayers to be 41, 49, 73, and 95 K, respectively. Moving from Cl to I would increase the strength of spin-orbit coupling of halogen, which accounts for the enhancement of MAE from 0.031 meV for CrCl3, to 0.186 meV for CrBr3, and then to 0.686 meV for CrI3.5353. W.-B. Zhang, Q. Qu, P. Zhu, and C.-H. Lam, J. Mater. Chem. C 3(48), 12457 (2015). https://doi.org/10.1039/C5TC02840J Similar theoretical results were also reported in the other four papers.54,104,155,15654. J. Liu, Q. Sun, Y. Kawazoe, and P. Jena, Phys. Chem. Chem. Phys. 18(13), 8777 (2016). https://doi.org/10.1039/C5CP04835D104. L. Webster and J.-A. Yan, Phys. Rev. B 98(14), 144411 (2018). https://doi.org/10.1103/PhysRevB.98.144411155. M. Moaied, J. Lee, and J. Hong, Phys. Chem. Chem. Phys. 20(33), 21755 (2018). https://doi.org/10.1039/C8CP03489C156. F. Iyikanat, M. Yagmurcukardes, R. T. Senger, and H. Sahin, J. Mater. Chem. C 6(8), 2019 (2018). https://doi.org/10.1039/C7TC05266A Experimentally, Gao et al.3131. Z. Zhang, J. Shang, C. Jiang, A. Rasmita, W. Gao, and T. Yu, Nano Lett. 19(5), 3138 (2019). https://doi.org/10.1021/acs.nanolett.9b00553 demonstrated ferromagnetism in 2D vdW CrBr3 using direct d-d transition induced photoluminescence probing. They argued that spontaneous magnetization persists in monolayer CrBr3 with Curie temperature of 34 K. The magnetic moment of each Cr3+ ion in monolayer CrBr3 aligns in the out-of-plane direction, and the corresponding magnetic moment is about 3 μB. Although the Curie temperature and MAE are slightly smaller than those of monolayer CrI3, monolayers of other chromium trihalides CrX3 (X= F, Cl, Br) could be more stable in air.28,15728. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391157. W. Jin, H. H. Kim, Z. Ye, S. Li, P. Rezaie, F. Diaz, S. Siddiq, E. Wauer, B. Yang, C. Li, S. Tian, K. Sun, H. Lei, A. W. Tsen, L. Zhao, and R. He, Nat. Commun. 9(1), 5122 (2018). https://doi.org/10.1038/s41467-018-07547-6

Beyond chromium halides, the magnetic properties of vanadium trihalides (e.g., VI3) monolayer were also intensively investigated as potential 2D magnetic materials. In the periodic table, vanadium locates as the left neighbor of chromium. Thus, V atom in VI3 tends to adopt high-spin state of V3+ with 3d2 electronic configuration, that is, two valence electrons occupy the triply degenerate t2g state. Such partial occupancy could raise the possibility for weak Jahn-Teller distortion of the octahedra and the orbital ordering in vanadium trihalides, which would modify the superexchange interactions in its planar honeycomb lattice. Recently, two experimental groups confirmed that bulk VI3 is a correlated Mott insulator with a bandgap of ∼1 eV.29,15829. S. Tian, J.-F. Zhang, C. Li, T. Ying, S. Li, X. Zhang, K. Liu, and H. Lei, J. Am. Chem. Soc. 141(13), 5326 (2019). https://doi.org/10.1021/jacs.8b13584158. T. Kong, K. Stolze, E. I. Timmons, J. Tao, D. Ni, S. Guo, Z. Yang, R. Prozorov, and R. J. Cava, Adv. Mater. 31(17), 1808074 (2019). https://doi.org/10.1002/adma.201808074 In addition, the exfoliation energy from first-principles calculation revealed that VI3 is more easily decoupled than CrI3.159159. J. Yan, X. Luo, F. C. Chen, J. J. Gao, Z. Z. Jiang, G. C. Zhao, Y. Sun, H. Y. Lv, S. J. Tian, Q. W. Yin, H. C. Lei, W. J. Lu, P. Tong, W. H. Song, X. B. Zhu, and Y. P. Sun, Phys. Rev. B 100(9), 094402 (2019). https://doi.org/10.1103/PhysRevB.100.094402 Hence, vanadium trihalides provide a new platform to investigate 2D magnets with S = 1. Using CVD method, Tian et al.2929. S. Tian, J.-F. Zhang, C. Li, T. Ying, S. Li, X. Zhang, K. Liu, and H. Lei, J. Am. Chem. Soc. 141(13), 5326 (2019). https://doi.org/10.1021/jacs.8b13584 firstly confirmed layered VI3 is a FM semiconductor with a Curie temperature of 50 K. It was further demonstrated to be a 2D Ising ferromagnet by DFT calculations, crystal field level diagrams, superexchange model analyses, and MC simulations.99. K. Yang, F. Fan, H. Wang, D. I. Khomskii, and H. Wu, Phys. Rev. B 101(10), 100402 (2020). https://doi.org/10.1103/PhysRevB.101.100402 The monolayer limit of VI3 has also been explored by first-principles calculations. The intrinsic ferromagnetism can persist and the Curie temperature is reduced to 17 K from the bulk value of 60 K.160160. M. An, Y. Zhang, J. Chen, H.-M. Zhang, Y. Guo, and S. Dong, J. Phys. Chem. C 123(50), 30545 (2019). https://doi.org/10.1021/acs.jpcc.9b08706 Based on DFT calculations combined with self consistently determined Hubbard U approach, He et al.161161. J. He, S. Ma, P. Lyu, and P. Nachtigall, J. Mater. Chem. C 4(13), 2518 (2016). https://doi.org/10.1039/C6TC00409A reported that monolayer VI3 possesses not only intrinsic ferromagnetism but also exciting Dirac half-metallicity, and VCl3 shows similar magnetic behavior. Their corresponding Curie temperatures were 80 and 98 K, respectively. For monolayer VBr3, first-principles calculations predicted that it has intrinsic half-metallicity and high Curie temperature of 190 K. Moreover, topological nontrivial states, which were identified by calculations of Berry curvature and the corresponding edge states, surprisingly emerge at the Fermi level.162162. J. Sun, X. Zhong, W. Cui, J. Shi, J. Hao, M. Xu, and Y. Li, Phys. Chem. Chem. Phys. 22(4), 2429 (2020). https://doi.org/10.1039/C9CP05084A

Manganese atom is the right neighbor of chromium in periodic table. In the manganese trihalides MnX3 (X = F, Cl, Br, I), low crystal field splitting is caused by the octahedral coordination of Mn ions. Thus, Mn ion has +3 oxide state with spin configuration of S = 2t2g3eg1, exhibiting a magnetic moment of c.a. 4 μB. Sun and Kioussis predicted that 2D MnX3 sheets are intrinsic Dirac half metals (DHMs).163163. Q. Sun and N. Kioussis, Phys. Rev. B 97(9), 094408 (2018). https://doi.org/10.1103/PhysRevB.97.094408 The bandgaps of the minority spin channel from PBE+U calculations were 6.3, 4.33, 3.85, and 3.10 eV for MnF3, MnCl3, MnBr3, and MnI3, respectively. In-plane magnetization orientation was found in all MnX3 systems and the magnetocrystalline anisotropy increases with increasing atomic size of halogen. Based on DFT derived exchange interaction parameters, the estimated Curie temperatures were greater than 450 K. Spin-polarized Dirac half metallic states in MnF3, MnCl3, and MnBr3 were also confirmed by Tomar et al.164164. S. Tomar, B. Ghosh, S. Mardanya, P. Rastogi, B. S. Bhadoria, Y. S. Chauhan, A. Agarwal, and S. Bhowmick, J. Magn. Magn. Mater. 489, 165384 (2019). https://doi.org/10.1016/j.jmmm.2019.165384 using DFT calculations with both PBE and HSE06 functionals. Based on Curie-Weiss mean field theory, MnF3 was demonstrated as a room-temperature ferromagnet.

Two-dimensional intrinsic magnets are also predicted for many other trihalides of open-shell 3d transition metals (M = Ti, Fe, Co, Ni). For instance, TiCl3 monolayer possesses weak interlayer interaction of 0.33 J/m2, half metallicity with a bandgap of 0.6 eV in the majority spin channel, long-range FM ordering contributed by 3d valence states, and a high Curie temperature of 376 K.165165. Y. Zhou, H. Lu, X. Zu, and F. Gao, Sci. Rep. 6(1), 19407 (2016). https://doi.org/10.1038/srep19407 FeX3 monolayers were found to have antiferromagnetic ground state with Néel temperature of 70∼180 K.162,164162. J. Sun, X. Zhong, W. Cui, J. Shi, J. Hao, M. Xu, and Y. Li, Phys. Chem. Chem. Phys. 22(4), 2429 (2020). https://doi.org/10.1039/C9CP05084A164. S. Tomar, B. Ghosh, S. Mardanya, P. Rastogi, B. S. Bhadoria, Y. S. Chauhan, A. Agarwal, and S. Bhowmick, J. Magn. Magn. Mater. 489, 165384 (2019). https://doi.org/10.1016/j.jmmm.2019.165384 Using DFT and DFT+U calculations, Sun et al.162162. J. Sun, X. Zhong, W. Cui, J. Shi, J. Hao, M. Xu, and Y. Li, Phys. Chem. Chem. Phys. 22(4), 2429 (2020). https://doi.org/10.1039/C9CP05084A found Dirac spin-gapless half-metallic features in NiBr3 monolayer, and the corresponding Curie temperature was 100 K. The NiCl3 monolayer was also shown to have Dirac spin-gapless semiconducting characteristics and high-temperature ferromagnetism.110110. J. He, X. Li, P. Lyu, and P. Nachtigall, Nanoscale 9(6), 2246 (2017). https://doi.org/10.1039/C6NR08522A The MC simulations based on Ising model demonstrated that the Curie temperature of NiCl3 monolayer is as high as ∼400 K. The calculated Fermi velocity of Dirac fermions was about 4 × 105 ms−1. Among them, Ti, Fe, and Ni ions are still octahedrally coordinated to the halogen atoms, thus they can exist in either high-spin or low-spin state due to crystal field splitting. According to the calculated magnetic moment listed in Table II, low-spin state is observed in the cases of Ti3+ and Ni3+ with magnetic moment of about 1 μB. The magnetic moment of iron ion is found to be close to 4 μB, which corresponds to neither high-spin (5 μB) nor low-spin (1 μB) state of Fe3+. It could explain why AFM coupling is only found in FeX3 series among the transition metal trihalides with CrI3 type structure. For Co ion located in the octahedral coordination environments of bromides, non-magnetic behavior was observed in CoBr3 with P-31m phase.162162. J. Sun, X. Zhong, W. Cui, J. Shi, J. Hao, M. Xu, and Y. Li, Phys. Chem. Chem. Phys. 22(4), 2429 (2020). https://doi.org/10.1039/C9CP05084A However, DFT calculations166166. W.-x. Zhang, Y. Li, H. Jin, and Y.-c. She, Phys. Chem. Chem. Phys. 21(32), 17740 (2019). https://doi.org/10.1039/C9CP03337H demonstrated that the P6/mmm phase of CoBr3 monolayer hosts 2D intrinsic ferromagnetism with metallic behavior, Dirac cone, and quantum anomalous Hall effect simultaneously. Its Curie temperature was 264 K and Chern number was C = 2.

Another important group of transition metal trihalides contains the heavier 4d and 5d open-shell transition metal elements like Mo, Ru, Rh, Tc, Pd, Ir, Pt, and Os. Moving from 3d to 4d and 5d series increases the spin-orbit coupling effect, which is beneficial for designing 2D spintronic devices with large MAE, topological phenomena, and spin controlling. Antiferromagnetic coupling between Mo atoms was confirmed in the high-temperature phase of α-MoCl3 by an combined experimental and theoretical study.167167. M. A. McGuire, J. Yan, P. Lampen-Kelley, A. F. May, V. R. Cooper, L. Lindsay, A. Puretzky, L. Liang, S. Kc, E. Cakmak, S. Calder, and B. C. Sales, Phys. Rev. Mater. 1(6), 064001 (2017). https://doi.org/10.1103/PhysRevMaterials.1.064001 Unlike CrCl3, α-MoCl3 adopts the monoclinic AlCl3 structure with space group of C2/m at room temperature. Originated from the magneto-structural phase transition, magnetic interactions in the high-temperature phase of α-MoCl3 are stronger by at least one order of magnitude than those in the analogous CrCl3 and CrBr3. Similar coupled structural and magnetic transition is also expected in TcCl3 and TiCl3. Experimentally, the fractional Majorana fermion excitations of a Kitaev quantum spin liquid have been observed in α-RuCl3,3232. A. Banerjee, J. Yan, J. Knolle, C. A. Bridges, M. B. Stone, M. D. Lumsden, D. G. Mandrus, D. A. Tennant, R. Moessner, and S. E. Nagler, Science 356(6342), 1055 (2017). https://doi.org/10.1126/science.aah6015 which leads to enormous amounts of research on the magnetic properties of layered α-RuCl3. Motivated by the exfoliation of α-RuCl3 monolayer from its 3D crystal,168168. D. Weber, L. M. Schoop, V. Duppel, J. M. Lippmann, J. Nuss, and B. V. Lotsch, Nano Lett. 16(6), 3578 (2016). https://doi.org/10.1021/acs.nanolett.6b00701 the magnetic property has been further analyzed by DFT calculations and MC simulations.55,15655. S. Sarikurt, Y. Kadioglu, F. Ersan, E. Vatansever, O. Ü. Aktürk, Y. Yüksel, Ü. Akıncı, and E. Aktürk, Phys. Chem. Chem. Phys. 20(2), 997 (2018). https://doi.org/10.1039/C7CP07953B156. F. Iyikanat, M. Yagmurcukardes, R. T. Senger, and H. Sahin, J. Mater. Chem. C 6(8), 2019 (2018). https://doi.org/10.1039/C7TC05266A It was demonstrated to be a stable 2D intrinsic ferromagnetic semiconductor. The obtained Curie temperature and MAE were 14.21 K and 0.95 meV, respectively. Using first-principles calculations, Kan et al.169169. C. Huang, J. Zhou, H. Wu, K. Deng, P. Jena, and E. Kan, Phys. Rev. B 95(4), 045113 (2017). https://doi.org/10.1103/PhysRevB.95.045113 predicted RuI3 monolayer to be an intrinsic ferromagnetic quantum anomalous Hall (QAH) insulator with topologically nontrivial global bandgap of 11 meV. The Curie temperature and nearest-neighboring exchange coupling parameter were estimated to be 360 K and 82 meV, respectively. It was also found that FM RuCl3 and RuBr3 monolayers show similar electronic behavior as RuI3 monolayer. However, their exchange energies are very small and sensitive to the choice of effective U value. For RuBr3 and RuI3 monolayers,170170. Q. Sun and N. Kioussis, Nanoscale 11(13), 6101 (2019). https://doi.org/10.1039/C9NR00315K the bandgap, possible magnetic ground state, Curie temperature, and magnetic anisotropy energy have been reexamined by DFT calculations with PBE+U and inclusion of SOC. It was shown that they are FM semiconductors with indirect bandgaps of 0.7 and 0.32 eV, respectively. According to MC simulations, their magnetic transition temperatures from FM to PM were 13.0 and 2.1 K, respectively. The magnetic anisotropy energies obtained for RuBr3 and RuI3 were 5.26 and 12.88 meV, respectively. Robust intrinsic ferromagnetism has also been realized in 2D rhenium trihalides.171171. F. Ersan, E. Vatansever, S. Sarikurt, Y. Yüksel, Y. Kadioglu, H. D. Ozaydin, O. Ü. Aktürk, Ü. Akıncı, and E. Aktürk, J. Magn. Magn. Mater. 476, 111 (2019). https://doi.org/10.1016/j.jmmm.2018.12.032 The dynamic and thermodynamic stabilities were found in the heavier halides (Br and I), in contrast to the lighter halides (F and Cl). ReBr3 and ReI3 are half metals with large bandgap in the spin-up channel. Moreover, high Curie temperatures (390 and 165 K) and Chern number (C = –4) were obtained from DFT calculations with PBE functional. Both Weyl half semimetal and tunable QAH effects were simultaneously realized in monolayer PtCl3,172172. J.-Y. You, C. Chen, Z. Zhang, X.-L. Sheng, S. A. Yang, and G. Su, Phys. Rev. B 100(6), 064408 (2019). https://doi.org/10.1103/PhysRevB.100.064408 as signified by the in-plane magnetization, high Curie temperature, and mirror symmetry protected two 2D Weyl points. A room-temperature intrinsic QAH insulator was predicted in the ferromagnetic insulating OsCl3 monolayer, which is characterized by an energy gap of 67 meV, a Chern number of C = 1, and a Curie temperature of 350 K.173173. X.-L. Sheng and B. K. Nikolić, Phys. Rev. B 95(20), 201402 (2017). https://doi.org/10.1103/PhysRevB.95.201402

2. MX2

Similar to transition metal trihalides, layered transition metal dihalides have also drawn significant attentions for exhibiting ferromagnetic, antiferromagnetic, and half-metallic characteristics. The structure of monolayer MX2 is analogous to transition metal dichalcogenides, which contains a triangular lattice of transition metal cations. In these compounds, the metal ions are in the formal oxidation state of +2. Divalence and octahedral coordination renders V, Cr, Mn, Fe, Co, and Ni cations partially filled 3d3, 3d4, 3d5, 3d6, 3d7, and 3d8 electronic configurations, with S = 3/2, 2, 5/2, 2, 3/2, and 1, respectively. Considering their structural similarity, the sign of superexchange interaction is mainly determined by the orbital occupations, and thus a variety of magnetic ground states are anticipated.

The evolution of electronic and magnetic properties of these first-row transition metal dihalides MX2 (M = V, Cr, Mn, Fe, Co, Ni; X = Cl, Br, I) has been systemically examined by first-principles calculations.100,111,142,174100. V. V. Kulish and W. Huang, J. Mater. Chem. C 5(34), 8734 (2017). https://doi.org/10.1039/C7TC02664A111. E. A. Kovaleva, I. Melchakova, N. S. Mikhaleva, F. N. Tomilin, S. G. Ovchinnikov, W. Baek, V. A. Pomogaev, P. Avramov, and A. A. Kuzubov, J. Phys. Chem. Solids 134, 324 (2019). https://doi.org/10.1016/j.jpcs.2019.05.036142. H. Y. Lv, W. J. Lu, X. Luo, X. B. Zhu, and Y. P. Sun, Phys. Rev. B 99(13), 134416 (2019). https://doi.org/10.1103/PhysRevB.99.134416174. A. S. Botana and M. R. Norman, Phys. Rev. Mater. 3(4), 044001 (2019). https://doi.org/10.1103/PhysRevMaterials.3.044001 Using PBE functional, T configuration (P-3m1) is energetically favorable for the monolayers of all considered cases, while correction by a Hubbard U term leads to inversion of the favorable monolayer configuration to H phase (P-6m2), as demonstrated for FeBr2 and FeI2.111111. E. A. Kovaleva, I. Melchakova, N. S. Mikhaleva, F. N. Tomilin, S. G. Ovchinnikov, W. Baek, V. A. Pomogaev, P. Avramov, and A. A. Kuzubov, J. Phys. Chem. Solids 134, 324 (2019). https://doi.org/10.1016/j.jpcs.2019.05.036 Among them, FeCl2, FeBr2, and FeI2 monolayers are ferromagnetic half metals, while CoCl2, CoBr2, NiCl2, NiBr2, and NiI2 monolayers are ferromagnetic insulators. For VCl2, VBr2, VI2, MnCl2, MnBr2, MnI2, CrI2, and CoI2 monolayers, they were found to be antiferromagnetic semiconductors with bandgap in range of 0.2∼2.5 eV. Introducing U correction will largely enlarge their bandgap.111111. E. A. Kovaleva, I. Melchakova, N. S. Mikhaleva, F. N. Tomilin, S. G. Ovchinnikov, W. Baek, V. A. Pomogaev, P. Avramov, and A. A. Kuzubov, J. Phys. Chem. Solids 134, 324 (2019). https://doi.org/10.1016/j.jpcs.2019.05.036 For example, the theoretical bandgaps of VBr2 monolayer are 1.1 and 3.1 eV at PBE and PBE+U level, respectively. The easy axis of all eight abovementioned MX2 monolayers in FM state is perpendicular to the basal plane with MAE in range of 0.02 to 0.89 meV. The highest TC is observed in NiCl2, which is 205 K predicted by Ising model.

Among the first-row transition metal dihalides, FeX2 series have attracted more attentions, mainly due to the following two reasons: (1) largest out-of-plane MAE is found in FeCl2, which is beneficial for the presence of 2D long-range magnetic ordering; (2) monolayer 1T-FeCl2 films on Au(111) and graphite have been successfully synthesized using MBE technique.175175. X. Zhou, B. Brzostowski, A. Durajski, M. Liu, J. Xiang, T. Jiang, Z. Wang, S. Chen, P. Li, Z. Zhong, A. Drzewiński, M. Jarosik, R. Szczęśniak, T. Lai, D. Guo, and D. Zhong, J. Phys. Chem. C 124(17), 9416 (2020). https://doi.org/10.1021/acs.jpcc.0c03050 Torun et al.176176. E. Torun, H. Sahin, S. K. Singh, and F. M. Peeters, Appl. Phys. Lett. 106(19), 192404 (2015). https://doi.org/10.1063/1.4921096 investigated the structural and magnetic properties of FeCl2 monolayer using first-principles calculations. They found that 1T-FeCl2 is more favorable than the 1H phase. Both PBE and HSE06 calculations demonstrated that 1T-FeCl2 is an intrinsic half-metallic ferromagnet with Curie temperature of 17 K.177177. E. Torun, H. Sahin, C. Bacaksiz, R. T. Senger, and F. M. Peeters, Phys. Rev. B 92(10), 104407 (2015). https://doi.org/10.1103/PhysRevB.92.104407 Hennig et al. have found that the Fe2+ ions in FeCl2, FeBr2, and FeI2 are in a high-spin octahedral d6 configuration, resulting in a large magnetic moment of 4 μB.178178. M. Ashton, D. Gluhovic, S. B. Sinnott, J. Guo, D. A. Stewart, and R. G. Hennig, Nano Lett. 17(9), 5251 (2017). https://doi.org/10.1021/acs.nanolett.7b01367 A classical XY model with nearest neighboring coupling was used to estimate their critical temperatures, which range from 122 K for FeI2 to 210 K for FeBr2. Moreover, all three 2D FeX2 materials as half metals were predicted to have appreciable electron densities of state at the Fermi level comparable to those of typical metals, suggesting good on/off ratios in spintronic devices.178178. M. Ashton, D. Gluhovic, S. B. Sinnott, J. Guo, D. A. Stewart, and R. G. Hennig, Nano Lett. 17(9), 5251 (2017). https://doi.org/10.1021/acs.nanolett.7b01367

In addition to first-row transition metals, the magnetic ground state of 4d/5d MX2 monolayers in both 1T and 2H phases have been investigated by high-throughput first-principles calculations.103103. X. Li, Z. Zhang, and H. Zhang, Nanoscale Adv. 2(1), 495 (2020). https://doi.org/10.1039/C9NA00588A Among them, 23 out of 90 MX2 monolayers exhibit robust magnetic ground states that are retained even after introducing the U terms. Besides the previously reported NiCl2, VCl2, MnCl2, VBr2, VI2, MnI2, and CoI2, PtCl2 is predicted to be a new noncollinear antiferromagnetic insulator. Meanwhile, AgCl2, AgBr2, and AuI2 are found to be half metallic ferromagnets with spin splitting of 0.2∼0.5 eV. To find more 2D intrinsic magnets in MH2 family, Shen et al.179179. J. Zhou, Y. P. Feng, and L. Shen, arXiv:1904.04952 (2019). also focused on 5d transition metal based MX2 monolayers. They screened more than 6000 kinds of 2D electrenes (i.e., materials with excess electrons acting as anions) and found that LaBr2 is one of most intriguing FM semiconductors with unusual long-range ferromagnetism induced by anions. From DFT calculations, its on-site moment, Curie temperature, and coercive field are 1 μB, 235 K, and 0.53 T, respectively.179179. J. Zhou, Y. P. Feng, and L. Shen, arXiv:1904.04952 (2019). For LaBr2 monolayer, delocalized spin density in the intermediate region between La atoms was also unveiled in another theoretical paper by Jiang et al.6565. Z. Jiang, P. Wang, J. Xing, X. Jiang, and J. Zhao, ACS Appl. Mater. Inter. 10(45), 39032 (2018). https://doi.org/10.1021/acsami.8b14037

3. MX

Among transition metal halides, MX compounds have the simplest stoichiometric ratio of 1:1. Without octahedral type crystal field, MX monolayer structures mainly consist of double hexagonal layers of metal atoms sandwiched by two hexagonal layers of halogen atoms. It is interesting to ask whether such MX monolayers still possess long-range magnetic ordering. By comprehensive first-principles calculations and MC simulations, Jiang et al.6565. Z. Jiang, P. Wang, J. Xing, X. Jiang, and J. Zhao, ACS Appl. Mater. Inter. 10(45), 39032 (2018). https://doi.org/10.1021/acsami.8b14037 have identified ScCl, YCl, and LaCl monolayers as ferromagnetic metals with appreciable Curie temperatures of 280, 240, and 260 K, respectively, while PBE+U calculations revised those values to 355, 460, and 260 K, respectively. Band structure analysis has shown that the spin density is relatively delocalized in the intermediate region between metal atoms, resulting in a small magnetic moment of 0.364, 0.333, and 0.317 μB per Sc, Y, and La atom, respectively. Wang et al.180180. B. Wang, Q. Wu, Y. Zhang, Y. Guo, X. Zhang, Q. Zhou, S. Dong, and J. Wang, Nanoscale Horiz. 3(5), 551 (2018). https://doi.org/10.1039/C8NH00101D also found that 2D ScCl monolayer is an intrinsic ferromagnet with large spin polarization. Their predicted Curie temperature was 185 K. Even so, both studies indicated that introduction of more transition metal in M-X systems would strongly quench its magnetic moment, while retaining Curie temperature at rather high value.

4. M3X8

Niobium halides form another kind of potential 2D vdW magnets with an unusual composition—Nb3X8. In Nb3X8 monolayer,181181. J. Jiang, Q. Liang, R. Meng, Q. Yang, C. Tan, X. Sun, and X. Chen, Nanoscale 9(9), 2992 (2017). https://doi.org/10.1039/C6NR07231C triangular Nb clusters are formed by Nb atoms; and consequently, every Nb atom is still arranged in a distorted octahedral environment. Therefore, both ferromagnetic ground state and semiconducting behavior were found in 2D Nb3X8 (X = Cl, Br, I) monolayers from GGA+U calculations. The Curie temperatures estimated by mean field approximation based on Heisenberg model were 31, 56, and 87 K for Nb3Cl8, Nb3Br8, and Nb3I8, respectively. Among them, the Nb3I8 monolayer has been successfully cleaved from its bulk phase.182182. B. J. Kim, B. J. Jeong, S. Oh, S. Chae, K. H. Choi, S. S. Nanda, T. Nasir, S. H. Lee, K.-W. Kim, H. K. Lim, L. Chi, I. J. Choi, M.-K. Hong, D. K. Yi, H. K. Yu, J.-H. Lee, and J.-Y. Choi, Phys. Status Solidi R 13(3), 1800448 (2019). https://doi.org/10.1002/pssr.201800448 Without considering U term, Xiao et al.7474. H. Xiao, X. Wang, R. Wang, L. Xu, S. Liang, and C. Yang, Phys. Chem. Chem. Phys. 21(22), 11731 (2019). https://doi.org/10.1039/C9CP00850K investigated the magnetic properties of the family 2D V3X8 (X = F, Cl, Br, I) in the framework of DFT. They found that V3Cl8 monolayer is an intrinsic AFM semiconductor, while the other three systems are FM half metals. The estimated Curie temperatures from MC simulations were 77 and 103 K for 2D V3F8 and V3I8, respectively.

B. Binary transition metal chalcogenides

Two-dimensional binary transition metal chalcogenides, including transition metal dichalcogenides, transition metal monochalcogenides, and other stoichiometries in a general form of MmXn (M refers to transition metal, and X represents S, Se, and Te), have provided a gorgeous platform for exploring interesting electronic and magnetic properties, such as valley polarization and 2D magnetism.

1. Transition metal dichalcogenides

Among 2D binary transition metal chalcogenides, the most widely studied ones are TMDs. Generally speaking, 2D TMDs form sandwich type structures in the X-M-X sequence, where transition metal atoms are sandwiched in between two layers of chalcogen atoms. There are four reported structural phases for TMDs, i.e., trigonal prismatic H-phase, octahedral T-phase, distorted octahedral 1T'-type, and Td-type lattices.183183. D. Puotinen and R. E. Newnham, Acta Crystallogr. 14(6), 691 (1961). https://doi.org/10.1107/S0365110X61002084 In all these phases, each transition metal atom is surrounded by six chalcogen atoms. The five formerly degenerate d orbitals of 3d transition metal ion would split in energy as it is bonded to the chalcogen ligands. Under the crystal field with D3h symmetry in H phase, the five degenerate 3d orbitals split into a single state a1 (dz2) and two twofold degenerate states e1 (dx2-y2/dxy) and e2 (dxz/dyz). While in T phase, the triangle sublattice of transition metal atoms gives rise to first-neighboring coordination number of 6, forming octahedral crystal field; thus, the d states split into t2g and eg manifolds. Due to the trigonal distortion, t2g degeneracy is further lifted to form higher-lying a1g level and twofold degenerate eg states in T′ and Td phases. Intuitively, the magnetic properties of 2D TMDs should be determined by splitting and filling behavior of d orbitals of the transition metal ions under various crystal fields. For the same transition metal ion, the electronegativity of a chalcogen atom also plays some role, such that the lighter chalcogen atom draws more electrons from the metal ions and affects their on-site magnetic moments.

It was computationally confirmed that intrinsic long-range magnetic ordering can be realized on the transition metal sites with respect to delocalized p states of S/Se/Te atoms in a variety of transition metal dichalcogenides. Early in 2002, extensive analyses of the stability of TMD monolayers based on DFT calculations predicted that, out of 88 combinations of TMDs compounds, 52 H or T structures can occur as the freestanding phase. Among them, H-phase TMDs with M = Cr, Mo, V, Mn, Co, and W, and X = S, Se, and Te were predicted to be ferromagnetic metals with net magnetic moment ranging from 0.2 to 3.0 μB per formula.5656. C. Ataca, H. Şahin, and S. Ciraci, J. Phys. Chem. C 116(16), 8983 (2012). https://doi.org/10.1021/jp212558p Similarly, Chen et al.5757. W. Chen, J.-m. Zhang, Y.-z. Nie, Q.-l. Xia, and G.-h. Guo, J. Magn. Magn. Mater. 508, 166878 (2020). https://doi.org/10.1016/j.jmmm.2020.166878 also systematically explored the magnetic properties of MTe2 (M = Ti, V, Cr, Mn, Fe, Co, Ni) monolayers in both H and T phases. Their results indicated that H-VTe2, T-MnTe2 and H-FeTe2 are ferromagnetic metals with magnetic moments of 0.78, 2.80, and 1.48 μB per formula unit (f.u.), respectively, while T-VTe2 is an indirect bandgap semiconductor with a magnetic moment of 1.0 μB per formula. Using 2D Ising model and MFT, the estimated Curie temperatures were 301, 33, 88, and 229 K for H-VTe2, T-VTe2, T-MnTe2, and H-FeTe2 monolayers, respectively. Moreover, non-collinear DFT calculations revealed that H-VTe2, T-VTe2, and H-FeTe2 monolayers have in-plane easy magnetization direction with MAE values of 0.51, 1.74, and 2.57 meV/f.u., respectively, while T-MnTe2 has a perpendicular easy magnetization axis with MAE of 0.54 meV/f.u. DFT calculations within LDA+U approximation demonstrated that single-layer VS2 of 1T phase is a strongly correlated material, where 2H structure of monolayer VS2 is a ferromagnetic semiconductor.1010. H. L. Zhuang and R. G. Hennig, Phys. Rev. B 93(5), 054429 (2016). https://doi.org/10.1103/PhysRevB.93.054429 The magnetic moments are localized on the V atoms and couple ferromagnetically via superexchange interactions mediated by the S atoms. Calculations of magnetic anisotropy showed an easy plane for the magnetic moment in 2H VS2. The magnetic properties of 2D NbS2 and ReS2 nanosheets have been investigated using the HSE06 hybrid functional.184,185184. Z. Sun, H. Lv, Z. Zhuo, A. Jalil, W. Zhang, X. Wu, and J. Yang, J. Mater. Chem. C 6(5), 1248 (2018). https://doi.org/10.1039/C7TC05303G185. Y. Sun, Z. Zhuo, and X. Wu, J. Mater. Chem. C 6(42), 11401 (2018). https://doi.org/10.1039/C8TC04188A Both of them are bipolar magnetic semiconductors with spin gaps of 0.27 and 1.63 eV. Furthermore, MC simulations predicted the Curie temperatures to be 141 and 157 K for 2D NbS2 and ReS2 systems, respectively.

Among the large family of potential 2D magnetic TMDs, VSe2, VTe2, MnSex, NbTe2, NbSe2, and CrTe2 have attracted more and more attentions from both experimental and theoretical aspects, mainly because of the reported room-temperature TC. In the following content, we will discuss the major developments that have paved the way to this point. First, all these six materials belong to the family of T phase [Fig. 9(a)] and exhibit metallic nature. The magnetic coupling mechanism stems from the competition between indirect superexchange and itinerant exchange interactions. Second, 2D metallic TMDs are well-known charge density wave (CDW) systems and the CDW phase transition steers the change of electronic structures in them. Therefore, the correlation effect and the possible competition between CDW ordering and magnetic ordering also needs to be clarified.

FIG. 9. (a) Top and side views of 1T TMD lattice. (b) M–H hysteresis loop of bare VSe2 flakes on SiO2 substrate under an in‐plane magnetic field at 300 and 10 K. (c) Temperature‐dependent saturated magnetization (Ms) of bare VSe2 from 10 to 500 K. Inset: M–H curve for the sample at 470 K indicating the loose of magnetization. (d), (e) Magnetic hysteresis loops for VTe2 at 10 and 300 K, respectively. (f) Magnetic hysteresis loop of ∼1 ML MnSex on the GaSe base layer showing ferromagnetic ordering. Inset: the unprocessed SQUID data prior to background subtraction. Panels (a)–(c) reproduced with permission from Yu et al., Adv. Mater. 31, 1903779 (2019). Copyright 2019 John Wiley and Sons.186186. W. Yu, J. Li, T. S. Herng, Z. Wang, X. Zhao, X. Chi, W. Fu, I. Abdelwahab, J. Zhou, J. Dan, Z. Chen, Z. Chen, Z. Li, J. Lu, S. J. Pennycook, Y. P. Feng, J. Ding, and K. P. Loh, Adv. Mater. 31(40), e1903779 (2019). https://doi.org/10.1002/adma.201903779 Panels (d) and (e) reproduced with permission from Li et al., Adv. Mater. 30, 1801043 (2018). Copyright 2018 John Wiley and Sons.3535. J. Li, B. Zhao, P. Chen, R. Wu, B. Li, Q. Xia, G. Guo, J. Luo, K. Zang, Z. Zhang, H. Ma, G. Sun, X. Duan, and X. Duan, Adv. Mater. 30(36), 1801043 (2018). https://doi.org/10.1002/adma.201801043 Panel (f) reproduced with permission from O'Hara et al., Nano Lett. 18, 3125 (2018). Copyright 2018 American Chemical Society.3636. D. J. O'Hara, T. Zhu, A. H. Trout, A. S. Ahmed, Y. K. Luo, C. H. Lee, M. R. Brenner, S. Rajan, J. A. Gupta, D. W. McComb, and R. K. Kawakami, Nano Lett. 18(5), 3125 (2018). https://doi.org/10.1021/acs.nanolett.8b00683

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Monolayer VSe2 material has been reported as one of the first room-temperature 2D ferromagnets.3434. M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan, and M. Batzill, Nature Nanotechnol. 13(4), 289 (2018). https://doi.org/10.1038/s41565-018-0063-9 From the electronic structure point of view, VSe2 exhibits a 3d1 configuration, which invokes both metallic and magnetic properties. Bonilla et al.3434. M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan, and M. Batzill, Nature Nanotechnol. 13(4), 289 (2018). https://doi.org/10.1038/s41565-018-0063-9 synthesized single- and few-layer VSe2 sheets on HOPG and MoS2 substrates using MBE and performed magnetic characterization by protecting the films with a Se capping layer. Their studies revealed a significant enhancement of magnetic moment in single-layer samples compared with multi-layer ones. Surprisingly, the ferromagnetic ordering is very robust and persists above room temperature. The room-temperature ferromagnetism was also observed on the exfoliated 2D VSe2 flakes using superconducting quantum interference device (SQUID), XMCD [Figs. 9(b) and 9(c)], and magnetic force microscopy (MFM), where the monolayer flake displayed the strongest ferromagnetic properties.186186. W. Yu, J. Li, T. S. Herng, Z. Wang, X. Zhao, X. Chi, W. Fu, I. Abdelwahab, J. Zhou, J. Dan, Z. Chen, Z. Chen, Z. Li, J. Lu, S. J. Pennycook, Y. P. Feng, J. Ding, and K. P. Loh, Adv. Mater. 31(40), e1903779 (2019). https://doi.org/10.1002/adma.201903779 First-principles calculations using both GGA and high-level LDA+DMFT (dynamical mean-field theory) approaches explained that it might be a ferromagnet with both itinerant and localized characters.17,18,2017. Y. Ma, Y. Dai, M. Guo, C. Niu, Y. Zhu, and B. Huang, ACS Nano 6(2), 1695 (2012). https://doi.org/10.1021/nn204667z18. F. Li, K. Tu, and Z. Chen, J. Phys. Chem. C 118(36), 21264 (2014). https://doi.org/10.1021/jp507093t20. G. V. Pushkarev, V. G. Mazurenko, V. V. Mazurenko, and D. W. Boukhvalov, Phys. Chem. Chem. Phys. 21(40), 22647 (2019). https://doi.org/10.1039/C9CP03726H For example, LDA+DMFT calculations predicted ferromagnetic ordering in VSe2 monolayer without CDW below 250 K. However, the origin of ferromagnetism in VSe2 has spurred great controversies. First, the reported experimental magnetic moments (5∼15 μB)34,18734. M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan, and M. Batzill, Nature Nanotechnol. 13(4), 289 (2018). https://doi.org/10.1038/s41565-018-0063-9187. G. Duvjir, B. K. Choi, I. Jang, S. Ulstrup, S. Kang, T. Thi Ly, S. Kim, Y. H. Choi, C. Jozwiak, A. Bostwick, E. Rotenberg, J.-G. Park, R. Sankar, K.-S. Kim, J. Kim, and Y. J. Chang, Nano Lett. 18(9), 5432 (2018). https://doi.org/10.1021/acs.nanolett.8b01764 are too large in comparison with the calculated values (0.365∼0.6 μB).17,18,2017. Y. Ma, Y. Dai, M. Guo, C. Niu, Y. Zhu, and B. Huang, ACS Nano 6(2), 1695 (2012). https://doi.org/10.1021/nn204667z18. F. Li, K. Tu, and Z. Chen, J. Phys. Chem. C 118(36), 21264 (2014). https://doi.org/10.1021/jp507093t20. G. V. Pushkarev, V. G. Mazurenko, V. V. Mazurenko, and D. W. Boukhvalov, Phys. Chem. Chem. Phys. 21(40), 22647 (2019). https://doi.org/10.1039/C9CP03726H Second, no magnetic signal was detected in another XMCD experiment and the angle resolved photoemission spectrum showed no exchange splitting.188,189188. P. Chen, W. W. Pai, Y. H. Chan, V. Madhavan, M. Y. Chou, S. K. Mo, A. V. Fedorov, and T. C. Chiang, Phys. Rev. Lett. 121(19), 196402 (2018). https://doi.org/10.1103/PhysRevLett.121.196402189. J. Feng, D. Biswas, A. Rajan, M. D. Watson, F. Mazzola, O. J. Clark, K. Underwood, I. Marković, M. McLaren, A. Hunter, D. M. Burn, L. B. Duffy, S. Barua, G. Balakrishnan, F. Bertran, P. Le Fèvre, T. K. Kim, G. van der Laan, T. Hesjedal, P. Wahl, and P. D. C. King, Nano Lett. 18(7), 4493 (2018). https://doi.org/10.1021/acs.nanolett.8b01649 Third, several studies145,187,189–191145. P. K. J. Wong, W. Zhang, F. Bussolotti, X. Yin, T. S. Herng, L. Zhang, Y. L. Huang, G. Vinai, S. Krishnamurthi, D. W. Bukhvalov, Y. J. Zheng, R. Chua, A. T. N'Diaye, S. A. Morton, C.-Y. Yang, K.-H. O. Yang, P. Torelli, W. Chen, K. E. J. Goh, J. Ding, M.-T. Lin, G. Brocks, M. P. de Jong, A. H. C. Neto, and A. T. S. Wee, Adv. Mater. 31(23), 1901185 (2019). https://doi.org/10.1002/adma.201901185187. G. Duvjir, B. K. Choi, I. Jang, S. Ulstrup, S. Kang, T. Thi Ly, S. Kim, Y. H. Choi, C. Jozwiak, A. Bostwick, E. Rotenberg, J.-G. Park, R. Sankar, K.-S. Kim, J. Kim, and Y. J. Chang, Nano Lett. 18(9), 5432 (2018). https://doi.org/10.1021/acs.nanolett.8b01764189. J. Feng, D. Biswas, A. Rajan, M. D. Watson, F. Mazzola, O. J. Clark, K. Underwood, I. Marković, M. McLaren, A. Hunter, D. M. Burn, L. B. Duffy, S. Barua, G. Balakrishnan, F. Bertran, P. Le Fèvre, T. K. Kim, G. van der Laan, T. Hesjedal, P. Wahl, and P. D. C. King, Nano Lett. 18(7), 4493 (2018). https://doi.org/10.1021/acs.nanolett.8b01649190. P. M. Coelho, K. Nguyen Cong, M. Bonilla, S. Kolekar, M.-H. Phan, J. Avila, M. C. Asensio, I. I. Oleynik, and M. Batzill, J. Phys. Chem. C 123(22), 14089 (2019). https://doi.org/10.1021/acs.jpcc.9b04281191. A. O. Fumega, M. Gobbi, P. Dreher, W. Wan, C. González-Orellana, M. Peña-Díaz, C. Rogero, J. Herrero-Martín, P. Gargiani, M. Ilyn, M. M. Ugeda, V. Pardo, and S. Blanco-Canosa, J. Phys. Chem. C 123(45), 27802 (2019). https://doi.org/10.1021/acs.jpcc.9b08868 suggested CDW transition distortion can suppress the intrinsic ferromagnetic ground states in VSe2. Wong et al.145145. P. K. J. Wong, W. Zhang, F. Bussolotti, X. Yin, T. S. Herng, L. Zhang, Y. L. Huang, G. Vinai, S. Krishnamurthi, D. W. Bukhvalov, Y. J. Zheng, R. Chua, A. T. N'Diaye, S. A. Morton, C.-Y. Yang, K.-H. O. Yang, P. Torelli, W. Chen, K. E. J. Goh, J. Ding, M.-T. Lin, G. Brocks, M. P. de Jong, A. H. C. Neto, and A. T. S. Wee, Adv. Mater. 31(23), 1901185 (2019). https://doi.org/10.1002/adma.201901185 observed traits of spin frustration in monolayer VSe2 with long-range intrinsic ferromagnetism from complementary temperature- and field-dependent susceptibility measurements. They have also reported that the frustrated intrinsic magnetism in 2D VSe2 can be lifted by the introduction of the Se-deficient defects.192192. R. Chua, J. Yang, X. He, X. Yu, W. Yu, F. Bussolotti, P. K. J. Wong, K. P. Loh, M. B. H. Breese, K. E. J. Goh, Y. L. Huang, and A. T. S. Wee, Adv. Mater. 32(24), 2000693 (2020). https://doi.org/10.1002/adma.202000693 Yu et al. inferred that a defect-free sample is the key to verify the intrinsic ferromagnetism of VSe2.186186. W. Yu, J. Li, T. S. Herng, Z. Wang, X. Zhao, X. Chi, W. Fu, I. Abdelwahab, J. Zhou, J. Dan, Z. Chen, Z. Chen, Z. Li, J. Lu, S. J. Pennycook, Y. P. Feng, J. Ding, and K. P. Loh, Adv. Mater. 31(40), e1903779 (2019). https://doi.org/10.1002/adma.201903779 Nakano et al.193193. M. Nakano, Y. Wang, S. Yoshida, H. Matsuoka, Y. Majima, K. Ikeda, Y. Hirata, Y. Takeda, H. Wadati, Y. Kohama, Y. Ohigashi, M. Sakano, K. Ishizaka, and Y. Iwasa, Nano Lett. 19(12), 8806 (2019). https://doi.org/10.1021/acs.nanolett.9b03614 demonstrated the emergence of intrinsic ferromagnetism in V5Se8 (V0.25VSe2) epitaxial thin films grown by MBE, which can be classified as itinerant 2D Heisenberg ferromagnets with weak magnetic anisotropy.

Due to strong 3d1 electron coupling in the neighboring M4+–M4+ pairs (M = V, Nb, Ta) of 2D TMDs, metallic VTe2, NbTe2, NbSe2, and TaTe2 systems composed of group VB elements have been regarded as the potential intrinsic magnets. In some theoretical investigations, 2D VTe2, NbTe2, and TaTe2 have been predicted to exhibit intrinsic magnetic ordering.58,59,194,19558. H.-R. Fuh, C.-R. Chang, Y.-K. Wang, R. F. L. Evans, R. W. Chantrell, and H.-T. Jeng, Sci. Rep. 6(1), 32625 (2016). https://doi.org/10.1038/srep3262559. H. Pan, J. Phys. Chem. C 118(24), 13248 (2014). https://doi.org/10.1021/jp503030b194. J. Zhang, B. Yang, H. Zheng, X. Han, and Y. Yan, Phys. Chem. Chem. Phys. 19(35), 24341 (2017). https://doi.org/10.1039/C7CP04445C195. H. Guo, N. Lu, L. Wang, X. Wu, and X. C. Zeng, J. Phys. Chem. C 118(13), 7242 (2014). https://doi.org/10.1021/jp501734s In particular, VTe2 monolayer was found to be a room-temperature ferromagnet with highest TC value of 553∼618 K. Meanwhile, MC simulation of the hysteresis features of VTe2 monolayer illustrated that it is possible to observe finite remanence and coercivity treatments nearly or well beyond room temperature.146146. E. Vatansever, S. Sarikurt, and R. F. L. Evans, Mater. Res. Express 5(4), 046108 (2018). https://doi.org/10.1088/2053-1591/aabca6 Similar to the discussions on VSe2, Wong et al.196196. P. K. J. Wong, W. Zhang, J. Zhou, F. Bussolotti, X. Yin, L. Zhang, A. T. N'Diaye, S. A. Morton, W. Chen, J. Goh, M. P. de Jong, Y. P. Feng, and A. T. S. Wee, ACS Nano 13(11), 12894 (2019). https://doi.org/10.1021/acsnano.9b05349 also found that CDW order would rule out the ferromagnetic behavior in VTe2 monolayer. Experimentally, the single crystalline ultrathin VTe2, NbTe2, and TaTe2 sheets were synthesized using atmospheric pressure CVD approach.3535. J. Li, B. Zhao, P. Chen, R. Wu, B. Li, Q. Xia, G. Guo, J. Luo, K. Zang, Z. Zhang, H. Ma, G. Sun, X. Duan, and X. Duan, Adv. Mater. 30(36), 1801043 (2018). https://doi.org/10.1002/adma.201801043 The magnetic hysteresis (M‐H) measurements demonstrated that VTe2 and NbTe2 exhibit room‐temperature ferromagnetism [Figs. 9(d) and 9(e)]. The reported saturation magnetization, coercivity, and remnant magnetization values of VTe2 were 0.3 emu g−1, 1173.0 Oe, 0.16 emu g−1 at 10 K, and 0.21 emu g−1, 592 Oe, 0.10 emu g−1 at 300 K, respectively. However, the competition between CDW and magnetic instability in VTe2 is still under debate. On the one hand, formation of the CDW phase in 2D VSe2 was observed in experiment, and three possible CDW transitions at 135, 240, and 186 K have been reported.35,197,19835. J. Li, B. Zhao, P. Chen, R. Wu, B. Li, Q. Xia, G. Guo, J. Luo, K. Zang, Z. Zhang, H. Ma, G. Sun, X. Duan, and X. Duan, Adv. Mater. 30(36), 1801043 (2018). https://doi.org/10.1002/adma.201801043197. Y. Wang, J. Ren, J. Li, Y. Wang, H. Peng, P. Yu, W. Duan, and S. Zhou, Phys. Rev. B 100(24), 241404 (2019). https://doi.org/10.1103/PhysRevB.100.241404198. X. Ma, T. Dai, S. Dang, S. Kang, X. Chen, W. Zhou, G. Wang, H. Li, P. Hu, Z. He, Y. Sun, D. Li, F. Yu, X. Zhou, H. Chen, X. Chen, S. Wu, and S. Li, ACS Appl. Mater. Inter. 11(11), 10729 (2019). https://doi.org/10.1021/acsami.8b21442 The CDW effect would suppress the magnetic instability and further lead to the absence of magnetic ordering. Through a combination of in situ microscopic and spectroscopic techniques, Wong et al.196196. P. K. J. Wong, W. Zhang, J. Zhou, F. Bussolotti, X. Yin, L. Zhang, A. T. N'Diaye, S. A. Morton, W. Chen, J. Goh, M. P. de Jong, Y. P. Feng, and A. T. S. Wee, ACS Nano 13(11), 12894 (2019). https://doi.org/10.1021/acsnano.9b05349 observed a 4 × 4 CDW order and further excluded the intrinsic ferromagnetic ordering in VTe2 by XMCD data. One the other hand, Sugawara and coworkers199199. K. Sugawara, Y. Nakata, K. Fujii, K. Nakayama, S. Souma, T. Takahashi, and T. Sato, Phys. Rev. B 99(24), 241404 (2019). https://doi.org/10.1103/PhysRevB.99.241404 recently found a large triangular Fermi surface at the K point that satisfies a nearly perfect nesting condition, whereas CDW is suppressed as highlighted by the observation of band crossing of the Fermi level at low temperature, in contrast to monolayer VSe2. Combining DFT calculations with scanning tunneling microscopy and spectroscopy (STM/STS) measurements, ferrimagnetic ground state of 2D NbSe2 was demonstrated with a magnetic moment of 1.09 μB.200200. S. Divilov, W. Wan, P. Dreher, M. M. Ugeda, and F. Ynduráin, arXiv:005.06210 (2020). More importantly, their results also inferred that substrate is the key to verifying the intrinsic ferromagnetism of TMD materials.196,200196. P. K. J. Wong, W. Zhang, J. Zhou, F. Bussolotti, X. Yin, L. Zhang, A. T. N'Diaye, S. A. Morton, W. Chen, J. Goh, M. P. de Jong, Y. P. Feng, and A. T. S. Wee, ACS Nano 13(11), 12894 (2019). https://doi.org/10.1021/acsnano.9b05349200. S. Divilov, W. Wan, P. Dreher, M. M. Ugeda, and F. Ynduráin, arXiv:005.06210 (2020). It was shown that single-layer NbSe2 does not display CDW instability unless a graphene layer is utilized as substrate.

Motivated by DFT calculations,56,6056. C. Ataca, H. Şahin, and S. Ciraci, J. Phys. Chem. C 116(16), 8983 (2012). https://doi.org/10.1021/jp212558p60. M. Kan, S. Adhikari, and Q. Sun, Phys. Chem. Chem. Phys. 16(10), 4990 (2014). https://doi.org/10.1039/c3cp55146f O'Hara et al.3636. D. J. O'Hara, T. Zhu, A. H. Trout, A. S. Ahmed, Y. K. Luo, C. H. Lee, M. R. Brenner, S. Rajan, J. A. Gupta, D. W. McComb, and R. K. Kawakami, Nano Lett. 18(5), 3125 (2018). https://doi.org/10.1021/acs.nanolett.8b00683 also observed room-temperature ferromagnetism in manganese selenide (MnSex) films grown by MBE. Magnetic and structural characterizations provided strong evidence that, at the monolayer limit, ferromagnetism originates from the vdW MnSe2 monolayer. Using DFT calculations combined with MC simulations, Kan et al.6060. M. Kan, S. Adhikari, and Q. Sun, Phys. Chem. Chem. Phys. 16(10), 4990 (2014). https://doi.org/10.1039/c3cp55146f have shown that 2D MnSe2 sheets are ideal magnetic semiconductors with long-range magnetic ordering, where all Mn atoms are ferromagnetically coupled and the estimated TC is 250 K [Fig. 9(f)]. Interestingly, first-principles calculations further revealed the great defect tolerance in MnSe2. Despite the presence of high-density Se vacancies, the defective MnSe2 monolayer can retain its stable ferromagnetic behavior.144144. I. Eren, F. Iyikanat, and H. Sahin, Phys. Chem. Chem. Phys. 21(30), 16718 (2019). https://doi.org/10.1039/C9CP03112J Magnetic tunneling junctions based on monolayer MnSe2 with room-temperature ferromagnetism were also observed with a large tunneling magnetoresistance of 725%.201201. L. Pan, H. Wen, L. Huang, L. Chen, H.-X. Deng, J.-B. Xia, and Z. Wei, Chin. Phys. B 28(10), 107504 (2019). https://doi.org/10.1088/1674-1056/ab3e45 Moreover, by optical and electronic measurements, Sun et al.147147. X. Sun, W. Li, X. Wang, Q. Sui, T. Zhang, Z. Wang, L. Liu, D. L. Li, S. Feng, S. Zhong, H. Wang, V. Bouchiat, M. N. Regueiro, N. Rougemaille, J. Coraux, Z. Wang, B. Dong, X. Wu, T. Yang, G. Yu, B. Wang, Z. V. Han, X. Han, and Z. Zhang, Nano Res. 13, 3358 (2020). https://doi.org/10.1007/s12274-020-3021-4 disclosed that the intrinsic ferromagnetically aligned spin polarization can hold up to 316 K in a metallic phase of 1T-CrTe2. Detailed spin transport measurements suggested half-metallicity in its spin polarized band structure as well as in-plane room-temperature negative anisotropic magnetoresistance. Importantly, their study found that exchange coupling due to an enhancement of itinerant type was the source of room-temperature ferromagnetism in both bulk and few-layered Cr2Te3.2121. Y. Wen, Z. Liu, Y. Zhang, C. Xia, B. Zhai, X. Zhang, G. Zhai, C. Shen, P. He, R. Cheng, L. Yin, Y. Yao, M. Getaye Sendeku, Z. Wang, X. Ye, C. Liu, C. Jiang, C. Shan, Y. Long, and J. He, Nano Lett. 20(5), 3130 (2020). https://doi.org/10.1021/acs.nanolett.9b05128

2. Other transition metal chalcogenides

Owing to the variable valence of transition metal elements, transition metal chalcogenides have diverse stoichiometric compositions. In addition to TMDs with M:X = 1:2, the 2D transition metal chalcogenide compounds with higher stoichiometries (M:X = 5:8, 2:3, 3:4, and 1:1) also exhibit interesting magnetic properties. In V5S8 nanosheets, an AFM to FM phase transition was observed when the thickness is down to 3.2 nm. Using DFT calculations, Zhang et al.202202. R. Z. Zhang, Y. Y. Zhang, and S. X. Du, Chin. Phys. B 29(7), 077504 (2020). https://doi.org/10.1088/1674-1056/ab8db1 further investigated the thickness-dependent magnetic ordering in V5S8 thin films, and confirmed an antiferromagnetic to ferromagnetic phase transition when V5S8 is thinned down to 2.2 nm. The magnetic moments of the thin films in both antiferromagnetic and ferromagnetic states are mainly located on V atoms in the intermediate layer. Utilizing vdW epitaxy techniques, Cr2S3 sheets with one-unit cell thickness down to 1.78 nm have been successfully synthesized, which exhibited ferrimagnetic behavior with a Néel temperature of 120 K and the maximum saturation magnetic momentum of up to 65 emu.203203. J. Chu, Y. Zhang, Y. Wen, R. Qiao, C. Wu, P. He, L. Yin, R. Cheng, F. Wang, Z. Wang, J. Xiong, Y. Li, and J. He, Nano Lett. 19(3), 2154 (2019). https://doi.org/10.1021/acs.nanolett.9b00386 In addition, Lv et al.204204. P. Lv, G. Tang, C. Yang, J. Deng, Y. Liu, X. Wang, X. Wang, and J. Hong, 2D Mater. 5(4), 045026 (2018). https://doi.org/10.1088/2053-1583/aadb5a identified Co2Se3 as a 2D half-metal among a series of M2Se3 candidate materials, and the calculated TC from the mean field theory was about 600 K. Using first-principles calculations, Ouyang and co-workers predicted a family of stable 2D honeycomb lattices of Cr2X3 (X = O, S, Se). Cr2S3 and Cr2Se3 are ferromagnetic half-metals with mirror symmetry protected nodal lines for the spin-down channels, while Cr2O3 layers are ferromagnetic semiconductors with large out-of-plane MAE.205205. J.-Y. Chen, X.-X. Li, W.-Z. Zhou, J.-L. Yang, F.-P. Ouyang, and X. Xiong, Adv. Electron. Mater. 6(1), 2070001 (2020). https://doi.org/10.1002/aelm.202070001 A hexagonal Ta2S3 sheet has also been predicted as 2D magnet from the spin-wave theory, which possesses sizeable out-of-plane MAE of 4.6 meV and high Curie temperature of 445 K.206206. L. Zhang, C.-w. Zhang, S.-F. Zhang, W.-x. Ji, P. Li, and P.-j. Wang, Nanoscale 11(12), 5666 (2019). https://doi.org/10.1039/C9NR00826H

Based on first-principles calculations, a new composition of stable 2D transition metal chalcogenides, i.e., Cr3X4 (X = S, Se, Te) monolayers, has been predicted to possess fascinating magnetic properties.1515. X. Zhang, B. Wang, Y. Guo, Y. Zhang, Y. Chen, and J. Wang, Nanoscale Horiz. 4(4), 859 (2019). https://doi.org/10.1039/C9NH00038K Among them, Cr3S4 monolayer is a ferrimagnetic semiconductor, while Cr3Se4 and Cr3Te4 monolayers are ferromagnetic half-metals with TC of 370 and 460 K, respectively. Unlike the d–p–d superexchange interaction found in the other transition metal compounds, double exchange magnetic coupling mechanism is dominated in these 2D Cr3X4 sheets, finally leading to enhanced FM ordering and room temperature TC. That is to say, a delocalized unpaired electron could hop between the two neighboring Cr ions with different oxidation states in 2D Cr3X4.

Using PSO technique combined with first-principles calculations, Zhang et al.207207. Y. Zhang, J. Pang, M. Zhang, X. Gu, and L. Huang, Sci. Rep. 7(1), 15993 (2017). https://doi.org/10.1038/s41598-017-16032-x predicted a new transition metal chalcogenide monolayer composed of cobalt and sulfur atoms—Co2S2. Their results revealed that a single-layer Co2S2 sheet is a ferromagnetic metal with a Curie temperature of 404 K. Two-dimensional ultrathin CrSe crystals were successfully synthesized on mica substrate via ambient pressure CVD method.208208. Y. Zhang, J. Chu, L. Yin, T. A. Shifa, Z. Cheng, R. Cheng, F. Wang, Y. Wen, X. Zhan, Z. Wang, and J. He, Adv. Mater. 31(19), 1900056 (2019). https://doi.org/10.1002/adma.201900056 Such CVD-grown 2D CrSe crystals exhibit evident ferromagnetic behavior at temperatures below 280 K. Kang et al.209209. L. Kang, C. Ye, X. Zhao, X. Zhou, J. Hu, Q. Li, D. Liu, C. M. Das, J. Yang, D. Hu, J. Chen, X. Cao, Y. Zhang, M. Xu, J. Di, D. Tian, P. Song, G. Kutty, Q. Zeng, Q. Fu, Y. Deng, J. Zhou, A. Ariando, F. Miao, G. Hong, Y. Huang, S. J. Pennycook, K.-T. Yong, W. Ji, X. R. Wang, and Z. Liu, Nat. Commun. 11(1), 3729 (2020). https://doi.org/10.1038/s41467-020-17253-x reported the synthesis of ultrathin FeTe film by CVD approach and discussed their structural and magnetic transition. Transport measurements revealed that tetragonal FeTe is an antiferromagnetic metal with TN of about 71.8 K, while hexagonal FeTe is a ferromagnetic metal with TC of around 220 K. Very recently, Yuan et al.210210. Q.-Q. Yuan, Z. Guo, Z.-Q. Shi, H. Zhao, Z.-Y. Jia, Q. Wang, J. Sun, D. Wu, and S.-C. Li, Chin. Phys. Lett. 37(7), 077502 (2020). https://doi.org/10.1088/0256-307X/37/7/077502 have grown FM MnSe monolayer on silicon substrate using MBE method. The thickness dependence of Curie temperature was found in the MnSe ultrathin films. The measured TC was 54 K for monolayer, while it sharply increased to 225 K for three-layer MnSe, and 235 K for four-layer MnSe.

C. MXene and MXene analogues

MXene, a category of 2D transition metal carbides, nitrides, and carbonitrides, possibly terminated by functional group (T) on the surface, with a general formula of Mn+1XnTx (M = transition metal; X = C and/or N; T = O, OH, F) are attractive additions to the family of 2D materials. Since the discovery of Ti3C2 in 2011, MXenes of Ti2C, V2C, Nb2C, Mo2C, Zr3C2, Nb4C3, Ta4C3, and Ti4N3, as well as of TiNbC, (Ti0.5Nb0.5)2C, (V0.5Cr0.5)3C2, Ti3CN, Mo2TiC2, Mo2ScC2, Cr2TiC2, Mo2Ti2C3, (Nb0.8Ti0.2)4C3, and (Nb0.8Zr0.2)4C3 have already been fabricated in a laboratory. According to the large number of M-X compositions, more than a hundred MXenes have been theoretically predicted.211211. M. Khazaei, A. Ranjbar, M. Arai, T. Sasaki, and S. Yunoki, J. Mater. Chem. C 5(10), 2488 (2017). https://doi.org/10.1039/C7TC00140A

The diverse compositions and controllable thickness of Mn+1XnTx systems provide an ideal playground to achieve 2D intrinsic magnetism (Table III).92,211,21292. X. Zhang and C. Gong, Science 363(6428), 4450 (2019). https://doi.org/10.1126/science.aav4450211. M. Khazaei, A. Ranjbar, M. Arai, T. Sasaki, and S. Yunoki, J. Mater. Chem. C 5(10), 2488 (2017). https://doi.org/10.1039/C7TC00140A212. N. C. Frey, C. C. Price, A. Bandyopadhyay, H. Kumar, and V. B. Shenoy, Predicted Magnetic Properties of MXenes ( Springer, Cham, 2019). As mentioned above, transition metal M atom usually has a partially filled d shell with unpaired electrons. First of all, the magnetic properties of MXene are influenced by the total number of d electrons. The M site can be also occupied by the ordered double transition metal species, i.e., M′M″. Generally, M′ atoms locate in the outer layers and M″ atoms occupy the middle layer, yielding [M′X]nM″ arrangement. However, some in-plane ordered double transition metal MXenes have also been reported. The competition of electron hopping and electronic coupling between M′ and M″ ions will further modify the magnetic ground state of MXene. Each X (C or N) anion bounds with six transition metal M cations, forming XM6 octahedral configuration. The transition metal atoms on the surface of M2X are subjected to a C3v ligand field contributed by the neighboring X atoms. Hence, the five 3d orbitals of transition metal atom would split into a single state a1 (dz2), two twofold degenerate states e1 (dx2-y2/dxy) and e2 (dxz/dyz). The splitting between a1 and e1/e2 is determined by the strengths of M–X interactions. In addition, long-range spin interaction between the metal atoms always occurs through X atoms in MXene, which plays an important role in mediating the magnetic coupling.

TABLE III. A list of 2D magnets in MXene family with their compositions and key electronic and magnetic properties, including the magnetic ground state (GS), the values of Hubbard U, energy gap (Eg), magnetic moment on per transition metal (Ms), Curie temperature (TC), and magnetic anisotropy energy per unit cell (MAE).

CompositionsGSU (eV)Eg (eV)Ms (μB)TC (K)MAE (meV)Ref.Mn+1XnCr2CFM–HM3––136136. C. Si, J. Zhou, and Z. Sun, ACS Appl. Mater. Inter. 7(31), 17510 (2015). https://doi.org/10.1021/acsami.5b05401Ti2CFM–M0.96––222222. S. Zhao, W. Kang, and J. Xue, Appl. Phys. Lett. 104(13), 133106 (2014). https://doi.org/10.1063/1.4870515Ti2CFM–HM0.96––223223. G. Gao, G. Ding, J. Li, K. Yao, M. Wu, and M. Qian, Nanoscale 8(16), 8986 (2016). https://doi.org/10.1039/C6NR01333CTi2CAFM2∼50.420.95––224224. B. Akgenc, A. Mogulkoc, and E. Durgun, J. Appl. Phys. 127(8), 084302 (2020). https://doi.org/10.1063/1.5140578Ti2CFM–M0.97146–243243. Y. Hu, X. L. Fan, W. J. Guo, Y. R. An, Z. F. Luo, and J. Kong, J. Magn. Magn. Mater. 486, 165280 (2019). https://doi.org/10.1016/j.jmmm.2019.1652802H-Ti2CFM2∼5HM1.0290–224224. B. Akgenc, A. Mogulkoc, and E. Durgun, J. Appl. Phys. 127(8), 084302 (2020). https://doi.org/10.1063/1.5140578Cr2NAFM3M4.45––226226. G. Wang, J. Phys. Chem. 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In experiments, MXene materials have been achieved by selective etching of the A-layers (mostly Al) using acid solution in the bulk MAX phases [Fig. 10(a)].213,214213. B. Anasori, M. R. Lukatskaya, and Y. Gogotsi, Nat. Rev. Mater. 2(2), 16098 (2017). https://doi.org/10.1038/natrevmats.2016.98214. M. Naguib, V. N. Mochalin, M. W. Barsoum, and Y. Gogotsi, Adv. Mater. 26(7), 992 (2014). https://doi.org/10.1002/adma.201304138 Therefore, the majority of MXenes are synthesized with mixed surface functional groups. In the functional group terminated M2X MXene, each transition metal ion is subjected to a new octahedral or distorted octahedral crystal field, which in turn splits the d orbitals into the lower-energy t2g states (dxy, dyz, and dxz) and higher-energy eg states (dx2-y2 and dz2).215,216215. Z. Jiang, P. Wang, X. Jiang, and J. Zhao, Nanoscale Horiz. 3(3), 335 (2018). https://doi.org/10.1039/C7NH00197E216. D. Khomskii, Transition Metal Compounds ( Cambridge University Press, Cambridge, 2014). Moreover, the functional groups have strong affinity with MXene surface and may serve as chemical dopants. The electron transfer from transition metal ions to functional groups would directly affect the magnetic configuration of transition metal ions, which can be interpreted as a competition between localized and itinerant d states. Generally speaking, the itinerant d electrons in MXene favor superexchange mechanism, while the localized d orbitals tend to have direct exchange interaction. In addition to MXenes in M2XTx stoichiometry, thicker MXene systems of Mn+1XnTx are also available in experiments, where the dimensionality, n, describes the number of XM6 octahedral layers in Mn+1XnTx. The stacking of octahedra and the number of occupied d orbitals would depend on the ratio of M and X atoms. The sensitive correlation between the magnetic ordering and dimensionality has also been observed.217,218217. Y. Xie and P. R. C. Kent, Phys. Rev. B 87(23), 235441 (2013). https://doi.org/10.1103/PhysRevB.87.235441218. N. J. Lane, M. W. Barsoum, and J. M. Rondinelli, EPL-Europhys. Lett. 101(5), 57004 (2013). https://doi.org/10.1209/0295-5075/101/57004

FIG. 10. (a) Structures of the MAX and MXene phases. (b) Band structure and partial density of states of Cr d orbitals for Cr2C MXene, and the Fermi level is set to zero. (c) Tunable magnetic anisotropy and noncollinear magnetism in MXenes. (d) Structure of i-MXene (M2/3M'1/3)2X and classification of the magnetic ground states for 319 kinds of i-MXene systems. (e) On-site magnetic moments of Mn atom as function of temperature in bare and functionalized MnB MBene. Panel (a) reproduced with permission from Naguib et al., Adv. Mater. 26, 992 (2014). Copyright 2014 John Wiley and Sons.214214. M. Naguib, V. N. Mochalin, M. W. Barsoum, and Y. Gogotsi, Adv. Mater. 26(7), 992 (2014). https://doi.org/10.1002/adma.201304138 Panel (b) reproduced with permission from Si et al., ACS Appl. Mater. Inter. 7, 17510 (2015). Copyright 2015 American Chemical Society.136136. C. Si, J. Zhou, and Z. Sun, ACS Appl. Mater. Inter. 7(31), 17510 (2015). https://doi.org/10.1021/acsami.5b05401 Panel (c) reproduced with permission from Frey et al., ACS Nano 12, 6319 (2018). Copyright 2018 American Chemical Society.238238. N. C. Frey, H. Kumar, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 12(6), 6319 (2018). https://doi.org/10.1021/acsnano.8b03472 Panel (d) reproduced with permission from Gao et al., Nanoscale 12, 5995 (2020). Copyright 2020 Royal Society of Chemistry.251251. Q. Gao and H. Zhang, Nanoscale 12(10), 5995 (2020). https://doi.org/10.1039/C9NR10181K Panel (e) reproduced with permission from Jiang et al., Nanoscale Horiz. 3, 335 (2018). Licensed under a Creative Commons Attribution (CC-BY-3.0).215215. Z. Jiang, P. Wang, X. Jiang, and J. Zhao, Nanoscale Horiz. 3(3), 335 (2018). https://doi.org/10.1039/C7NH00197E

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1. Pristine MXene (Mn+1Xn)

We start from discussing the simplest case—the magnetic properties of pristine MXenes. Although most MXenes have been synthesized with surface functional groups, few pristine MXene materials Mn+1Xn are also evidenced by experimental observations and theoretical calculations. For instance, a recent experiment confirmed that the surface functional groups F and OH on Ti2C monolayer can be eliminated by heat treatment at different temperatures.219219. J. Li, Y. Du, C. Huo, S. Wang, and C. Cui, Ceram. Int. 41(2), 2631 (2015). https://doi.org/10.1016/j.ceramint.2014.10.070 The Mn2C MXene as the global minimum structure in two dimensions was confirmed by PSO structure search combined with first-principles calculations.220220. L. Hu, X. Wu, and J. Yang, Nanoscale 8(26), 12939 (2016). https://doi.org/10.1039/C6NR02417C Mo2C MXene was successfully prepared with the traditional CVD method.221221. C. Xu, L. Wang, Z. Liu, L. Chen, J. Guo, N. Kang, X.-L. Ma, H.-M. Cheng, and W. Ren, Nat. Mater. 14(11), 1135 (2015). https://doi.org/10.1038/nmat4374

Table III summarizes the unterminated MXenes that have been theoretically predicted to be stable 2D intrinsic magnets, such as Fe2C, Cr2C, Cr2N, Mn2N, Ru2C, Fe2N, Co2N, Ni2N, Ti2C, Zr2C, Ti2N, Ti3C2, Ti3CN, Cr3C2, Tan+1Cn, Tin+1Cn, and Tin+1Nn. Si et al.136136. C. Si, J. Zhou, and Z. Sun, ACS Appl. Mater. Inter. 7(31), 17510 (2015). https://doi.org/10.1021/acsami.5b05401 firstly pointed out that Cr2C is a half-metallic ferromagnet with a bandgap of 2.85 eV. The ferromagnetism arises from the itinerant Cr 3d electrons fractionally occupied in the majority spin channel [Fig. 10(b)]. Similar to Cr2C, Fe2C is also an itinerant ferromagnet, and Stoner model is able to explain the mechanism to induce magnetic orderings.9797. Y. Yue, J. Magn. Magn. Mater. 434, 164 (2017). https://doi.org/10.1016/j.jmmm.2017.03.058 The corresponding exchange interaction parameters are J1= 6.17 meV and J2 = 5.70 meV, which provide further evidences for the robust ferromagnetic coupling of Fe atoms. Moreover, the calculated MAE of Fe2C in reciprocal space is –22.8 μeV per unit cell, which has an easy plane for the magnetization. From the distribution of MAEs, the negative contributions around the sides of hexagonal Brillouin zone are responsible for the in-plane magnetization. The Curie temperature within mean-field approximation was 861 K. First-principles calculations were carried out to investigate the electronic and magnetic properties of a series of M2C (M = Hf, Nb, Sc, Ta, Ti, V, Zr) monolayers.222222. S. Zhao, W. Kang, and J. Xue, Appl. Phys. Lett. 104(13), 133106 (2014). https://doi.org/10.1063/1.4870515 Among them, Ti2C and Zr2C possesses magnetic moments of 1.92 and 1.25 μB/unit, respectively. Gao et al. further confirmed that Ti2C exhibits nearly half-metallicity with a magnetic moment of 0.96 μB/Ti.223223. G. Gao, G. Ding, J. Li, K. Yao, M. Wu, and M. Qian, Nanoscale 8(16), 8986 (2016). https://doi.org/10.1039/C6NR01333C Based on the spin-resolved partial density of states, it is not surprising that the large exchange splitting of Ti 3d electrons and the strong hybridization of Ti 3d electrons with C 2p electrons are responsible for the formation of half-metallic magnetism. By considering all possible spin configurations, Akgenc et al.224224. B. Akgenc, A. Mogulkoc, and E. Durgun, J. Appl. Phys. 127(8), 084302 (2020). https://doi.org/10.1063/1.5140578 indicated that Ti2C MXene is antiferromagnetic metal that is 36 meV/cell lower in energy than FM state. However, room-temperature half-metallic ferromagnetism was observed in 2H-Ti2C. The room-temperature half-metallic ferromagnetism was also found in Ti2N MXene, and the magnetic moments were mainly located at Ti ions with 1.00 μB per formula unit. Although the individual atom of W, Mo, Ru, Os, Tc, and Re has a magnetic moment of 4, 6, 2, 4, 5, and 3 μB, respectively, most MXenes with 4d/5d transition metals are non-magnetic, except that 2H-Ru2C is a FM metal with magnetic moment of 0.86 μB per Ru.225225. B. Akgenc, Solid State Commun. 303–304, 113739 (2019). https://doi.org/10.1016/j.ssc.2019.113739

Besides the above discussed ferromagnetic MXenes, Mn2C is an antiferromagnetic metal with magnetic moment of 3 μB per Mn atom.220220. L. Hu, X. Wu, and J. Yang, Nanoscale 8(26), 12939 (2016). https://doi.org/10.1039/C6NR02417C Both high Néel temperature (720 K) and appreciable in-plane MAE (25 μeV) are simultaneously observed in this system. Strong Mn–Mn coupling within the basal plane is responsible for both AFM ordering and magnetic anisotropy. Cr2N is also an AFM metal. Each Cr atom has a magnetic moment of 4.45 μB, while each N atom possesses a magnetic moment of −0.30 μB. These values are quite different from those of FM Cr2C system.226226. G. Wang, J. Phys. Chem. C 120(33), 18850 (2016). https://doi.org/10.1021/acs.jpcc.6b05224 Ni2N MXene also prefers AFM ground state.227227. G. Wang and Y. Liao, Appl. Surf. Sci. 426, 804 (2017). https://doi.org/10.1016/j.apsusc.2017.07.249 In bare Ni2N MXene, the direct Ni–Ni exchange interaction within short distance is strong, which results in antiferromagnetic coupling between Ni atoms. Similar results have also been found in Fe2N and Co2N.227227. G. Wang and Y. Liao, Appl. Surf. Sci. 426, 804 (2017). https://doi.org/10.1016/j.apsusc.2017.07.249

To reveal the effect of dimensionality, we have compared the magnetic behavior of different Mn+1Xn (n > 1) systems. In MXene with the formula of M3X2, there are three metal atoms per unit cell, i.e., one in the middle (M_m) and two on the surface (M_s). The distance between M_m and M_s is short, which enhances the direct interaction between d orbitals and thus induces AFM coupling between them. Since both M_s atoms couple antiferromagnetically with the M_m atom, these two M_s atoms must couple ferromagnetically with each other. Additionally, after insertion of X atoms, the M_m–M_s antiferromagnetic coupling is weakened. Therefore, Ti3C2, Ti3CN, and Cr3C2 sheets are indeed ferromagnetic metals, and their magnetism originates from Ti and Cr ions on the surface.228,229228. F. Wu, K. Luo, C. Huang, W. Wu, P. Meng, Y. Liu, and E. Kan, Solid State Commun. 222, 9 (2015). https://doi.org/10.1016/j.ssc.2015.08.023229. Y. Zhang and F. Li, J. Magn. Magn. Mater. 433, 222 (2017). https://doi.org/10.1016/j.jmmm.2017.03.031 The possible magnetic ground states of Tin+1Cn and Tin+1Nn (n = 1∼9) were examined by DFT calculations with PBE functional.217217. Y. Xie and P. R. C. Kent, Phys. Rev. B 87(23), 235441 (2013). https://doi.org/10.1103/PhysRevB.87.235441 The results suggested that these unterminated carbide and nitride MXenes with different thicknesses are all magnetic. The magnetism still originates from the 3d electrons of Ti atoms on the surface. However, Tin+1Cn and Tin+1Nn MXene show different magnetic characteristics. The total magnetic moment of carbides increases from 2 to 3 μB per f.u. with increasing n, while the total magnetic moment fluctuates with n around 1.2 μB per f.u. for nitrides. Using first-principles calculations, Lane et al.218218. N. J. Lane, M. W. Barsoum, and J. M. Rondinelli, EPL-Europhys. Lett. 101(5), 57004 (2013). https://doi.org/10.1209/0295-5075/101/57004 have also investigated the effect of dimensionality and electron correlations on the magnetic ordering in Ta-C (Tan+1Cn, n = 1∼3). With LDA+U formulism, AFM configurations were predicted for Ta2C and Ta4C3, whereas ferrimagnetism was predicted for Ta3C2. Without U term, however, their magnetic ground states are non-magnetic for Ta2C and antiferromagnetic for Ta3C2 and Ta4C3, respectively. Using the salt-templating method, Xiao et al. recently synthesized ultrathin Mn3N2 flakes on KCl substrate, which represent the first solution-processed 2D transition metal nitride with intrinsic antiferromagnetism at room temperature.230230. X. Xiao, P. Urbankowski, K. Hantanasirisakul, Y. Yang, S. Sasaki, L. Yang, C. Chen, H. Wang, L. Miao, S. H. Tolbert, S. J. L. Billinge, H. D. Abruña, S. J. May, and Y. Gogotsi, Adv. Funct. Mater. 29(17), 1809001 (2019). https://doi.org/10.1002/adfm.201809001

2. Functional terminated MXenes (Mn+1XnTx)

As stated above, surface functional group is a key degree of freedom in MXene, which are originally introduced during MXene synthesis. Experimentally, when MXenes are chemically exfoliated by HF acid solutions, the outer layers are often saturated with F, O, and/or OH groups. According to the distributions of these functional groups, MXenes can be categorized as symmetrically functionalized MXenes, asymmetrically functionalized MXene (namely, Janus MXene), and mixed functionalized MXenes. The symmetrically functionalized MXenes are terminated by identical groups on both sides of transition metal surfaces, while the top and bottom transition metals surfaces are terminated by two alternative functional groups in the asymmetrically functionalized MXenes. In the mixed functionalized MXenes, the distribution of functional groups is random and nonuniform. The positions and proportions of functional groups in MXene are highly dependent on the synthesis route and post-synthesis treatments. It is necessary to point out that the MXenes produced to date may prefer to have mixed functional groups of F, OH, and O.231231. M. A. Hope, A. C. Forse, K. J. Griffith, M. R. Lukatskaya, M. Ghidiu, Y. Gogotsi, and C. P. Grey, Phys. Chem. Chem. Phys. 18(7), 5099 (2016). https://doi.org/10.1039/C6CP00330C From a theoretical point of view, Singh et al.232232. P. Srivastava, A. Mishra, H. Mizuseki, K.-R. Lee, and A. K. Singh, ACS Appl. Mater. Inter. 8(36), 24256 (2016). https://doi.org/10.1021/acsami.6b08413 also found that the mixed functionalized Ti3C2Fx(OH)1–x (x = 0∼1) MXenes are very close in Gibbs free energy.

Remarkably, magnetism has already been realized in the functional group terminated MXene. Yoon et al.233233. Y. Yoon, T. A. Le, A. P. Tiwari, I. Kim, M. W. Barsoum, and H. Lee, Nanoscale 10(47), 22429 (2018). https://doi.org/10.1039/C8NR06854B developed a low-temperature solution based synthetic method to reduce 2D Ti3C2Tx multilayers. The X-ray photoelectron spectroscopy, electron spin resonance, and magnetization measurements implied that the reduced Ti3C2Tx is Pauli paramagnetic, which is important experimental evidence for magnetism in MXene. The presence of Ti3+ ions is the origin of the electron spin resonance signal. At temperature less than 10 K, a Curie-like concentration was observed, as indicative of singly occupied states at the Fermi level.

The correlation between the magnetic properties of MXene and the functional groups is a subject of increasing concern in the research of 2D MXenes. The effects of different functional groups on the magnetic ground state of MXenes have been widely investigated by theoretical simulations, which will be described in detail below. Similar to the discussions about transition metal trihalides in Sec. III A 1, the relative strengths of direct, superexchange, and double exchange interactions can explain the diverse magnetic ground states of the functionalized MXenes.12,1312. H. Kumar, N. C. Frey, L. Dong, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 11(8), 7648 (2017). https://doi.org/10.1021/acsnano.7b0257813. J. He, P. Lyu, and P. Nachtigall, J. Mater. Chem. C 4(47), 11143 (2016). https://doi.org/10.1039/C6TC03917K

First, it is believed that magnetism can been introduced in the originally non-magnetic MXene after the presence of functional groups. Zha et al.234234. X.-H. Zha, J.-C. Ren, L. Feng, X. Bai, K. Luo, Y. Zhang, J. He, Q. Huang, J. S. Francisco, and S. Du, Nanoscale 10(18), 8763 (2018). https://doi.org/10.1039/C8NR01292J have investigated the mechanism for structural conversion from Sc2C(OH)2 to Sc2CO2 MXene. The atomic configurations and magnetic properties for all the intermediate states were determined. Bipolar magnetic semiconductors were identified from these rearranged configurations with inhomogeneous distribution of hydrogen atoms on different sides with x approximately in the range of 0.188 ≤ x ≤ 0.812. First-principles calculations predicted a novel ferrimagnetic half-metallic state in 2D F-terminated Mo3N2 with a Curie temperature of 237 K.235235. S.-s. Li, S.-j. Hu, W.-x. Ji, P. Li, K. Zhang, C.-w. Zhang, and S.-s. Yan, Appl. Phys. Lett. 111(20), 202405 (2017). https://doi.org/10.1063/1.4993869 Such ferrimagnetic coupling comes mainly from the interactions of itinerant d electrons between different Mo layers, and thus endows 100% spin polarization at the Fermi level with a sizable half-metallic gap of 0.47 eV. Kumar et al.1212. H. Kumar, N. C. Frey, L. Dong, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 11(8), 7648 (2017). https://doi.org/10.1021/acsnano.7b02578 carried out a comprehensive theoretical study on the magnetic properties of twelve nitride MXenes of M2NT2 (M = Ti, V, Cr, Mn; T = F, OH, O). They identified a new series of Mn2NF2, Mn2NO2, and Mn2N(OH)2 that exhibit FM half metallic behavior. The total magnetic moments are 9.0, 8.8, and 7.0 μB per f.u. for Mn2NF2, Mn2NO2, and Mn2N(OH)2, respectively. Both the exchange parameters between intralayer nearest neighbors and interlayer nearest neighbors are positive, indicating FM coupling. Impressively, the Curie temperatures from MC simulations for Mn2NF2, Mn2NO2, and Mn2N(OH)2 are as high as 1877, 1379, and 1745 K, respectively.

Second, theoretical calculations predicted that magnetism would disappear in certain kinds of MXenes due to the presence of surface termination. In the bare Tin+1Cn and Tin+1Nn, the magnetism originates mainly from the unpaired electrons in Ti atoms. Upon functionalization of F, O, OH, and H, the unpaired electron on each Ti atom would be completely donated to the functional group by forming ionic bonds. Thus, the magnetically ordered ground states would be destroyed in the functionalized Tin+1Cn and Tin+1Nn.217217. Y. Xie and P. R. C. Kent, Phys. Rev. B 87(23), 235441 (2013). https://doi.org/10.1103/PhysRevB.87.235441 Once two sides of Ti3C2 surfaces are saturated by external groups, a large number of electronic states distributed around the Fermi level would be removed and the whole system would become non-magnetic.228228. F. Wu, K. Luo, C. Huang, W. Wu, P. Meng, Y. Liu, and E. Kan, Solid State Commun. 222, 9 (2015). https://doi.org/10.1016/j.ssc.2015.08.023 Urbankowski et al.236236. P. Urbankowski, B. Anasori, T. Makaryan, D. Er, S. Kota, P. L. Walsh, M. Zhao, V. B. Shenoy, M. W. Barsoum, and Y. Gogotsi, Nanoscale 8(22), 11385 (2016). https://doi.org/10.1039/C6NR02253G also reported that the magnetic moment of FM bare Ti4N3 with 7.0 μB per unit cell is reduced to almost zero by OH termination. One can therefore conclude that the magnetism of Ti atoms in MXene would be destroyed by –1 valence functional group such as F, Cl, and OH.

Third, an interesting magnetic phase transition could be induced by functionalization. Compared to pristine FM Cr2C, Cr2C terminated by F, H, OH, or Cl groups are AFM. The underlying mechanism for such FM-AFM transition is that the functional groups induce stronger localization behavior on the d electrons of Cr atoms.136136. C. Si, J. Zhou, and Z. Sun, ACS Appl. Mater. Inter. 7(31), 17510 (2015). https://doi.org/10.1021/acsami.5b05401 Fe2N(OH)2, Fe2NO2, Co2NO2, Ni2NF2, Ni2N(OH)2, and Ni2NO2 have FM ground state, which are different from the AFM ground state in bare phase of Fe2N, Co2N, and Ni2N. In those functionalized MXenes, the nearest interlayer distance of metal atoms increases after O, OH, and F terminations.226226. G. Wang, J. Phys. Chem. C 120(33), 18850 (2016). https://doi.org/10.1021/acs.jpcc.6b05224 The ferromagnetic coupling between metal atoms is stronger than AFM coupling, which is explained by a superexchange interaction mechanism mediated by the spin polarized N atoms.227227. G. Wang and Y. Liao, Appl. Surf. Sci. 426, 804 (2017). https://doi.org/10.1016/j.apsusc.2017.07.249 Although bare Cr2N MXene is an AFM metal, Cr2NO2 has a ferromagnetic ground state that acts as a half-metal.226226. G. Wang, J. Phys. Chem. C 120(33), 18850 (2016). https://doi.org/10.1021/acs.jpcc.6b05224 The electrons with minority spin at the Fermi level are suppressed by O groups. Similar to Cr2N, Mn2C monolayer also transforms from AFM to FM state under hydrogenation and oxygenation.237237. X. Zhang, T. He, W. Meng, L. Jin, Y. Li, X. Dai, and G. Liu, J. Phys. Chem. C 123(26), 16388 (2019). https://doi.org/10.1021/acs.jpcc.9b04445 The magnetic moments are 3.22 μB per Mn atom under 100% degree of hydrogenation, and 3.10 and 3.06 μB per Mn atom under 75% and 100% oxygenation degrees, respectively, which are slightly higher than that of bare Mn2C.220220. L. Hu, X. Wu, and J. Yang, Nanoscale 8(26), 12939 (2016). https://doi.org/10.1039/C6NR02417C The Stoner criterion can explain the AFM to FM transition in Mn2C well. From MC simulations, the Curie temperatures are 293 and 323 K for fully hydrogenated and oxygenated Mn2C, respectively.237237. X. Zhang, T. He, W. Meng, L. Jin, Y. Li, X. Dai, and G. Liu, J. Phys. Chem. C 123(26), 16388 (2019). https://doi.org/10.1021/acs.jpcc.9b04445 By modifying the surface termination, the spin-orbit interaction and bond directionality of M2NTx nitride can be also manipulated.238238. N. C. Frey, H. Kumar, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 12(6), 6319 (2018). https://doi.org/10.1021/acsnano.8b03472 These two important factors give rise to a rich diversity of noncollinear spin structures and finely tunable magnetocrystalline anisotropy [Fig. 10(c)]. Specifically, Ti2NO2 and Mn2NF2 have continuous O(3) and O(2) spin symmetries, respectively, while Cr2NO2 and Mn2NO2 are intrinsic Ising ferromagnets with out-of-plane easy axes and magnetic anisotropy energies up to 63 μeV/atom. The magnetic properties of Mn2CT2 (T = F, Cl, OH, O, H) have been computationally investigated.1313. J. He, P. Lyu, and P. Nachtigall, J. Mater. Chem. C 4(47), 11143 (2016). https://doi.org/10.1039/C6TC03917K Depending on the electronegativity of functional groups, the AFM Mn2C change to FM ground state upon functionalization of F, Cl, or OH groups. They are intrinsic half metals with high Curie temperature (280∼520 K) and sizable magnetic anisotropy (MAE = 24∼38 μeV). Theoretical studies of the asymmetrically functionalized MXenes have predicted that Janus Cr2C behaves as a bipolar antiferromagnetic semiconductor with zero magnetization and high Néel temperatures (270∼430 K).239239. J. He, P. Lyu, L. Z. Sun, Á. Morales García, and P. Nachtigall, J. Mater. Chem. C 4(27), 6500 (2016). https://doi.org/10.1039/C6TC01287F With appropriate choice of surface functional group pairs (H, F, Cl, Br, and OH), one can tailor the bandgap of Cr2C from 0.15 to 1.51 eV. The itinerant d electrons in Cr2C are favorable to Cr1↑-C↓-Cr2↑ superexchange mechanism, while the localized CrT′↑ d orbitals can directly interact with the CrT″↓ one in Cr2CT′T″. In other words, the distinct characteristics of d electrons in Cr2C and Cr2CT′T″ induce FM and AFM ordering, respectively.239239. J. He, P. Lyu, L. Z. Sun, Á. Morales García, and P. Nachtigall, J. Mater. Chem. C 4(27), 6500 (2016). https://doi.org/10.1039/C6TC01287F

In addition, magnetism can be retained by precisely controlling the surface functional groups on MXenes. For example, the fully covered functional groups of O2– and H+ keep the magnetic properties of bare Mn2C, showing AFM semiconductor and AFM metal, respectively.1313. J. He, P. Lyu, and P. Nachtigall, J. Mater. Chem. C 4(47), 11143 (2016). https://doi.org/10.1039/C6TC03917K The stable magnetic configurations of both V2C and V2C derivatives, i.e., V2CF2 and V2C(OH)2, are antiferromagnetic coupling.240240. J. Hu, B. Xu, C. Ouyang, S. A. Yang, and Y. Yao, J. Phys. Chem. C 118(42), 24274 (2014). https://doi.org/10.1021/jp507336x Moreover, metal-semiconductor transition behavior upon functionalization was also observed. Two-dimensional Fe2N, Co2N, and Ni2N as well as their surface passivated structures were investigated using DFT calculations. All the bare MXenes and functionalized systems, including Fe2NF2, Co2NF2, and Co2NF2, prefer AFM state. For Cr2N, the bare system is an antiferromagnetic metal, and passivation of F atoms or OH groups would not change the antiferromagnetic characteristics.226226. G. Wang, J. Phys. Chem. C 120(33), 18850 (2016). https://doi.org/10.1021/acs.jpcc.6b05224 If only one side is saturated, long-range FM ordering can be retained in F and H modified Ti3C2 monolayers. However, the strength of spin-spin coupling is weakened after chemical modification, in comparison with that of pristine Ti3C2 monolayer. The simulated Curie temperatures of Ti3C2, Ti3CN, and HTi3C2 were about 300, 350, and 1000 K, respectively.228228. F. Wu, K. Luo, C. Huang, W. Wu, P. Meng, Y. Liu, and E. Kan, Solid State Commun. 222, 9 (2015). https://doi.org/10.1016/j.ssc.2015.08.023 CrC2 with single-side and two-side functionalization (H, O, F) have also been investigated by first-principles calculations. The CrC2 monolayer functionalized with O atoms on both sides shows bipolar half-metallic characteristics, while it becomes a half-metal with O atoms terminated on one side only. CrC2 monolayer with H/F at one side and F at two sides are half semiconductors, while it is a bipolar magnetic semiconductor (BMS) after being functionalized with H atoms on both sides.241241. X. Ma and W. Mi, J. Phys. Chem. C 124(5), 3095 (2020). https://doi.org/10.1021/acs.jpcc.9b10598

3. Double transition metal MXenes [(MM′)n+1XnTx]

The MXenes of double transition metal carbides are also synthesized and predicted to be robust magnetic semiconductor or metal, making them desirable in spintronics.242242. B. Anasori, Y. Xie, M. Beidaghi, J. Lu, B. C. Hosler, L. Hultman, P. R. C. Kent, Y. Gogotsi, and M. W. Barsoum, ACS Nano 9(10), 9507 (2015). https://doi.org/10.1021/acsnano.5b03591 Hu et al.243243. Y. Hu, X. L. Fan, W. J. Guo, Y. R. An, Z. F. Luo, and J. Kong, J. Magn. Magn. Mater. 486, 165280 (2019). https://doi.org/10.1016/j.jmmm.2019.165280 investigated the magnetic properties of ordered double-metal MXenes MM'C for M being Ti and M' being the other transition metal elements. They found that TiZrC and TiHfC are FM metals with TC = 418 and 329 K, respectively, while TiCrC is an AFM metal. The magnetic moments of TiZrC and TiHfC mainly come from the Ti atoms, and the magnetic moments of Ti atoms in TiZrC (0.57 μB) and TiHrC (0.52 μB) are much less than the value of Ti atoms in Ti2C (0.97 μB).243243. Y. Hu, X. L. Fan, W. J. Guo, Y. R. An, Z. F. Luo, and J. Kong, J. Magn. Magn. Mater. 486, 165280 (2019). https://doi.org/10.1016/j.jmmm.2019.165280 The magnetic properties of Cr2M′C2T2 (M' = Ti, V; T = O, OH, F) systems have been investigated by first-principles calculations.244244. J. Yang, X. Zhou, X. Luo, S. Zhang, and L. Chen, Appl. Phys. Lett. 109(20), 203109 (2016). https://doi.org/10.1063/1.4967983 Cr2TiC2F2 and Cr2TiC2(OH)2 were predicted to be antiferromagnetic, while Cr2VC2(OH)2, Cr2VC2F2, and Cr2VC2O2 were ferromagnets with Curie temperatures of 618, 77, and 695 K, respectively. Among Hf2MnC2Tx and Hf2MnC2Tx systems,245245. L. Dong, H. Kumar, B. Anasori, Y. Gogotsi, and V. B. Shenoy, J. Phys. Chem. Lett. 8(2), 422 (2017). https://doi.org/10.1021/acs.jpclett.6b02751 only Hf2MnC2O2 and Hf2MnC2O2 are ferromagnetic semiconductors, while the ground states of the rest of OH and F terminated ones are antiferromagnetic. More interestingly, the Curie temperatures of four reported MXenes, i.e., Ti2MnC2O2, Ti2MnC2(OH)2, Hf2MnC2O2, and Hf2VC2O2, are in the range from 495 to 1133 K, which are much higher than room temperature. For the experimentally realized Mo2TiC2Tx, F and OH terminations are shown to lead to antiferromagnetic semiconductors.246246. B. Anasori, C. Shi, E. J. Moon, Y. Xie, C. A. Voigt, P. R. C. Kent, S. J. May, S. J. L. Billinge, M. W. Barsoum, and Y. Gogotsi, Nanoscale Horiz. 1(3), 227 (2016). https://doi.org/10.1039/C5NH00125K The magnetism of Mo2TiC2Tx originates from the unpaired Mo 3d orbitals that locate in the outer layer. The magnetic properties of Cr2M2C3T2 (M = Ti, V, Nb, Ta; T = OH, O, F) were investigated using DFT calculations.247247. J. Yang, X. Luo, X. Zhou, S. Zhang, J. Liu, Y. Xie, L. Lv, and L. Chen, Comput. Mater. Sci. 139, 313 (2017). https://doi.org/10.1016/j.commatsci.2017.08.016 It was shown that ferromagnetic ordering is energetically more favorable for Cr2Ti2C3O2 and Cr2V2C3O2, while the magnetic ground states of the rest of Cr2M2C3T2 systems prefer AFM ordering. The Curie temperatures of FM Cr2Ti2C3O2 and Cr2V2C3O2 are 720 and 246 K, respectively. For the asymmetrically functionalized double MXene Cr2TiC2FCl, theoretical study by Sun et al. found that it behaves as bipolar antiferromagnetic semiconductors (BAFS) with opposite spin character in the conduction band minimum and valence band maximum.248248. J. He, G. Ding, C. Zhong, S. Li, D. Li, and G. Zhang, Nanoscale 11(1), 356 (2019). https://doi.org/10.1039/C8NR07692H The different chemical environments induce a mismatch of d states for the Cr atoms in the upper and lower surfaces, thereby resulting in the BAFS feature. Moreover, the mixed functionalized double MXenes remain as a BAFS. Based on the experimental synthesis, Sun et al.249249. W. Sun, Y. Xie, and P. R. C. Kent, Nanoscale 10(25), 11962 (2018). https://doi.org/10.1039/C8NR00513C focused on the group of Ti-centered double transition metal TiM2X2T (M = V, Cr, Mn; X = C, N; T = H, F, O, OH). After screening various combinations of metal elements and terminating groups, only TiMn2C2F showed FM ordering, whereas AFM state is energetically more favorable in all other systems.

Motivated by the synthesis of in-plane ordered MAXs, i.e., (M2/3M1/3)2AX,250250. Q. Tao, J. Lu, M. Dahlqvist, A. Mockute, S. Calder, A. Petruhins, R. Meshkian, O. Rivin, D. Potashnikov, E. a. N. Caspi, H. Shaked, A. Hoser, C. Opagiste, R.-M. Galera, R. Salikhov, U. Wiedwald, C. Ritter, A. R. Wildes, B. Johansson, L. Hultman, M. Farle, M. W. Barsoum, and J. Rosen, Chem. Mater. 31(7), 2476 (2019). https://doi.org/10.1021/acs.chemmater.8b05298 the magnetic properties of 319 kinds of (M2/3M′1/3)2X MXene were investigated by high-throughput DFT calculations [Fig. 10(d)], from which 40 FM compounds and 26 AFM compounds were found.251251. Q. Gao and H. Zhang, Nanoscale 12(10), 5995 (2020). https://doi.org/10.1039/C9NR10181K Among these magnetic systems, there are five MXenes with out-of-plane MAE larger than 0.5 meV per f.u. Furthermore, the predicted TC of (Zr2/3Fe1/3)2C and (Hf2/3Fe1/3)2C are higher than room temperature.

Although the method to precisely control the surface functional group species and/or double transition metal MXene is yet to be discovered, one can see that the magnetism in a few MXenes, such as Ti2MnC2T2245245. L. Dong, H. Kumar, B. Anasori, Y. Gogotsi, and V. B. Shenoy, J. Phys. Chem. Lett. 8(2), 422 (2017). https://doi.org/10.1021/acs.jpclett.6b02751 and Mn2NTx,252252. N. C. Frey, A. Bandyopadhyay, H. Kumar, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 13(3), 2831 (2019). https://doi.org/10.1021/acsnano.8b09201 is not sensitive to the nature of surface terminations. Using first-principles and Monte Carlo calculations, Frey et al.252252. N. C. Frey, A. Bandyopadhyay, H. Kumar, B. Anasori, Y. Gogotsi, and V. B. Shenoy, ACS Nano 13(3), 2831 (2019). https://doi.org/10.1021/acsnano.8b09201 have studied the effects of mixed termination and characterized a wide variety of magnetic and transport behavior in Janus M2X. Janus Mn2N systems were found to be robust ferromagnets regardless of surface termination structures and compositions. By analyzing the electron filling in transition metal cations and performing DFT calculations, Dong et al.245245. L. Dong, H. Kumar, B. Anasori, Y. Gogotsi, and V. B. Shenoy, J. Phys. Chem. Lett. 8(2), 422 (2017). https://doi.org/10.1021/acs.jpclett.6b02751 designed a series of 2D magnetic materials based on ordered double transition metal MXenes. They revealed that Ti2MnC2Tx are ferromagnetic metals or semimetals, regardless of their surface termination of O, OH, or F. In short, the high Curie temperature and robust magnetism make these MXenes very attractive for experimental realization of 2D magnets.

4. MBene

MAB phases, as boron analog of MAX phases, are formed by stacked M–B blocks and interleaved A atomic planes.253–256253. W. Jeitschko, Monatshefte für Chemie und verwandte Teile anderer Wissenschaften 97(5), 1472 (1966). https://doi.org/10.1007/BF00902599254. W. Jeitschko, Acta Crystallograph. Sec. B 25(1), 163 (1969). https://doi.org/10.1107/S0567740869001944255. M. Ade and H. Hillebrecht, Inorg. Chem. 54(13), 6122 (2015). https://doi.org/10.1021/acs.inorgchem.5b00049256. Y. Liu, Z. Jiang, X. Jiang, and J. Zhao, RSC Adv. 10(43), 25836 (2020). https://doi.org/10.1039/D0RA04385K Recently, boride analogues of MXene termed as MBene were predicted theoretically215,257215. Z. Jiang, P. Wang, X. Jiang, and J. Zhao, Nanoscale Horiz. 3(3), 335 (2018). https://doi.org/10.1039/C7NH00197E257. Z. Guo, J. Zhou, and Z. Sun, J. Mater. Chem. A 5(45), 23530 (2017). https://doi.org/10.1039/C7TA08665B and were soon confirmed in experiment by topochemical deintercalation of Al atoms from MAB structures (M2A2B2 and M2AB2),258–261258. L. T. Alameda, P. Moradifar, Z. P. Metzger, N. Alem, and R. E. Schaak, J. Am. Chem. Soc. 140(28), 8833 (2018). https://doi.org/10.1021/jacs.8b04705259. H. Zhang, F.-Z. Dai, H. Xiang, X. Wang, Z. Zhang, and Y. Zhou, J. Mater. Sci. Technol. 35(8), 1593 (2019). https://doi.org/10.1016/j.jmst.2019.03.031260. L. T. Alameda, R. W. Lord, J. A. Barr, P. Moradifar, Z. P. Metzger, B. C. Steimle, C. F. Holder, N. Alem, S. B. Sinnott, and R. E. Schaak, J. Am. Chem. Soc. 141(27), 10852 (2019). https://doi.org/10.1021/jacs.9b04726261. J. Wang, T.-N. Ye, Y. Gong, J. Wu, N. Miao, T. Tada, and H. Hosono, Nat. Commun. 10(1), 2284 (2019). https://doi.org/10.1038/s41467-019-10297-8 including 2D sheets of MoB, CrB, FeB, and TiB. Since the number of valence electrons of boron is one/two less than carbon/nitrogen, its electron deficiency and lower electronegativity would endow MBene with distinctly different magnetic performance from the conventional carbide or nitride based MXenes. For example, using DFT-based high-throughput search, Jiang et al.215215. Z. Jiang, P. Wang, X. Jiang, and J. Zhao, Nanoscale Horiz. 3(3), 335 (2018). https://doi.org/10.1039/C7NH00197E identified 12 stable MBene nanosheets that are feasible to synthesize. Among them, 2D MnB MBene exhibits robust metallic ferromagnetism with 3.2 μB per Mn atom and a high Curie temperature of 345 K. After functionalization with F and OH groups, the ferromagnetic ground state of 2D MnB is well preserved. More excitingly, the Curie temperatures are even elevated to 405 K (with F groups) and 600 K (with OH groups), respectively, suggesting that careful choice of functional groups might be beneficial to the increase of TC in MBene [Fig. 10(e)]. Similar to MnB MBene, the electronic and magnetic properties of Ti2B monolayer were also investigated by DFT calculations. Its FM spin configuration corresponds to the magnetic ground state, and the predicted Curie temperature of is TC = 39 K based on Heisenberg model.262262. I. Ozdemir, Y. Kadioglu, O. Ü. Aktürk, Y. Yuksel, Ü. Akıncı, and E. Aktürk, J. Phys.: Condens. Matter 31(50), 505401 (2019). https://doi.org/10.1088/1361-648X/ab3d1d

D. Other binary transition metal compounds

The itinerant and localized behavior of the d electrons in transition metals and the coupling between them are still the starting point of designing the 2D magnetic materials for spintronics using other binary transition metal compounds, such as carbides, nitrides, oxides, borides, phosphides, silicides, arsenides, and hydrides. The local environments of the transition metal ions, including symmetry, bonding types, and orbital hybridizations, are identified as the key factors to understand the details of crystal field splitting. Therefore, it is essential to establish a relationship between the local environment and the spin-polarized orbital filling of the central transition metal ion. Most reported binary transition metal compounds are listed in Table IV and categorized by their compositions as well as magnetic properties for discussions.

TABLE IV. A list of 2D magnets in binary transition metal compounds with their compositions and key electronic and magnetic properties, including the magnetic ground state (GS), the values of Hubbard U, energy gap (Eg), magnetic moment on per transition metal (Ms), Curie temperature (TC), and magnetic anisotropy energy per unit cell (MAE).

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Lv, X. Qu, M. Zhang, J. Wang, S. Wen, Q. Li, Y. Geng, Z. Su, X. Wu, Y. Li, and Y. Ma, J. Mater. Chem. C 7(21), 6406 (2019). https://doi.org/10.1039/C9TC00635Dβ-CoCAFM–M1.61––0.216267267. C. Zhu, H. Lv, X. Qu, M. Zhang, J. Wang, S. Wen, Q. Li, Y. Geng, Z. Su, X. Wu, Y. Li, and Y. Ma, J. Mater. Chem. C 7(21), 6406 (2019). https://doi.org/10.1039/C9TC00635Dα-NiCFM–M0.43––0.166267267. C. Zhu, H. Lv, X. Qu, M. Zhang, J. Wang, S. Wen, Q. Li, Y. Geng, Z. Su, X. Wu, Y. Li, and Y. Ma, J. Mater. Chem. C 7(21), 6406 (2019). https://doi.org/10.1039/C9TC00635Dβ-NiCFM–M0.27––0.107267267. C. Zhu, H. Lv, X. Qu, M. Zhang, J. Wang, S. Wen, Q. Li, Y. Geng, Z. Su, X. Wu, Y. Li, and Y. Ma, J. Mater. Chem. C 7(21), 6406 (2019). https://doi.org/10.1039/C9TC00635DFeC2FM5HM4245–0.98268268. T. Zhao, J. Zhou, Q. Wang, Y. Kawazoe, and P. Jena, ACS Appl. Mater. Inter. 8(39), 26207 (2016). https://doi.org/10.1021/acsami.6b07482CrC2FM4HM8.0––269269. B. Zhou, X. Wang, and W. Mi, J. Mater. Chem. C 6(15), 4290 (2018). https://doi.org/10.1039/C7TC05383EVC2FM4M2.21––269269. B. Zhou, X. Wang, and W. Mi, J. Mater. Chem. C 6(15), 4290 (2018). https://doi.org/10.1039/C7TC05383EMnC2FM4M6.81––269269. B. Zhou, X. Wang, and W. Mi, J. Mater. Chem. C 6(15), 4290 (2018). https://doi.org/10.1039/C7TC05383EFeC2FM41.628––269269. B. Zhou, X. Wang, and W. Mi, J. Mater. Chem. C 6(15), 4290 (2018). https://doi.org/10.1039/C7TC05383ECoC2FM4SC6.03––269269. B. Zhou, X. Wang, and W. Mi, J. Mater. Chem. C 6(15), 4290 (2018). https://doi.org/10.1039/C7TC05383ENiC2FM4M2.85––269269. B. Zhou, X. Wang, and W. Mi, J. Mater. Chem. C 6(15), 4290 (2018). https://doi.org/10.1039/C7TC05383EBoridest-MnBFM3.32M2.654060.218271271. Y. Z. Abdullahi, Z. D. Vatansever, E. Aktürk, Ü. Akıncı, and O. Ü. Aktürk, Phys. Chem. Chem. Phys. 22, 10893 (2020). https://doi.org/10.1039/D0CP00503GCoB6FM3.5/6.0D1.377/1.382––7878. X. Tang, W. Sun, Y. Gu, C. Lu, L. Kou, and C. Chen, Phys. Rev. B 99(4), 045445 (2019). https://doi.org/10.1103/PhysRevB.99.045445Oxidest-VOAFM–SC2.27––277277. H. van Gog, W.-F. Li, C. Fang, R. S. Koster, M. Dijkstra, and M. van Huis, npj 2D Mater. Appl. 3(1), 18 (2019). https://doi.org/10.1038/s41699-019-0100-zt-CrOAFM–SC3.36––277277. H. van Gog, W.-F. Li, C. Fang, R. S. Koster, M. Dijkstra, and M. van Huis, npj 2D Mater. Appl. 3(1), 18 (2019). https://doi.org/10.1038/s41699-019-0100-zt-MnOAFM–SC4.42––277277. H. van Gog, W.-F. Li, C. Fang, R. S. Koster, M. Dijkstra, and M. van Huis, npj 2D Mater. Appl. 3(1), 18 (2019). https://doi.org/10.1038/s41699-019-0100-zSq-TiOAFM–M1.22––277277. H. van Gog, W.-F. Li, C. Fang, R. S. Koster, M. Dijkstra, and M. van Huis, npj 2D Mater. Appl. 3(1), 18 (2019). https://doi.org/10.1038/s41699-019-0100-zSq-VOAFM–SC3.66––277277. H. van Gog, W.-F. Li, C. Fang, R. S. Koster, M. Dijkstra, and M. van Huis, npj 2D Mater. Appl. 3(1), 18 (2019). https://doi.org/10.1038/s41699-019-0100-zSq-MnOAFM–SM4.64––277277. 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Wang, and X. C. Zeng, J. Phys. Chem. Lett. 9(15), 4260 (2018). https://doi.org/10.1021/acs.jpclett.8b01976NiH2AFM41.901.17––283283. Q. Wu, Y. Zhang, Q. Zhou, J. Wang, and X. C. Zeng, J. Phys. Chem. Lett. 9(15), 4260 (2018). https://doi.org/10.1021/acs.jpclett.8b01976SilicideFe2SiFM3.5HM3.0377800.325280280. Y. Sun, Z. Zhuo, X. Wu, and J. Yang, Nano Lett. 17(5), 2771 (2017). https://doi.org/10.1021/acs.nanolett.6b04884TiSi2FM–M0.563––281281. N. Han, H. Liu, and J. Zhao, J. Supercond. Nov. Magn. 28(6), 1755 (2015). https://doi.org/10.1007/s10948-014-2940-2VSi2FM–M2.148––281281. N. Han, H. Liu, and J. Zhao, J. Supercond. Nov. Magn. 28(6), 1755 (2015). https://doi.org/10.1007/s10948-014-2940-2CrSi2FM–M3.008––281281. N. Han, H. Liu, and J. Zhao, J. Supercond. Nov. Magn. 28(6), 1755 (2015). https://doi.org/10.1007/s10948-014-2940-2MnSi2AFM–M2.512––281281. N. Han, H. Liu, and J. Zhao, J. Supercond. Nov. Magn. 28(6), 1755 (2015). https://doi.org/10.1007/s10948-014-2940-2FeSi2AFM–M1.508––281281. N. Han, H. Liu, and J. Zhao, J. Supercond. Nov. Magn. 28(6), 1755 (2015). https://doi.org/10.1007/s10948-014-2940-2NbSi2FM–M0.618––281281. N. Han, H. Liu, and J. Zhao, J. Supercond. Nov. Magn. 28(6), 1755 (2015). https://doi.org/10.1007/s10948-014-2940-2MoSi2FM–M0.207––281281. N. Han, H. Liu, and J. Zhao, J. Supercond. Nov. Magn. 28(6), 1755 (2015). https://doi.org/10.1007/s10948-014-2940-2Ti2SiFM1,2M0.685––282282. Q. Wu, J.-J. Zhang, P. Hao, Z. Ji, S. Dong, C. Ling, Q. Chen, and J. Wang, J. Phys. Chem. Lett. 7(19), 3723 (2016). https://doi.org/10.1021/acs.jpclett.6b01731PhosphideMnPFM4HM44950.1667575. B. Wang, Y. Zhang, L. Ma, Q. Wu, Y. Guo, X. Zhang, and J. Wang, Nanoscale 11(10), 4204 (2019). https://doi.org/10.1039/C8NR09734HFe2PAFM–M1.623–0.05555. Q. Liu, J. Xing, Z. Jiang, X. Jiang, Y. Wang, and J. Zhao, Nanoscale 12(12), 6776 (2020). https://doi.org/10.1039/D0NR00092BCo2PFM–M0.685800.0455. Q. Liu, J. Xing, Z. Jiang, X. Jiang, Y. Wang, and J. Zhao, Nanoscale 12(12), 6776 (2020). https://doi.org/10.1039/D0NR00092BFe3PFM2M2.554200.3567676. S. Zheng, C. Huang, T. Yu, M. Xu, S. Zhang, H. Xu, Y. Liu, E. Kan, Y. Wang, and G. Yang, J. Phys. Chem. Lett. 10(11), 2733 (2019). https://doi.org/10.1021/acs.jpclett.9b00970ArsenidesMnAsFM4HM47110.2817575. B. Wang, Y. Zhang, L. Ma, Q. Wu, Y. Guo, X. Zhang, and J. Wang, Nanoscale 11(10), 4204 (2019). https://doi.org/10.1039/C8NR09734HFeAs-IFM4M3.076450.6457373. Y. Jiao, W. Wu, F. Ma, Z.-M. Yu, Y. Lu, X.-L. Sheng, Y. Zhang, and S. A. Yang, Nanoscale 11(35), 16508 (2019). https://doi.org/10.1039/C9NR04338AFeAs-IIFM4M3.02170–7373. Y. Jiao, W. Wu, F. Ma, Z.-M. Yu, Y. Lu, X.-L. Sheng, Y. Zhang, and S. A. Yang, Nanoscale 11(35), 16508 (2019). https://doi.org/10.1039/C9NR04338AFeAs-IIIAFM40.273.473500.8207373. Y. Jiao, W. Wu, F. Ma, Z.-M. Yu, Y. Lu, X.-L. Sheng, Y. Zhang, and S. A. Yang, Nanoscale 11(35), 16508 (2019). https://doi.org/10.1039/C9NR04338A

1. Transition metal carbides/nitrides

The magnetic properties of many transition metal carbides/nitrides have already been described as the 2D MXene family in Sec. III C. However, they are not limited to MXenes, which can be regarded as the transition metal rich compounds. In contrast, the 2D transition metal carbides/nitrides with fewer metal atoms, such as MN2, MN, MC2, and MC monolayers, show higher chemical stability. Compared to MXenes, these monolayers of transition metal carbides/nitrides have fewer exposed metal sites. As a result, the effect of surface modification might be avoided in them, which is in principle more favorable than MXenes for practical spintronic applications.

For the transition metal nitrides with stoichiometric ratio of 1:1, a monolayer structure obtained from (100) surface of rocksalt-structured CrN crystal was predicted to be a ferromagnet using PSO technique.263263. S. Zhang, Y. Li, T. Zhao, and Q. Wang, Sci. Rep. 4(1), 5241 (2014). https://doi.org/10.1038/srep05241 Analyses of its band structure and DOS revealed that this material is a half-metal, and the origin of ferromagnetism was ascribed to the p-d exchange interaction between Cr and N atoms. The corresponding Curie temperature was about 675 K. Hexagonal CrN,264264. A. V. Kuklin, A. A. Kuzubov, E. A. Kovaleva, N. S. Mikhaleva, F. N. Tomilin, H. Lee, and P. V. Avramov, Nanoscale 9(2), 621 (2017). https://doi.org/10.1039/C6NR07790K VN,265265. A. V. Kuklin, S. A. Shostak, and A. A. Kuzubov, J. Phys. Chem. Lett. 9(6), 1422 (2018). https://doi.org/10.1021/acs.jpclett.7b03276 and MnN266266. Z. Xu and H. Zhu, J. Phys. Chem. C 122(26), 14918 (2018). https://doi.org/10.1021/acs.jpcc.8b02323 monolayers were also identified as intrinsic half-metallic ferromagnets. In their flat atomically thin hexagonal lattices, the coordinate number of the transition metal ions is three. Hence, the d orbital diagram is a typical example of crystalline orbitals of trigonal-type complexes in terms of crystal field theory, which is quite different from those of the octahedral Oh and C3v crystal fields. In these transition metal mononitrides, the non-degenerate non-bonding dz2 orbital has highest energy and is localized on the top of the valence band. The next ones in energy are the doubly degenerate dxz and dyz orbitals, which overlap with N pz states and form bonding π-dative orbitals localized above and below the sheet. The lowest-lying orbitals in energy are doubly degenerate dxy and dx2-y2 states, which hybridize with s orbitals of transition metals to form sd22. X. Li and J. Yang, Natl. Sci. Rev. 3(3), 365 (2016). https://doi.org/10.1093/nsr/nww026 hybridization. Bader population and orbital analyses revealed that the local magnetic moments on Cr, Mn, and V atom are 3, 4, and 2.1 μB, respectively. The Curie temperatures of 368 K for h-MnN monolayer and 768 K for h-VN monolayer were estimated from MC simulations.265,266265. A. V. Kuklin, S. A. Shostak, and A. A. Kuzubov, J. Phys. Chem. Lett. 9(6), 1422 (2018). https://doi.org/10.1021/acs.jpclett.7b03276266. Z. Xu and H. Zhu, J. Phys. Chem. C 122(26), 14918 (2018). https://doi.org/10.1021/acs.jpcc.8b02323 Their results indicated that the easy axis for both 2D materials is in the in-plane direction, and the corresponding MAE values are 134 and 100 μeV per transition metal atom for h-MnN and h-VN, respectively. More interestingly, MnN monolayer can maintain FM half-metallicity and constant magnetic moment even under ±10% strain, because 100% spin polarization of the electronic states near the Fermi level is fully preserved by the robust bandgap of the spin-down states.266266. Z. Xu and H. Zhu, J. Phys. Chem. C 122(26), 14918 (2018). https://doi.org/10.1021/acs.jpcc.8b02323 The half metallic nature of h-VN and h-CrN will be retained even after contact with semiconducting 2D sheets of MoS2 or MoSe2, which can be used as the substrates for h-VN and h-CrN devices.264,265264. A. V. Kuklin, A. A. Kuzubov, E. A. Kovaleva, N. S. Mikhaleva, F. N. Tomilin, H. Lee, and P. V. Avramov, Nanoscale 9(2), 621 (2017). https://doi.org/10.1039/C6NR07790K265. A. V. Kuklin, S. A. Shostak, and A. A. Kuzubov, J. Phys. Chem. Lett. 9(6), 1422 (2018). https://doi.org/10.1021/acs.jpclett.7b03276 In addition, robust magnetic behavior was also observed in the buckled tetragonal t-VN monolayer, which has 99.9% spin polarization at the Fermi level and shows a rare p2d2 hybridization for V atoms.

Monolayer structures of transition metal carbides with 1:1 stoichiometry, including CoC, NiC, and CuC, were predicted by PSO structure search method and first-principles calculations. Among them, CoC monolayer is antiferromagnetic and NiC monolayer is ferromagnetic, while CuC monolayer is non-magnetic.267267. C. Zhu, H. Lv, X. Qu, M. Zhang, J. Wang, S. Wen, Q. Li, Y. Geng, Z. Su, X. Wu, Y. Li, and Y. Ma, J. Mater. Chem. C 7(21), 6406 (2019). https://doi.org/10.1039/C9TC00635D The local magnetic moments of α-CoC, β-CoC, α-NiC and β-NiC are 1.4, 1.61, 0.43, and 0.27 μB per metal atom, respectively. After considering magnetic anisotropy, the easy axis of α-CoC monolayer is [100] direction and the easy axis of β-CoC, α-NiC and β-NiC monolayers is [010] direction. Notably, the computed MAEs for antiferromagnetic CoC and ferromagnetic NiC are 107∼545 μeV per metal atom, which are at least one order of magnitude higher than those of Co (65 μeV per Co atom) and Ni (2.7 μeV per Ni atom) crystals.

Two-dimensional FeC2268268. T. Zhao, J. Zhou, Q. Wang, Y. Kawazoe, and P. Jena, ACS Appl. Mater. Inter. 8(39), 26207 (2016). https://doi.org/10.1021/acsami.6b07482 and CrC2269269. B. Zhou, X. Wang, and W. Mi, J. Mater. Chem. C 6(15), 4290 (2018). https://doi.org/10.1039/C7TC05383E sheets with 1:2 stoichiometry were predicted as half metals, and their spin polarization at the Fermi level is 100%. The C atoms in these 2D structures bind with each other to form C2 dimers, which possess high electron affinity and gain electrons from Fe/Cr atoms. The significant amount of charge accumulation adjacent to C2 dimers indicates strong interaction between the Fe/Cr atoms and the C2 units. Therefore, Fe and Cr atoms are in high-spin states in FeC2 and CrC2 sheets, with magnetic moments of 4 and 3.83 μB per Fe/Cr atom, respectively. Based on MC simulation and mean-field theory, their Curie temperatures were estimated to be 245 and 965 K, respectively. N2 dimers are also found in the penta-MnN2 monolayer. The ferromagnetic state of penta-MnN2 is energetically more favorable than the antiferromagnetic one, with predicted Curie temperature as high as 913 K.270270. K. Zhao and Q. Wang, Appl. Surf. Sci. 505, 144620 (2020). https://doi.org/10.1016/j.apsusc.2019.144620

2. Transition metal borides

Combining DFT calculations and MC simulations, Abdullahi et al.271271. Y. Z. Abdullahi, Z. D. Vatansever, E. Aktürk, Ü. Akıncı, and O. Ü. Aktürk, Phys. Chem. Chem. Phys. 22, 10893 (2020). https://doi.org/10.1039/D0CP00503G have presented a new phase of freestanding tetragonal Mn2B2 monolayer. The 2D tetra-Mn2B2 sheet showed metallic ferromagnetism with a magnetic moment of 2.65 μB per Mn atom and a Curie temperature of 406 K. Using an advanced crystal structure search method and extensive first-principles energetic and dynamic calculations, Tang et al.7878. X. Tang, W. Sun, Y. Gu, C. Lu, L. Kou, and C. Chen, Phys. Rev. B 99(4), 045445 (2019). https://doi.org/10.1103/PhysRevB.99.045445 have identified a planar CoB6 monolayer exhibiting robust ferromagnetic ground state, which remains stable upon the adsorption of common environmental gases like O2, CO2, and H2O. Electronic band structure calculations revealed remarkable features of Dirac cones with characteristic linear dispersions and high Fermi velocities. The atomically thin CoB6 monolayer could be fabricated by either depositing Co atoms on the δ4 boron sheet or direct chemical growth based on precursors of planar Co4B8+ cluster.

3. Transition metal oxides

In the on-going research of 2D materials, 2D metal oxides are tempting, owing to their natural abundance, suitable bandgap in a wide range, and high chemical inertness.272272. Y. Guo, L. Ma, K. Mao, M. Ju, Y. Bai, J. Zhao, and X. C. Zeng, Nanoscale Horiz. 4(3), 592 (2019). https://doi.org/10.1039/C8NH00273H Originated from the half-filled 3d shell of Mn atom, the magnetic properties of 2D manganese oxide monolayer have been systematically investigated by first-principles calculations as representatives of the transition metal oxides family.273,274273. M. Kan, J. Zhou, Q. Sun, Y. Kawazoe, and P. Jena, J. Phys. Chem. Lett. 4(20), 3382 (2013). https://doi.org/10.1021/jz4017848274. E. Kan, M. Li, S. Hu, C. Xiao, H. Xiang, and K. Deng, J. Phys. Chem. Lett. 4(7), 1120 (2013). https://doi.org/10.1021/jz4000559 In experiment, 2D MnO2 sheets were successfully synthesized by tetrabutylammonium intercalation and exfoliation.275275. Y. Omomo, T. Sasaki, Wang, and M. Watanabe, J. Am. Chem. Soc. 125(12), 3568 (2003). https://doi.org/10.1021/ja021364p It is an indirect semiconductor with a bandgap of 3.41 eV. Each unit cell of this 2D material possesses a magnetic moment of 3 μB, which is mainly contributed by the Mn atoms. In 2D MnO2, Mn atoms prefer ferromagnetic coupling [Fig. 11(a)]. Furthermore, the Curie temperature is about 140 K, which can be further increased by strain.273273. M. Kan, J. Zhou, Q. Sun, Y. Kawazoe, and P. Jena, J. Phys. Chem. Lett. 4(20), 3382 (2013). https://doi.org/10.1021/jz4017848 Using first-principles calculations, Kan et al.274274. E. Kan, M. Li, S. Hu, C. Xiao, H. Xiang, and K. Deng, J. Phys. Chem. Lett. 4(7), 1120 (2013). https://doi.org/10.1021/jz4000559 found that ultrathin films of the experimentally realized wurtzite MnO transform into a stable graphitic structure with ordered spin arrangement. Moreover, the AFM ordering of graphitic MnO monolayer can be switched into half-metallic ferromagnetism by moderate doping. They found that the Curie temperature is about 350 K when 0.25 hole/Mn is doped in single-layer MnO.

FIG. 11. (a) Total magnetic moment per unit cell as a function of temperature for 2D MnO2 monolayer. (b) Spin charge density, band structures, total DOS, partial DOS, and simulated magnetic moment and specific heat as a function of temperature for 2D Fe2Si monolayer. (c) Average magnetization per unit cell and specific heat (Cv) as a function of temperature for Fe3P monolayer from MC simulations. (d) Schematic diagram of electronic band structure, and the magnetic susceptibility and magnetic moment as a function of temperature for CoH2 monolayer from MC simulations. The atomic configurations of MnO2, Fe2Si, Fe3P, and CoH2 monolayers are also shown in insets. Panel (a) reproduced with permission from Kan et al., J. Phys. Chem. Lett. 4, 3382 (2013). Copyright 2013 American Chemical Society.273273. M. Kan, J. Zhou, Q. Sun, Y. Kawazoe, and P. Jena, J. Phys. Chem. Lett. 4(20), 3382 (2013). https://doi.org/10.1021/jz4017848 Panel (b) reproduced with permission from Sun et al., Nano Lett. 17, 2771 (2017). Copyright 2017 American Chemical Society.280280. Y. Sun, Z. Zhuo, X. Wu, and J. Yang, Nano Lett. 17(5), 2771 (2017). https://doi.org/10.1021/acs.nanolett.6b04884 Panel (c) reproduced with permission from Zheng et al., J. Phys. Chem. Lett. 10, 2733 (2019). Copyright 2019 American Chemical Society.7676. S. Zheng, C. Huang, T. Yu, M. Xu, S. Zhang, H. Xu, Y. Liu, E. Kan, Y. Wang, and G. Yang, J. Phys. Chem. Lett. 10(11), 2733 (2019). https://doi.org/10.1021/acs.jpclett.9b00970 Panel (d) reproduced with permission from Wu et al., J. Phys. Chem. Lett. 9, 4260 (2018). Copyright 2018 American Chemical Society.283283. Q. Wu, Y. Zhang, Q. Zhou, J. Wang, and X. C. Zeng, J. Phys. Chem. Lett. 9(15), 4260 (2018). https://doi.org/10.1021/acs.jpclett.8b01976

• PPT
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• High resolution

Aguilera-Granja and Ayuela276276. F. Aguilera-Granja and A. Ayuela, J. Phys. Chem. C 124(4), 2634 (2020). https://doi.org/10.1021/acs.jpcc.9b06496 investigated the magnetic properties of monolayer metal oxides under MO2 stoichiometry, including all 3d, 4d, and 5d transition metals. It is noteworthy that CrO2 and FeO2 layers are half-metals, while MnO2 and TcO2 layers with half-filled d orbitals in the transition metal elements behave as magnetic semiconductors. A simple model, depending on the hybridization between d orbitals of transition metals and 2p orbitals of oxygen, allows us to rationalize the magnetic behavior of the complete series of 2D metal oxides. In general, the Curie temperatures were estimated in the range of 170∼220 K for 3d oxides and below 100 K for 4d oxides, respectively.276276. F. Aguilera-Granja and A. Ayuela, J. Phys. Chem. C 124(4), 2634 (2020). https://doi.org/10.1021/acs.jpcc.9b06496 Recently, Gog et al.277277. H. van Gog, W.-F. Li, C. Fang, R. S. Koster, M. Dijkstra, and M. van Huis, npj 2D Mater. Appl. 3(1), 18 (2019). https://doi.org/10.1038/s41699-019-0100-z carried out a systematic DFT study (with HSE06 hybrid functional) on the atomically thin metal oxide films with compositions of MO, M2O3, and MO2 for typical 3d transition metal elements (M = Sc, Ti, V, Cr, Mn). Of 20 2D transition metal oxides studied, a rich variety of magnetic properties were discovered for the thermally stable TMOs. Among them, the square MnO (Sq-MnO) was predicted to be a semimetal with antiferromagnetic ordering; h-V2O3, sq-ScO2, and sq-CrO2 were found to be ferromagnetic half-metals; and sq-MnO2 was an antiferromagnetic half-metal. The magnetic moments are mainly originated from transition metal atoms, varying from 0.95 to 4.6 μB. 1T-RuO2 and 1T-OsO2 monolayers were also assigned as intrinsic 2D ferromagnets with large MAE. Their magnetic moments of 1.60 and 1.34 μB per transition metal atom and large MAE values come from Ru and Os atoms. In particular, the MAE of monolayer 1T-OsO2 is as high as 42.67 meV per unit cell along [100] direction due to the strong SOC of Os atom, which is two orders of magnitude higher than the MAE of ferromagnetic monolayer materials composed of 3d transition metals (Table IV). According to the mean field theory, the Curie temperatures were 38 K for 1T-RuO2 and 197 K for 1T-OsO2 monolayer, respectively. By analyzing the density of states and d orbital resolved MAE of Os atom based on second-order perturbation theory, it is revealed that the large MAE of monolayer 1T-OsO2 is mainly contributed by the matrix element differences between the opposite-spin dxy and dx2-y2 orbitals of Os atoms.278278. Y. Wang, F. Li, H. Zheng, X. Han, and Y. Yan, Phys. Chem. Chem. Phys. 20(44), 28162 (2018). https://doi.org/10.1039/C8CP05467C Olsson et al.279279. P. A. T. Olsson, L. R. Merte, and H. Grönbeck, Phys. Rev. B 101(15), 155426 (2020). https://doi.org/10.1103/PhysRevB.101.155426 studied the magnetic order of a novel three-layered Fe3O4 film by means of Hubbard-corrected DFT calculations. The Fe3O4 film comprises a center layer with octahedrally coordinated Fe2+ ions sandwiched between two layers with tetrahedrally coordinated Fe3+ ions. The film exhibits an antiferromagnetic type I spin order.

4. Transition metal silicides

Two-dimensional Fe2Si crystal has a slightly buckled triangular lattice composed of planar hexacoordinated Si and Fe atoms. DFT calculations with hybrid HSE06 functions indicated that 2D Fe2Si in its ground state is a ferromagnetic half-metal with 100% spin-polarization ratio at the Fermi level. Its 2D lattice can be retained at very high temperature up to 1200 K [Fig. 11(b)]. MC simulations based on Ising model also predicted TC as high as 780 K, which can be further modulated by biaxial strain. Moreover, the planar structure and strong in-plane Fe–Fe interaction endow Fe2Si nanosheet sizable MAE (325 μeV per Fe atom), which is at least one to two orders of magnitude larger than those of Fe, Co, and Ni solids.280280. Y. Sun, Z. Zhuo, X. Wu, and J. Yang, Nano Lett. 17(5), 2771 (2017). https://doi.org/10.1021/acs.nanolett.6b04884

Twenty 3d and 4d TM silicides with a fixed chemical formula of MSi2 (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd) have been investigated by first-principles calculations.281281. N. Han, H. Liu, and J. Zhao, J. Supercond. Nov. Magn. 28(6), 1755 (2015). https://doi.org/10.1007/s10948-014-2940-2 The transition metal silicides exhibit a variety of magnetic properties. Among them, TiSi2, VSi2, CrSi2, NbSi2, and MoSi2 are ferromagnetic; MnSi2 and FeSi2 are antiferromagnetic; and the rest systems are nonmagnetic. The on-site moments of transition metal atom in TiSi2, VSi2, CrSi2, NbSi2, and MoSi2 monolayers are 0.563, 2.148, 3.008, 0.618, and 0.207 μB, respectively, while the local spin moments of Mn and Fe atom in MnSi2 and FeSi2 are 2.512 and 1.508 μB, respectively.281281. N. Han, H. Liu, and J. Zhao, J. Supercond. Nov. Magn. 28(6), 1755 (2015). https://doi.org/10.1007/s10948-014-2940-2 Two-dimensional titanium silicide monolayers with different chemical compositions were globally searched by PSO simulations combined with DFT calculations. Among the explored 2D Ti-Si structures, Ti2Si is ferromagnetic with a magnetic moment of 1.37 μB per unit cell.282282. Q. Wu, J.-J. Zhang, P. Hao, Z. Ji, S. Dong, C. Ling, Q. Chen, and J. Wang, J. Phys. Chem. Lett. 7(19), 3723 (2016). https://doi.org/10.1021/acs.jpclett.6b01731

5. Transition metal phosphides/arsenides

Motivated by 2D FeSi2 and FeC2 as well as 3D Fe–P compounds, Zheng et al.7676. S. Zheng, C. Huang, T. Yu, M. Xu, S. Zhang, H. Xu, Y. Liu, E. Kan, Y. Wang, and G. Yang, J. Phys. Chem. Lett. 10(11), 2733 (2019). https://doi.org/10.1021/acs.jpclett.9b00970 focused on the 2D materials with Fe-rich compositions of FexP (x = 1∼3). With the aid of first-principles swarm structural search calculations, they have identified an unreported planar Fe3P monolayer in Kagome lattice, showing several desirable properties for its application in spintronic devices, e.g., robust ferromagnetism with large MAE, and high thermal stability. As shown in Fig. 11(c), MC simulation yielded a Curie temperature of 420 K. In addition, five stable M2P monolayers (M = Fe, Co, Ni, Ru, Pd) under P4/mmm symmetry group were predicted by high-throughput search and DFT calculations, which showed peculiar features of coexistence of in-plane M–P covalent bonds and M–M interlayer metallic bonds. Importantly, the distinct electronic configurations of transition metal atoms under a tetragonal crystal field lead to diverse magnetic properties in 2D M2Ps. Among them, Co2P is ferromagnetic with a Curie temperature of 580 K, while Fe2P is antiferromagnetic with a Néel temperature of 23 K. Their long-range magnetic orderings originate from the interplay of M–P–M superexchange interactions and M–M direct exchange interactions.55. Q. Liu, J. Xing, Z. Jiang, X. Jiang, Y. Wang, and J. Zhao, Nanoscale 12(12), 6776 (2020). https://doi.org/10.1039/D0NR00092B Two experimentally feasible 2D intrinsic ferromagnetic materials, MnP and MnAs monolayers, were predicted by first-principles calculations,7575. B. Wang, Y. Zhang, L. Ma, Q. Wu, Y. Guo, X. Zhang, and J. Wang, Nanoscale 11(10), 4204 (2019). https://doi.org/10.1039/C8NR09734H which posses appreciable out-of-plane anisotropies with MAE of 166 and 281 μeV, respectively. These two monolayer sheets exhibit remarkable half-metallicity with high Curie temperatures of 495 K for MnP and 711 K for MnAs, respectively. Moreover, the excellent ferromagnetism and half-metallicity can be well preserved in few-layer MnP and MnAs. Based on DFT calculations combined with PSO algorithm, Jiao et al.7373. Y. Jiao, W. Wu, F. Ma, Z.-M. Yu, Y. Lu, X.-L. Sheng, Y. Zhang, and S. A. Yang, Nanoscale 11(35), 16508 (2019). https://doi.org/10.1039/C9NR04338A identified three new monolayer phases of iron arsenide with high stability. Specifically, monolayer FeAs-I and FeAs-III sheets crystallize in a tetragonal lattice with space group of P4/nmm, while 2D FeAs-II has a trigonal P-3m1 lattice. Among them, FeAs-I and FeAs-II are ferromagnetic metals, while FeAs-III is an antiferromagnetic semiconductor. FeAs-I and FeAs-III have Curie temperatures of 645 and 350 K, respectively, both of which are above room temperature. Importantly, their magnetic anisotropy energies of 645 and 820 μeV are comparable to the magnetic recording materials such as FeCo alloy (700∼800 μeV per atom).

6. Transition metal hydrides

Wu et al.283283. Q. Wu, Y. Zhang, Q. Zhou, J. Wang, and X. C. Zeng, J. Phys. Chem. Lett. 9(15), 4260 (2018). https://doi.org/10.1021/acs.jpclett.8b01976 predicted a stable family of 2D transition metal dihydride MH2 (M = Sc, Ti, V, Cr, Fe, Co, Ni) monolayers featuring pyramidal symmetry (C3v). Among them, CoH2 and ScH2 monolayers are ferromagnetic metals, while the others are antiferromagnetic semiconductors. CoH2 monolayer is a perfect half-metal with a wide spin gap of 3.48 eV and an above-room-temperature TC of 339 K [Fig. 11(d)]. ScH2 monolayer also possesses half-metallicity through hole doping. Notably, their half-metallicity can be well retained on some substrates such as Cu (111) surface, BN, MoS2, and MoSe2.

E. Ternary transition metal compounds

Ternary transition metal compounds of type M-X′-X″, where M is transition metal element, usually magnetic elements like Fe, Co, Ni, and X′/X″ is a nonmagnetic main group element from main groups IV, V, VI, or VII of the Periodic Table. These compounds exhibit a rich variety of compositions and diverse magnetic properties. Only recently, ternary transition chalcogenides and halides with common transition metal centered octahedral units have attracted attentions. Compared with the above discussed binary magnetic materials, ternary ones are composed of one type of metal cations and two kinds of non-metal elements. The fascinating magnetism still mainly stems from the cations. The metal atoms occupy different crystallographic sites and form distinct magnetic sublattices, while the addition of two kinds of non-metal elements provides sufficient flexibility to tune the structure and magnetic properties. For example, 2D CrXTe3 systems (X = Si, Ge, Sn) have a layered structure with CrTe6 octahedra forming a honeycomb lattice and are typically FM semiconductor. However, 2D CrXTe3 for X = Sb and Ga as AFM semiconductors exhibit a pseudo-one-dimensional crystalline structure, in which CrTe6 octahedra form an infinite, edge-sharing, and double rutile chain.284284. T. Kong, K. Stolze, D. Ni, S. K. Kushwaha, and R. J. Cava, Phys. Rev. Mater. 2(1), 014410 (2018). https://doi.org/10.1103/PhysRevMaterials.2.014410 So far, the ongoing researches in identifying the 2D ternary vdW magnets include CrGe(Si, Sn)Te3, FeGe(Si)Te3, MnBi2Te4, MPS3, transition oxyhalides, transition nitrohalides, and CrSI. In Secs. III E 1 through III E 5, we will review their important experimental and theoretical progress.

1. CrXTe3 (X = Si, Ge, Sn)

The strong coupling between magnetic and lattice degrees of freedom was verified by Raman spectroscopy in ternary CrGeTe3 and infrared spectroscopy in CrSiTe3, respectively.49,28549. Y. Tian, M. J. Gray, H. Ji, R. J. Cava, and K. S. Burch, 2D Mater. 3(2), 025035 (2016). https://doi.org/10.1088/2053-1583/3/2/025035285. L. D. Casto, A. J. Clune, M. O. Yokosuk, J. L. Musfeldt, T. J. Williams, H. L. Zhuang, M. W. Lin, K. Xiao, R. G. Hennig, B. C. Sales, J. Q. Yan, and D. Mandrus, APL Mater. 3(4), 041515 (2015). https://doi.org/10.1063/1.4914134 Actually, CrGeTe3 is the first reported 2D ternary ferromagnetic material. As a representative of layered vdW materials, Cr2Ge2Te6 has been mechanically exfoliated and the intrinsic long-range ferromagnetic ordering has persevered in bilayer Cr2Ge2Te6, as revealed by scanning magneto-optic Kerr microscopy.3737. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature 546(7657), 265 (2017). https://doi.org/10.1038/nature22060 The optical image of the exfoliated Cr2Ge2Te6 atomic layer is shown in Fig. 12(a). From Fig. 12(b), one can see that the long bilayer strip becomes clearly distinguishable at liquid helium temperature from the bare surrounding substrate. Figure 12(c) shows a monotonic decrease in Curie point with reducing thickness. The Curie temperature of bulk Cr2Ge2Te6 is 68 K, and the bilayer value is about 30 K.3737. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature 546(7657), 265 (2017). https://doi.org/10.1038/nature22060 Subsequently, theoretical calculations have predicted that Cr2Ge2Te6 is a semiconductor with a bandgap of 0.13 eV,286286. Y. Fang, S. Wu, Z.-Z. Zhu, and G.-Y. Guo, Phys. Rev. B 98(12), 125416 (2018). https://doi.org/10.1103/PhysRevB.98.125416 and 2D Cr2Ge2Te6 possesses a magnetic moment of 2.4 μB per Cr atom with out-of-plane magnetic anisotropy.9999. W. Xing, Y. Chen, P. M. Odenthal, X. Zhang, W. Yuan, T. Su, Q. Song, T. Wang, J. Zhong, S. Jia, X. C. Xie, Y. Li, and W. Han, 2D Mater. 4(2), 024009 (2017). https://doi.org/10.1088/2053-1583/aa7034 Similar to its bulk counterpart, the magnetic behavior of Cr2Ge2Te6 is well described by Heisenberg model, where spins can freely rotate and adopt any direction.4444. N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17(22), 1133 (1966). https://doi.org/10.1103/PhysRevLett.17.1133 The mechanism of ferromagnetism in Cr2Ge2Te6 structure is dominated by the superexchange interaction between half-filled Cr t2g and empty eg states via Te p orbitals.286286. Y. Fang, S. Wu, Z.-Z. Zhu, and G.-Y. Guo, Phys. Rev. B 98(12), 125416 (2018). https://doi.org/10.1103/PhysRevB.98.125416 The lengths of Cr–Cr bonds are too long to support strong antiferromagnetic coupling between direct Cr t2g exchange interaction.1111. Y. Sun, R. C. Xiao, G. T. Lin, R. R. Zhang, L. S. Ling, Z. W. Ma, X. Luo, W. J. Lu, Y. P. Sun, and Z. G. Sheng, Appl. Phys. Lett. 112(7), 072409 (2018). https://doi.org/10.1063/1.5016568

FIG. 12. (a) Optical image of exfoliated Cr2Ge2Te6 atomic layer. (b) Kerr rotation signal under different temperatures. (c) Temperature-dependent Kerr rotation intensity of 2∼5 layer and bulk samples under a 0.075 T field. (d) The atomic models and schematic diagram of three magnetic structures of MPS3. Type I, type II, and type III are for NiPS3, MnPS3, and FePS3, respectively. (e) The schematic diagram of exchange coupling in Fe3GeTe2. (f) The measured TC in Fe3GeTe2 with different thickness. The left one uses three measures with Remanent anomalous Hall resistance Rxyr Arrott plots and RMCD, and the right one only chooses the RMCD measure. Panels (a)–(c) reproduced with permission from Gong et al., Nature 546, 265 (2017). Copyright 2017 Springer Nature.3737. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature 546(7657), 265 (2017). https://doi.org/10.1038/nature22060 Panel (d) reproduced with permission from Wang et al., Adv. Funct. Mater. 28, 1802151 (2018). Copyright 2018 John Wiley and Sons.297297. F. Wang, T. A. Shifa, P. Yu, P. He, Y. Liu, F. Wang, Z. Wang, X. Zhan, X. Lou, F. Xia, and J. He, Adv. Funct. Mater. 28(37), 1802151 (2018). https://doi.org/10.1002/adfm.201802151 Panel (f) left reproduced with permission from Deng et al., Nature 563, 94 (2018). Copyright 2018 Springer Nature.5050. Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen, and Y. Zhang, Nature 563(7729), 94 (2018). https://doi.org/10.1038/s41586-018-0626-9 Panel (f) right reproduced with permission from Fei et al., Nat. Mater. 17, 778 (2018). Copyright 2018 Springer Nature.4141. Z. Fei, B. Huang, P. Malinowski, W. Wang, T. Song, J. Sanchez, W. Yao, D. Xiao, X. Zhu, A. F. May, W. Wu, D. H. Cobden, J. H. Chu, and X. Xu, Nat. Mater. 17(9), 778 (2018). https://doi.org/10.1038/s41563-018-0149-7

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Similar magnetic behavior also exists in ferromagnetic semiconductor Cr2Si2Te6 due to the identical geometry, especially the same Te ligands. However, larger vdW interlayer gap and smaller in-plane Cr–Cr distance is presented in Cr2Si2Te6 with regard to Cr2Ge2Te6. In their bulk phase, the above two factors would weaken the TC from 63 K for Cr2Ge2Te6 to 32 K for Cr2Si2Te6287287. Y. Liu and C. Petrovic, Phys. Rev. Mater. 3(1), 014001 (2019). https://doi.org/10.1103/PhysRevMaterials.3.014001 and strength the magnetic anisotropy simultaneously. Neutron scattering measurements revealed that bulk Cr2Si2Te6 is a strongly anisotropic 2D Ising-like ferromagnet.109109. V. Carteaux, F. Moussa, and M. Spiesser, Europhys. Lett. 29(3), 251 (1995). https://doi.org/10.1209/0295-5075/29/3/011 The exfoliation of bulk Cr2Si2Te6 to monolayer or few-layer 2D crystals and transfer onto Si/SiO2 substrate have been achieved. Temperature-dependent resistivity measurements for the few-layer 2D Cr2Si2Te6 FET devices observed a clear change in resistivity at 80∼120 K, which corresponds to the theoretically predicted TC = 80 K.6262. M.-W. Lin, H. L. Zhuang, J. Yan, T. Z. Ward, A. A. Puretzky, C. M. Rouleau, Z. Gai, L. Liang, V. Meunier, B. G. Sumpter, P. Ganesh, P. R. C. Kent, D. B. Geohegan, D. G. Mandrus, and K. Xiao, J. Mater. Chem. C 4(2), 315 (2016). https://doi.org/10.1039/C5TC03463A The higher TC in monolayer Cr2Si2Te6 than Cr2Ge2Te6 can be ascribed to the fact that intralayer Cr–Te–Cr superexchange interaction becomes dominant at the monolayer limit. Moreover, the ferromagnetic mechanism could be maintained when monolayer Cr2Si2Te6 is described by the Heisenberg model.288288. M. S. Baranava, D. C. Hvazdouski, V. A. Skachkova, V. R. Stempitsky, and A. L. Danilyuk, Mater. Today: Proc. 20, 342 (2020). https://doi.org/10.1016/j.matpr.2019.10.072

Using first-principles calculations with HSE06 functional, Zhuang et al.289289. H. L. Zhuang, Y. Xie, P. R. C. Kent, and P. Ganesh, Phys. Rev. B 92(3), 035407 (2015). https://doi.org/10.1103/PhysRevB.92.035407 predicted that single-layer CrSnTe3 is also a ferromagnetic semiconductor. Moreover, the important magnetic parameters of CrXTe3 (X = Si, Ge, Sn) have been comparatively analyzed within a unified framework. The estimated Curie temperature of CrSnTe3 was 170 K, which is significantly higher than that of single-layer CrSiTe3 (90 K) and CrGeTe3 (130 K). Such enhancement is originated from the shorter Sn–Te bond length and stronger ionicity, which in turn increase the superexchange coupling between the magnetic Cr atoms. The corresponding exchange integral J parameters for CrSnTe3, CrSnTe3, and CrSnTe3 are 3.92, 3.07, and 2.10 meV, respectively. Considerable magnitude of MAE was also obtained in these three CrXTe3 systems. The calculated MAE values ranged from 69 to 419 μeV/f.u., whereas z axis is the easy direction for the magnetization in CrXTe3 family.289289. H. L. Zhuang, Y. Xie, P. R. C. Kent, and P. Ganesh, Phys. Rev. B 92(3), 035407 (2015). https://doi.org/10.1103/PhysRevB.92.035407

In 2017, an in-depth DFT survey with vdW-D2 correction on the magnetic phases of single-layer transition metal trichalcogenide ternary compounds (MAX3) with a total of 54 compositions was performed, covering 3d transition metals (M = V, Cr, Mn, Fe, Co, Ni), main group IV elements (A = Si, Ge, Sn), and chalcogen elements (X = S, Se, Te).290290. B. L. Chittari, D. Lee, N. Banerjee, A. H. MacDonald, E. Hwang, and J. Jung, Phys. Rev. B 101(8), 085415 (2020). https://doi.org/10.1103/PhysRevB.101.085415 Besides the reported FM CrXTe3, their results indicated that a variety of magnetic ground states, including AFM phases in Néel, stripy, and zigzag configurations, as well as FM configurations, may exist depending on material composition. Among them, 2D MnSiSe3 and MnGeSe3 are highly anticipated, since their Curie temperatures from DFT-D2+U calculations are 345.4 and 310.1 K, respectively. Recently, You et al.291291. J.-Y. You, Z. Zhang, X.-J. Dong, B. Gu, and G. Su, Phys. Rev. Res. 2(1), 013002 (2020). https://doi.org/10.1103/PhysRevResearch.2.013002 proposed three stable 2D ferromagnetic semiconductors TcSiTe3, TcGeSe3, and TcGeTe3, with TC of 538, 212, and 187 K, respectively, which were given by MC simulations. All of them have a spin moment of about 2 μB and an extraordinarily large orbital moment of about 0.5 μB per Tc atom. In addition, large MAE (26.5∼42.5 meV), high Kerr rotation angle (3.6°), and anomalous Hall conductivity have also been found. Replacing Si/Ge/Sn by Ga atom, CrGaTe3 monolayer is an intrinsic ferromagnetic semiconductor with an indirect bandgap of 0.3 eV. Its Curie temperature estimated by Monte Carlo simulations was 71 K.292292. M. Yu, X. Liu, and W. Guo, Phys. Chem. Chem. Phys. 20(9), 6374 (2018). https://doi.org/10.1039/C7CP07912E

2. MPX3 (X = S, Se, Te)

Next, we discuss another series of ternary single-layer compounds MPX3, which are structurally closely related to the above discussed transition metal trichalcogenide cousins MAX3. The top and side view of 2D MPX3 are shown in Fig. 12(d). In detail, each unit cell of MPS3 is composed of two cations and one [P2S6]4– cluster. The M atoms are coordinated with six S atoms, while the P atoms are coordinated with three S atoms and one P atom to form a [P2S6]4– skeleton, which is arranged in a 2D honeycomb structure.2828. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391 The main difference between MPX3 and MAX3 compounds is that the main group IV atom (A = Si, Ge, Sn) inside the (A2X6)6– bipyramids are replaced by the main group V element (P) inside the (P2X6)4– skeleton. The change from group IV element to group V element is responsible for the significant modifications in electronic structures and especially magnetic properties. Because of the surface S atoms, MPS3 layers exhibit strong van der Waals character and can be easily exfoliated from the bulk phase. In 2015, Xiong et al.293293. K.-z. Du, X.-z. Wang, Y. Liu, P. Hu, M. I. B. Utama, C. K. Gan, Q. Xiong, and C. Kloc, ACS Nano 10(2), 1738 (2015). https://doi.org/10.1021/acsnano.5b05927 first observed the mechanically fabricated 2D FePSe3 and MnPS3 sheets in the MPS3 family, and finally they successfully obtained monolayer FePS3. Soon after, bulk NiPS3 and MnPS3 materials were also mechanically exfoliated into 2D nanoflakes in the laboratory.294,295294. C. T. Kuo, M. Neumann, K. Balamurugan, H. J. Park, S. Kang, H. W. Shiu, J. H. Kang, B. H. Hong, M. Han, T. W. Noh, and J. G. Park, Sci. Rep. 6, 20904 (2016). https://doi.org/10.1038/srep20904295. Y.-J. Sun, Q.-H. Tan, X.-L. Liu, Y.-F. Gao, and J. Zhang, J. Phys. Chem. Lett. 10(11), 3087 (2019). https://doi.org/10.1021/acs.jpclett.9b00758 Therefore, it is natural to investigate their magnetic properties and those of the other stable MPS3 systems at the monolayer limit. As a new catalogue of 2D vdW magnets, in the following we will discuss the details of magnetic properties of experimentally exfoliable FePS3, NiPS3, and MnPS3, and recently predicted CoPS3, CrPS3, and V0.9PS3, and correlated the critical magnetic parameters with the number of layers.

Considering their (P2X6)4– skeleton, the metal cations in 2D MPS3 have M2+ ionization states and are in their high-spin configurations. The Néel temperatures of 2D FePS3, NiPS3, and MnPS3 were extracted from Raman spectroscopy, which is a common means to probe the spin properties. In principle, the appearance of two-magnon scattering and the change in Raman peak positions or intensities suggest ordered spin states.4848. J.-U. Lee, S. Lee, J. H. Ryoo, S. Kang, T. Y. Kim, P. Kim, C.-H. Park, J.-G. Park, and H. Cheong, Nano Lett. 16(12), 7433 (2016). https://doi.org/10.1021/acs.nanolett.6b03052 All the three MPS3 monolayers were predicted to be semiconductors with localized magnetic moments of 1∼4 μB and long-range antiferromagnetic ordering.296296. B. L. Chittari, Y. Park, D. Lee, M. Han, A. H. MacDonald, E. Hwang, and J. Jung, Phys. Rev. B 94(18), 184428 (2016). https://doi.org/10.1103/PhysRevB.94.184428 The electronic structures are greatly affected by metal and chalcogenide atoms, with bandgaps in range of 0.12 to 1.33 eV from PBE calculations.107107. A. Hashemi, H.-P. Komsa, M. Puska, and A. V. Krasheninnikov, J. Phys. Chem. C 121(48), 27207 (2017). https://doi.org/10.1021/acs.jpcc.7b09634 The AFM ground state is governed by the competition between direct M–M exchange and indirect M–S–M superexchange interactions within atomic layers, as well as interlayer exchange interactions.112112. D. Lançon, R. A. Ewings, T. Guidi, F. Formisano, and A. R. Wildes, Phys. Rev. B 98(13), 134414 (2018). https://doi.org/10.1103/PhysRevB.98.134414 Meanwhile, different metal atoms induce different distributions of magnetic moments and magnetic coupling—FePS3 of Ising-type, NiPS3 of XXZ type, and MnPS3 of Heisenberg-type297297. F. Wang, T. A. Shifa, P. Yu, P. He, Y. Liu, F. Wang, Z. Wang, X. Zhan, X. Lou, F. Xia, and J. He, Adv. Funct. Mater. 28(37), 1802151 (2018). https://doi.org/10.1002/adfm.201802151 [Fig. 12(d)].

Two-dimensional FePS3 with a honeycomb lattice and that behaves as a large spin Mott insulator is an Ising-type antiferromagnetic material with Néel temperature of about 120 K.298298. P. A. Joy and S. Vasudevan, Phys. Rev. B 46(9), 5425 (1992). https://doi.org/10.1103/PhysRevB.46.5425 Owing to the absence of long-range superexchange interaction between the Fe atoms from adjacent layers, multilayer FePS3 systems do not show stronger magnetic exchange interaction. As a consequence, TN decreases from 117 K in bulk to 104 K in monolayer FePS3. Fortunately, the Ising-type magnetic ordering of FePS3 is preserved down to the monolayer limit, which is demonstrated by the emergence of a series of new Raman modes pointing to antiferromagnetic ordering.3838. X. Wang, K. Du, Y. Y. F. Liu, P. Hu, J. Zhang, Q. Zhang, M. H. S. Owen, X. Lu, C. K. Gan, P. Sengupta, C. Kloc, and Q. Xiong, 2D Mater. 3(3), 031009 (2016). https://doi.org/10.1088/2053-1583/3/3/031009 As 2D Ising magnets, the magnetic ordering is mainly dominated by the in-plane third nearest-neighboring Fe–Fe exchange interaction in 2D FePS3, and the spins are aligned along the out-of-plane direction with MAE of 3.7 meV.299299. A. R. Wildes, K. C. Rule, R. I. Bewley, M. Enderle, and T. J. Hicks, J. Phys.: Condens. Matter 24(41), 416004 (2012). https://doi.org/10.1088/0953-8984/24/41/416004 The intralayer spin moments are arranged ferromagnetically in each chain but coupled antiferromagnetically with their neighboring chains, and the neighboring planes are also coupled antiferromagnetically along the out-of-plane direction.4848. J.-U. Lee, S. Lee, J. H. Ryoo, S. Kang, T. Y. Kim, P. Kim, C.-H. Park, J.-G. Park, and H. Cheong, Nano Lett. 16(12), 7433 (2016). https://doi.org/10.1021/acs.nanolett.6b03052

The second member in the 2D MPS3 family is 2D MnPS3. Kim et al.3939. K. Kim, S. Y. Lim, J. Kim, J.-U. Lee, S. Lee, P. Kim, K. Park, S. Son, C.-H. Park, J.-G. Park, and H. Cheong, 2D Mater. 6(4), 041001 (2019). https://doi.org/10.1088/2053-1583/ab27d5 discovered a unique feature of Raman spectrum that correlates well with the stable antiferromagnetic ordering at the bilayer limit of MnPS3. Its TN could maintain at 78 K from bulk phase to five-layer system. The independence of number of layers stems from the weak interlayer coupling in MnPS3. In the antiferromagnetic state of MnPS3, each Mn atom is antiferromagnetically coupled with three nearest neighbors within the basal plane. The direction of spin moments is ∼8° along c axis, and there exists ferromagnetic coupling between the planes. By exploiting the spin-flop transition, Long et al. have shown that the magnetoresistance persists as thickness is reduced. The characteristic temperature and scale of magnetic field are nearly unchanged, albeit with a different dependence on magnetic field, indicating again the persistence of magnetism at the ultimate limit of individual monolayer.300300. G. Long, H. Henck, M. Gibertini, D. Dumcenco, Z. Wang, T. Taniguchi, K. Watanabe, E. Giannini, and A. F. Morpurgo, Nano Lett. 20(4), 2452 (2020). https://doi.org/10.1021/acs.nanolett.9b05165 Fascinatingly, MnPS3 exhibits three spin-related critical transitions, including 2D single-ion anisotropy antiferromagnetic phase transition at 120 K, paramagnetic-antiferromagnetic transition at 80 K, and XY-like behavior at 55 K.295295. Y.-J. Sun, Q.-H. Tan, X.-L. Liu, Y.-F. Gao, and J. Zhang, J. Phys. Chem. Lett. 10(11), 3087 (2019). https://doi.org/10.1021/acs.jpclett.9b00758 In addition, long-distance magnon transport was also detected in MnPS3 crystal as antiferromagnet.301301. W. Xing, L. Qiu, X. Wang, Y. Yao, Y. Ma, R. Cai, S. Jia, X. C. Xie, and W. Han, Phys. Rev. X 9(1), 011026 (2019). https://doi.org/10.1103/PhysRevX.9.011026 The antiferromagnetic transition at Néel temperature of around 78 K in few-layered MnPS3 is completely suppressed by Mn vacancy, which leads to a lower magnetic transition temperature of 38 K.302302. W. Bai, Z. Hu, C. Xiao, J. Guo, Z. Li, Y. Zou, X. Liu, J. Zhao, W. Tong, W. Yan, Z. Qu, B. Ye, and Y. Xie, J. Am. Chem. Soc. 142, 10849 (2020). https://doi.org/10.1021/jacs.0c04101 Moreover, long-range magnon transport over several micrometers in the 2D antiferromagnet MnPS3 has been observed experimentally.301301. W. Xing, L. Qiu, X. Wang, Y. Yao, Y. Ma, R. Cai, S. Jia, X. C. Xie, and W. Han, Phys. Rev. X 9(1), 011026 (2019). https://doi.org/10.1103/PhysRevX.9.011026

NiPS3 is the third member of 2D MPS3 family. In NiPS3, eight d electrons from Ni atom occupy the split 3d shell under octahedral crystal field. The t2g orbitals are fully occupied and two eg orbitals are half filled. Combined with its honeycomb lattice, Gu et al.303303. Y. Gu, Q. Zhang, C. Le, Y. Li, T. Xiang, and J. Hu, Phys. Rev. B 100(16), 165405 (2019). https://doi.org/10.1103/PhysRevB.100.165405 suggested that 2D NiPS3 is a Dirac material with strong electron-electron correlation. The unpaired electrons in the two eg orbitals would “long-range” hop between two third nearest-neighboring Ni sites in the Ni honeycomb lattice via superexchange interaction. Similar to 2D FePS3 and MnPS3, both DFT calculations296296. B. L. Chittari, Y. Park, D. Lee, M. Han, A. H. MacDonald, E. Hwang, and J. Jung, Phys. Rev. B 94(18), 184428 (2016). https://doi.org/10.1103/PhysRevB.94.184428 and experimental measurements4040. G. Le Flem, R. Brec, G. Ouvard, A. Louisy, and P. Segransan, J. Phys. Chem. Solids 43(5), 455 (1982). https://doi.org/10.1016/0022-3697(82)90156-1 suggested that the Ni honeycomb lattice forms zigzag antiferromagnetic insulating ground state, which is featured by AFM coupling between the double parallel ferromagnetic chains, while the planes are ferromagnetically coupled along the out-of-plane direction.112112. D. Lançon, R. A. Ewings, T. Guidi, F. Formisano, and A. R. Wildes, Phys. Rev. B 98(13), 134414 (2018). https://doi.org/10.1103/PhysRevB.98.134414 Unlike 2D FePS3 and MnPS3, on the one hand, the single-ion anisotropy of NiPS3 would change from XY type to XXZ type as the number of layers decreases.304304. K. Kim, S. Y. Lim, J.-U. Lee, S. Lee, T. Y. Kim, K. Park, G. S. Jeon, C.-H. Park, J.-G. Park, and H. Cheong, Nat. Commun. 10(1), 345 (2019). https://doi.org/10.1038/s41467-018-08284-6 On the other hand, the antiferromagnetic ordering persists down to biayer NiPS3, and its TN is about 130 K. However, the antiferromagnetic ordering is drastically suppressed in the monolayer, indicating that intralayer exchange interactions are much stronger than the interlayer ones. Such variation could be understood by the strong spin fluctuations, which drastically suppress the bulk antiferromagnetic ordering.304304. K. Kim, S. Y. Lim, J.-U. Lee, S. Lee, T. Y. Kim, K. Park, G. S. Jeon, C.-H. Park, J.-G. Park, and H. Cheong, Nat. Commun. 10(1), 345 (2019). https://doi.org/10.1038/s41467-018-08284-6

With the aid of DFT calculations, the metal element M in 2D MPX3 family has been further extended to 3d/4d/5d transition metals and the non-metal X element extended to S, Se, and Te. Hence, a series of stable trichalcogenides were predicted. Due to weak interlayer coupling, parts of them are exfoliable 2D magnetic materials. For example, Chittari et al.296296. B. L. Chittari, Y. Park, D. Lee, M. Han, A. H. MacDonald, E. Hwang, and J. Jung, Phys. Rev. B 94(18), 184428 (2016). https://doi.org/10.1103/PhysRevB.94.184428 have systemically investigated the magnetic properties of 2D MPX3 (M = V, Cr, Mn, Fe, Co, Ni, Cu, Zn; X = S, Se, Te). They concluded that the ground-state spin configuration depends on the combination of transition metal and chalcogen elements. Besides the reported Mn-, Fe-, and Ni-based 2D MPS3 antiferromagnetic semiconductors, V-based compounds also exhibit semiconducting Néel antiferromagnetic states. Interestingly, isostructural Mott transition was observed in VPS3.305305. M. J. Coak, S. Son, D. Daisenberger, H. Hamidov, C. R. S. Haines, P. L. Alireza, A. R. Wildes, C. Liu, S. S. Saxena, and J.-G. Park, npj Quantum Mater. 4(1), 38 (2019). https://doi.org/10.1038/s41535-019-0178-8 When M changes from the strongly correlated 3d transition metals to the weakly correlated 4d and 5d elements, the ground state would transform from FM to PM. In the case of 4d PdPS3, the lowest-energy state is still AFM,306306. Y. Sugita, T. Miyake, and Y. Motome, Phys. Rev. B 97(3), 035125 (2018). https://doi.org/10.1103/PhysRevB.97.035125 while 2D PtPS3 with 5d element is PM. Both Pt and Pd possess half-filled eg orbitals; thus, they may also exhibit multiple Dirac cones at the same time. Moreover, replacing a smaller chalcogen atom (S) with a larger chalcogen atom (Se or Te) reduces the energy bandgap as well as the energy difference between FM and AFM states.107,296,307107. A. Hashemi, H.-P. Komsa, M. Puska, and A. V. Krasheninnikov, J. Phys. Chem. C 121(48), 27207 (2017). https://doi.org/10.1021/acs.jpcc.7b09634296. B. L. Chittari, Y. Park, D. Lee, M. Han, A. H. MacDonald, E. Hwang, and J. Jung, Phys. Rev. B 94(18), 184428 (2016). https://doi.org/10.1103/PhysRevB.94.184428307. X. Li, X. Wu, and J. Yang, J. Am. Chem. Soc. 136(31), 11065 (2014). https://doi.org/10.1021/ja505097m

3. Fe-Ge-Te ternary compounds

Previously mentioned 2D ternary compounds are ferromagnetic/antiferromagnetic semiconductors, while the series of Fe-Ge-Te (FGT) ternary compounds are ferromagnetic metals with significant uniaxial magnetocrystaline anisotropy. As a unique kind of itinerant ferromagnetic metals, the exchange mechanism in FGT can be described by Stoner model, whose exchange splitting is induced by Coulomb repulsion among itinerant electrons.308308. E. C. Stoner, Proc. R. Soc. London, Ser. A 165, 372 (1938). https://doi.org/10.1098/rspa.1938.0066 In addition, the itinerant ferromagnetism could be understood by mapping a classical Heisenberg model with RKKY exchange interaction.309309. R. Prange and V. Korenman, Phys. Rev. B 19(9), 4691 (1979). https://doi.org/10.1103/PhysRevB.19.4691 Advantageously, the metallic nature enables the interplay of both spin and lattice degrees of freedom, which is the heart of various spintronic architectures.310310. S. Bhatti, R. Sbiaa, A. Hirohata, H. Ohno, S. Fukami, and S. N. Piramanayagam, Mater. Today 20(9), 530 (2017). https://doi.org/10.1016/j.mattod.2017.07.007

The most widely studied 2D FGT materials is Fe3GeTe2. Bulk Fe3GeTe2 crystal is a layered material with vdW gap of 2.95 Å. In a pioneer study in 2016, Zhuang et al. predicted that mechanical exfoliated single-layer Fe3GeTe2 exhibited strong out-plane magnetocrystalline anisotropy with MAE of 0.92 meV.1616. H. L. Zhuang, P. R. C. Kent, and R. G. Hennig, Phys. Rev. B 93(13), 134407 (2016). https://doi.org/10.1103/PhysRevB.93.134407 Very soon, this proposal was confirmed by Chu et al., who successfully fabricated few-layered flakes of Fe3GeTe2 by cleaving Fe3GeTe2 crystal onto a gold film. The RMCD measurement probed the TC values to be 180 and 130 K for bilayer and monolayer Fe3GeTe2, respectively. In addition, it was stated that monolayer Fe3GeTe2 with large out-of-plane anisotropy is a truly 2D itinerant ferromagnet.4141. Z. Fei, B. Huang, P. Malinowski, W. Wang, T. Song, J. Sanchez, W. Yao, D. Xiao, X. Zhu, A. F. May, W. Wu, D. H. Cobden, J. H. Chu, and X. Xu, Nat. Mater. 17(9), 778 (2018). https://doi.org/10.1038/s41563-018-0149-7 Subsequently, Zhang et al. used Al2O3-addisted exfoliation method instead of conventional mechanical exfoliation to protect the intralayer bonding. The Curie temperature of monolayer Fe3GeTe2 was determined to be 30 K by probing Remanent anomalous Hall resistance and 68 K by RMCD measurement, respectively. Moreover, a definite out-of-plane magnetocrystalline anisotropy energy of 2 meV was found, which is large enough to protect the magnetic ordering below a finite TC.5050. Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen, and Y. Zhang, Nature 563(7729), 94 (2018). https://doi.org/10.1038/s41586-018-0626-9 This series of works opens a new era in the development of high-temperature 2D magnets.

Different from many other 2D magnets, Fe3GeTe2 exhibits two values of on-site spin moment because the Fe atoms occupy two different lattice sites, labeled as Fe1 and Fe2. The magnetic moment of Fe13+ is about 1.7 μB and that of Fe22+ is about 1 μB. The Stoner criterion states that formation of ferromagnetic ordering is dictated by density of states at the Fermi level. In turn, the half-filled d orbitals of Fe mainly affect the ferromagnetism in Fe3GeTe2. As shown in Fig. 12(e), the magnetic coupling parameters for interlayer Fe1-Fe1 coupling and Fe1-Fe2 coupling are 23.48 meV and 20.41 meV, respectively, which collaborate to determine the ferromagnetism in Fe3GeTe2. That is to say, the ferromagnetism in Fe3GeTe2 is dominated by the coupling between perpendicular Fe atoms. As it is known, the distance between adjacent Fe3GeTe2 layers also plays a crucial role in modulating the magnetic interactions. Wang et al. substantiated that the effective coupling becomes negligible when interlayer distance is increased by 1 Å in bilayer Fe3GeTe2.311311. C. Hu, D. Zhang, F. Yan, Y. Li, Q. Lv, W. Zhu, Z. Wei, K. Chang, and K. Wang, Sci. Bull. 65(13), 1072 (2020). https://doi.org/10.1016/j.scib.2020.03.035 Furthermore, Hwang et al. found that formation of oxide at the interface of Fe3GeTe2 induces antiferromagnetic coupling between pristine Fe3GeTe2 layer and oxidized Fe3GeTe2 layer in a bilayer system. The interlayer distance is too large to generate direct Fe-Fe coupling. Therefore, magnetic information between adjacent layers can only be mediated by the indirect interaction between oxygen p orbitals.312312. D. Kim, S. Park, J. Lee, J. Yoon, S. Joo, T. Kim, K. J. Min, S. Y. Park, C. Kim, K. W. Moon, C. Lee, J. Hong, and C. Hwang, Nanotechnology 30(24), 245701 (2019). https://doi.org/10.1088/1361-6528/ab0a37

As a kind of vdW ferromagnets, the effect of number of layers is clearly manifested in Fe3GeTe2. As shown in Fig. 12(f), TC of Fe3GeTe2 closely depends on the thickness of flakes. As the number of layers decreases to 7, a dramatic drop of TC would occur.41,5041. Z. Fei, B. Huang, P. Malinowski, W. Wang, T. Song, J. Sanchez, W. Yao, D. Xiao, X. Zhu, A. F. May, W. Wu, D. H. Cobden, J. H. Chu, and X. Xu, Nat. Mater. 17(9), 778 (2018). https://doi.org/10.1038/s41563-018-0149-750. Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen, and Y. Zhang, Nature 563(7729), 94 (2018). https://doi.org/10.1038/s41586-018-0626-9 Experimental observation confirmed that TC decreases monotonically with decreasing number of layers, while the strong perpendicular magnetic anisotropy is retained. The difference of the probed TC might come from different environments of Fe3GeTe2 during experimental synthesis.313,314313. L. Zhang, L. Song, H. Dai, J.-H. Yuan, M. Wang, X. Huang, L. Qiao, H. Cheng, X. Wang, W. Ren, X. Miao, L. Ye, K.-H. Xue, and J.-B. Han, Appl. Phys. Lett. 116(4), 042402 (2020). https://doi.org/10.1063/1.5142077314. J. Seo, D. Y. Kim, E. S. An, K. Kim, G.-Y. Kim, S.-Y. Hwang, D. W. Kim, B. G. Jang, H. Kim, G. Eom, S. Y. Seo, R. Stania, M. Muntwiler, J. Lee, K. Watanabe, T. Taniguchi, Y. J. Jo, J. Lee, B. I. Min, M. H. Jo, H. W. Yeom, S.-Y. Choi, J. H. Shim, and J. S. Kim, Sci. Adv. 6(3), eaay8912 (2020). https://doi.org/10.1126/sciadv.aay8912 Han et al. deposited Fe3GeTe2 flakes onto three types of substrates—Al, Au, and SiO2. The change of substrate from Al to Au could elevate the value of TC significantly from 105 to 180 K for Fe3GeTe2 film of 10 nm thickness. Such big modulation of TC by substrates could be attributed to lattice distortion and charge redistribution between the Fe3GeTe2 sample and the substrate.313313. L. Zhang, L. Song, H. Dai, J.-H. Yuan, M. Wang, X. Huang, L. Qiao, H. Cheng, X. Wang, W. Ren, X. Miao, L. Ye, K.-H. Xue, and J.-B. Han, Appl. Phys. Lett. 116(4), 042402 (2020). https://doi.org/10.1063/1.5142077 Recently, Kim et al. successful synthesized and exfoliated Fe4GeTe2 flakes and obtained TC of about 270 K for 7-layer Fe4GeTe2.314314. J. Seo, D. Y. Kim, E. S. An, K. Kim, G.-Y. Kim, S.-Y. Hwang, D. W. Kim, B. G. Jang, H. Kim, G. Eom, S. Y. Seo, R. Stania, M. Muntwiler, J. Lee, K. Watanabe, T. Taniguchi, Y. J. Jo, J. Lee, B. I. Min, M. H. Jo, H. W. Yeom, S.-Y. Choi, J. H. Shim, and J. S. Kim, Sci. Adv. 6(3), eaay8912 (2020). https://doi.org/10.1126/sciadv.aay8912

Fe5GeTe2 has a similar structure with Fe3GeTe2, which is also made up of 2D slabs of Fe and Ge between layers of Te, but with two additional layers of Fe atoms. The magnetic state in Fe5GeTe2 is even more complicated than Fe3GeTe2 due to structural disorder and presence of short-range order associated with the occupation of split sites. May et al. exfoliated Fe5GeTe2 nanoflakes (12 nm/4 unit-cell layers) on SiO2 substrates and determined TC to be in range of 270 to 300 K. The magnetic moment of Fe5GeTe2 along the out-of-plane is 0.8∼2.6 μB per Fe atom on different Fe sites.4242. A. F. May, D. Ovchinnikov, Q. Zheng, R. Hermann, S. Calder, B. Huang, Z. Fei, Y. Liu, X. Xu, and M. A. McGuire, ACS Nano 13(4), 4436 (2019). https://doi.org/10.1021/acsnano.8b09660 In contrast to Fe3GeTe2, however, bulk Fe5GeTe2 crystal does not exhibit a perpendicular magnetic anisotropy. Recently, Joe et al. predicted that both monolayer and bilayer Fe5GeTe2 systems remain metallic and ferromagnetic. The ferromagnetism originates from Fe atoms and the splitting of d orbitals occurs for both spin-up and spin-down states, presenting exchange splitting to satisfy Stoner's theory of ferromagnetism.143143. M. Joe, U. Yang, and C. Lee, Nano Mater. Sci. 1(4), 299 (2019). https://doi.org/10.1016/j.nanoms.2019.09.009 In addition, Zhang et al. reported that Fe5-xGeTe2 shows glassy cluster behavior below 110 K and revealed a transition from ferromagnet to ferrimagnet at 275 K. Meanwhile, they observed that the Fe-Ge-Te crystal with more Fe contents favors an in-plane easy magnetization at all temperatures up to TC.315315. H. Zhang, R. Chen, K. Zhai, X. Chen, L. Caretta, X. Huang, R. V. Chopdekar, J. Cao, J. Sun, J. Yao, R. Birgeneau, and R. Ramesh, Phys. Rev. B 102(6), 064417 (2020). https://doi.org/10.1103/PhysRevB.102.064417

Compared to 2D MPX3 family, 2D MPX4 sheets show different electron configuration formally with M3+[PX4]3–. In the monolayer structure of MPS4, six S atoms form a slightly distorted octahedron encapsulated with a transition atom (M) in the center. Meanwhile, the P atoms are in the center of tetrahedron consisting of four S atoms, suggesting a distinct magnetic ordering. Experimentally, single- and few-layered CrPS4 sheets were mechanically isolated in 2016.316316. J. Lee, T. Y. Ko, J. H. Kim, H. Bark, B. Kang, S.-G. Jung, T. Park, Z. Lee, S. Ryu, and C. Lee, ACS Nano 11(11), 10935 (2017). https://doi.org/10.1021/acsnano.7b04679 Further DFT calculations revealed that monolayer CrPS4 is a ferromagnetic semiconductor, which is quite different from the antiferromagnetic ordering of its bulk form.317317. H. L. Zhuang and J. Zhou, Phys. Rev. B 94(19), 195307 (2016). https://doi.org/10.1103/PhysRevB.94.195307 Later, Chen et al.9595. Q. Chen, Q. Ding, Y. Wang, Y. Xu, and J. Wang, J. Phys. Chem. C 124(22), 12075 (2020). https://doi.org/10.1021/acs.jpcc.0c02432 systematically discussed the magnetic ordering in monolayer MPS4 and proposed that VPS4, MnPS4, and NiPS4 prefer antiferromagnetic states while CrPS4 and FePS4 are ferromagnetic. The calculated TC was 50 K for CrPS4.9595. Q. Chen, Q. Ding, Y. Wang, Y. Xu, and J. Wang, J. Phys. Chem. C 124(22), 12075 (2020). https://doi.org/10.1021/acs.jpcc.0c02432 From their first-principles calculations, it was unveiled that V, Cr, Mn, Fe, and Ni in TMPS4 monolayers carries local moment of 1.8, 2.9, 3.6, 0.9, and 0.5 μB, respectively. Indeed, Fe, Co, and Ni atoms in TMPS4 are in the low-spin configuration because of the relatively strong field ligands, while V, Mn, and Cr atoms adopt the high-spin configurations. After replacing Cr (P) by Mn (As) atoms, the magnetic properties of single-layer MnAsS4 have also been investigated.318318. T. Hu, W. Wan, Y. Ge, and Y. Liu, J. Phys.: Condens. Matter 32, 385803 (2020). https://doi.org/10.1088/1361-648X/ab95cc The half-metallic spin gap for monolayer MnAsS4 is about 1.46 eV, and it has a large spin splitting energy of about 0.49 eV in the conduction band. MC simulations predicted a rather high TC of about 740 K.

4. MnBi2Te4 and CoGa2X4 (X = S, Se, or Te)

An emerging family of intrinsic magnets with tetrachalcogenides is also found on a 2D triangular lattice, i.e., MnBi2Te4 and CoGa2X4 (X = S, Se, Te). Based on DFT calculations, Li et al.1414. J. Li, Y. Li, S. Du, Z. Wang, B.-L. Gu, S.-C. Zhang, K. He, W. Duan, and Y. Xu, Sci. Adv. 5(6), eaaw5685 (2019). https://doi.org/10.1126/sciadv.aaw5685 predicted a series of novel magnetic materials from MnBi2Te4 related ternary chalcogenides MB2T4, where M is transition metal or rare earth metal; B is Bi or Sb; and T is Te, Se, or S [Fig. 13(a)]. In these materials, the intralayer exchange coupling is ferromagnetic, giving rise to 2D ferromagnetism in the monolayer. By carefully controlling the film thickness and external magnetic fields, many interesting topological quantum states can be induced in MnBi2Te4 monolayer [Fig. 13(b)], including QAH insulators, axion insulators, and quantum spin Hall insulators. Intriguingly, magnetic and topological states are well combined in MnBi2Te4, where Mn atom introduces magnetism and Bi–Te layers could generate topological properties. The schematic mechanism is depicted in Fig. 13(c). The monolayer MnBi2Te4 is a topologically trivial FM insulator with a direct bandgap of 0.70 eV [Fig. 13(d)]. Moreover, the magnetic and topological transitions in MnBi2Te4 are thickness dependent.319319. M. M. Otrokov, I. P. Rusinov, M. Blanco-Rey, M. Hoffmann, A. Y. Vyazovskaya, S. V. Eremeev, A. Ernst, P. M. Echenique, A. Arnau, and E. V. Chulkov, Phys. Rev. Lett. 122(10), 107202 (2019). https://doi.org/10.1103/PhysRevLett.122.107202 The MnBi2Te4 systems with odd numbers of building blocks are uncompensated interlayer antiferromagnets, while those with even numbers of building blocks are compensated interlayer antiferromagnets. Thickness dependent wide-band-gap quantum anomalous Hall and zero plateau quantum anomalous Hall states are observed. Li et al.320320. Y. Li, Z. Jiang, J. Li, S. Xu, and W. Duan, Phys. Rev. B 100(13), 134438 (2019). https://doi.org/10.1103/PhysRevB.100.134438 further analyzed its magnetic anisotropy and found that the magnetic anisotropy comes mainly from single ion anisotropy, which is caused by the SOC effect of Mn and Te atoms. The exchange interaction in the monolayer MnBi2Te4 is nearly isotropic, which has no contribution to the magnetic anisotropy. Thus, the Curie temperature was estimated to be about 20 K.

FIG. 13. (a) Monolayer MnBi2Te4 with FM configurations. (b) Various topological quantum states in MB2T4. (c) Schematic diagram of band magnetism and topology. (d) Band structure of monolayer MnBi2Te4. (e) Curie temperatures of eight MXY 2D ferromagnets, including ScCl, YCl, LaCl, LaBr2, CrSCl, CrSBr, CrSI, and CrSeBr. (f) Exfoliation mechanism of 2D FM sheet from 3D vdW AFM crystal and the Curie temperatures of CrOCl, CrOBr, and strained CrOCl. (g) Temperature dependence of zero-field-cooled (ZFC) and field-cooled (FC) curves for magnetization of the as-synthesized δ-FeOOH ultrathin nanosheets. Inset: the magnified part of ZFC and FC curves in temperature range from 280 to 300 K. Panels (a)–(d) reproduced with permission from Li et al., Sci. Adv. 5, eaaw5685 (2019). Copyright 2019 American Association for the Advancement of Science.1414. J. Li, Y. Li, S. Du, Z. Wang, B.-L. Gu, S.-C. Zhang, K. He, W. Duan, and Y. Xu, Sci. Adv. 5(6), eaaw5685 (2019). https://doi.org/10.1126/sciadv.aaw5685 Panel (e) reproduced with permission from Jiang et al., ACS Appl. Mater. Inter. 10, 39032 (2018). Copyright 2018 American Chemical Society.6565. Z. Jiang, P. Wang, J. Xing, X. Jiang, and J. Zhao, ACS Appl. Mater. Inter. 10(45), 39032 (2018). https://doi.org/10.1021/acsami.8b14037 Panel (f) reproduced with permission from Miao et al., J. Am. Chem. Soc. 140, 2417 (2018). Copyright 2018 American Chemical Society.322322. N. Miao, B. Xu, L. Zhu, J. Zhou, and Z. Sun, J. Am. Chem. Soc. 140(7), 2417 (2018). https://doi.org/10.1021/jacs.7b12976 Panel (g) reproduced with permission from Chen et al., Chem. Sci. 5, 2251 (2014). Copyright 2014 Royal Society of Chemistry.325325. P. Chen, K. Xu, X. Li, Y. Guo, D. Zhou, J. Zhao, X. Wu, C. Wu, and Y. Xie, Chem. Sci. 5(6), 2251 (2014). https://doi.org/10.1039/C3SC53303D

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Two-dimensional half-metallic ferromagnets, CoGa2X4 (X = S, Se, Te), are also found to be stable against spin flipping at room temperature. Its robust HM ferromagnetism originates from the superexchange interaction of Co-X–Co bonds with bond angles close to 90°. The calculations of magnetic anisotropy with inclusion of SOC indicated that CoGa2X4 systems have easy plane magnetizations, which are expected to have Berezinsky-Kosterlitz-Thouless transitions following the classical 2D XY model.9696. S. Zhang, R. Xu, W. Duan, and X. Zou, Adv. Funct. Mater. 29(14), 1808380 (2019). https://doi.org/10.1002/adfm.201808380 Other 2D magnets in ternary sulfides with two nonmetal elements are also observed for single-layer pentagonal CoAsS321321. L. Liu and H. L. Zhuang, APL Mater. 7(1), 011101 (2019). https://doi.org/10.1063/1.5079867 and CrP2S7.6666. H. Liu, J.-T. Sun, M. Liu, and S. Meng, J. Phys. Chem. Lett. 9(23), 6709 (2018). https://doi.org/10.1021/acs.jpclett.8b02783

5. MXY-type compounds

A class of 2D magnetic materials, MXY (M = transition metal; X = O, S, Se, Te, N; Y = Cl, Br, I) will crystalize in an orthorhombic structure with Pmmn space group, which consists of M2X2 layers sandwiched by halogen atoms. The transition metal M atoms are in the center of distorted octahedron (D2h symmetry) and bound with X and Y atoms.

In H phase, five d orbitals split into three groups, i.e., dxy/yz, dx2-y2/xy, and dz2 under trigonal prismatic ligand field. In T phase, the d orbitals can be divided into t2g (dxy, dyz, dxz) and eg (dx2-y2, dz2) orbitals under octahedral ligand field. In D2h phase of MX2, the degenerated d orbitals further split owing to the reduction of symmetry. As observed in MoS2 monolayer with D2h symmetry, it induces two spin-polarized electrons occupying dxy and dz2, leaving dxz state unoccupied. Obviously, moderate splitting between the occupied and the unoccupied d orbitals brings out a relatively small gap of 0.21 eV in D2h symmetry instead of a severe splitting of ∼1.0 eV in semiconducting H phase. As a result of such electronic structure, the magnetic moment per Mo atom reaches 2.0 μB at high-spin state (S = 1).

Chromium sulfide halides Cr-X-Y (X = S, Se, Te; Y = Cl, Br, I) with chemical composition from transition metal dichalcohalides to di-halides have been theoretically predicted. Similar to transition metal di-halides discussed in Sec. III A 2, monolayer Cr-X-Y systems are ferromagnetic semiconductors, having large spin polarization and high Curie temperature of 100∼500 K. Based on 1825 easily or potentially exfoliable compounds from high-throughput search of the crystalline materials database, 36 monolayer 2D ferromagnets have been identified.6767. N. Mounet, M. Gibertini, P. Schwaller, D. Campi, A. Merkys, A. Marrazzo, T. Sohier, I. E. Castelli, A. Cepellotti, G. Pizzi, and N. Marzari, Nat. Nanotechnol. 13(3), 246 (2018). https://doi.org/10.1038/s41565-017-0035-5 Among them, a noticeable system is CrSBr monolayer. By carefully examining its magnetic behavior, Jiang et al.6565. Z. Jiang, P. Wang, J. Xing, X. Jiang, and J. Zhao, ACS Appl. Mater. Inter. 10(45), 39032 (2018). https://doi.org/10.1021/acsami.8b14037 demonstrated that 2D CrSBr is a semiconductor possessing a large magnetic moment of ∼3 μB per Cr atom and a high Curie temperature (TC = 290 K). The robust ferromagnetism of the CrSBr monolayer has been ascribed to the halogen-mediated (Cr−Br−Cr) and chalcogen-mediated (Cr−S−Cr) superexchange interactions. Based on that mechanism, they further proposed an isoelectronic substitution strategy to tailor the magnetic coupling strength. Finally, CrSI, CrSCl, and CrSeBr were also predicted as stable FM semiconductors with appreciable Curie temperatures of 330, 500, and 500 K, respectively [see Fig. 13(e)].6565. Z. Jiang, P. Wang, J. Xing, X. Jiang, and J. Zhao, ACS Appl. Mater. Inter. 10(45), 39032 (2018). https://doi.org/10.1021/acsami.8b14037 Several other theoretical studies also found that CrTX (T = S, Se, Te; X = Cl, Br, I) monolayers are FM semiconductors.26,70,13126. C. Wang, X. Zhou, L. Zhou, N.-H. Tong, Z.-Y. Lu, and W. Ji, Sci. Bull. 64(5), 293 (2019). https://doi.org/10.1016/j.scib.2019.02.01170. R. Han, Z. Jiang, and Y. Yan, J. Phys. Chem. C 124(14), 7956 (2020). https://doi.org/10.1021/acs.jpcc.0c01307131. Y. Guo, Y. Zhang, S. Yuan, B. Wang, and J. Wang, Nanoscale 10(37), 18036 (2018). https://doi.org/10.1039/C8NR06368K Besides high Curie temperature (100∼500 K), large perpendicular magnetic anisotropy, wide range of bandgaps, high carrier mobilities, strong anisotropy of carrier effective mass, and large light absorption are also found in these materials, suggesting that this 2D family holds potential for high performance electronic and spintronic devices. From a material database containing around 560 monolayer compounds of MXY (M = metal; X = S, Se, Te; Y = F, Cl, Br, I), 46 potential magnetic semiconductors have been further identified from HSE06 calculations.132132. J. Pan, J. Yu, Y.-F. Zhang, S. Du, A. Janotti, C.-X. Liu, and Q. Yan, npj Computat. Mater. 6, 152 (2020). https://doi.org/10.1038/s41524-020-00419-y Among them, Curie temperatures of the newly reported TiTeI, VSI, VSeI, MoSI, WSeI, WTeI monolayers are 46, 1100, 913, 270, 76, 302, and 479 K, respectively.

Starting from 3D AFM transition metal oxyhalides, Miao et al.322322. N. Miao, B. Xu, L. Zhu, J. Zhou, and Z. Sun, J. Am. Chem. Soc. 140(7), 2417 (2018). https://doi.org/10.1021/jacs.7b12976 proposed that the 2D CrOCl and CrOBr monolayers can be obtained by mechanical cleavage and further predicted that they are intrinsic ferromagnetic semiconductors with bandgaps of 2.38 and 1.59 eV as well as Curie temperatures of 160 and 129 K [Fig. 13(f)], respectively. Calculated with the same method, the TC of CrOF sheet may even exceed those of CrOCl and CrOBr and reach up to ∼200 K.323323. T. Xiao, G. Wang, and Y. Liao, Chem. Phys. 513, 182 (2018). https://doi.org/10.1016/j.chemphys.2018.08.007 The spins in both CrOCl and CrOBr monolayers align along the out-of-plane direction with considerably large MAE (0.03∼0.29 meV). These results have motivated some successive investigations on the magnetic properties of transition metal oxyhalides MOX (X = Cl, Br, I). All these FeOX (X = F, Cl, Br, I) monolayers are theoretically stable and could be exfoliated from their bulk phase.133133. S. Wang, J. Wang, and M. Khazaei, Phys. Chem. Chem. Phys. 22(20), 11731 (2020). https://doi.org/10.1039/D0CP01767A These FeOX monolayers are revealed to be Mott insulators with bandgaps from 2.73 to 0.48 eV as element X changes from F to I. For all FeOX monolayers, the in-plane and inter-plane magnetic interactions between Fe atoms are dominated by AFM coupling. The Néel temperatures of FeOF and FeOI monolayers are 130 and 150 K, respectively. In addition, 2D VBrO, TiClO, VClO were predicted to be FM half-metals,132132. J. Pan, J. Yu, Y.-F. Zhang, S. Du, A. Janotti, C.-X. Liu, and Q. Yan, npj Computat. Mater. 6, 152 (2020). https://doi.org/10.1038/s41524-020-00419-y while 2D VOF was a FM semiconductor.6666. H. Liu, J.-T. Sun, M. Liu, and S. Meng, J. Phys. Chem. Lett. 9(23), 6709 (2018). https://doi.org/10.1021/acs.jpclett.8b02783

Similar to transition halides, the ground state of 2D δ-FeOOH monolayer is AFM with an indirect bandgap of 2.4 eV, which is derived from bulk Fe(OH)2 via oxidation.324324. I. Khan, A. Hashmi, M. U. Farooq, and J. Hong, ACS Appl. Mater. Inter. 9(40), 35368 (2017). https://doi.org/10.1021/acsami.7b08499 The δ-FeOOH ultrathin films with thicknesses of 1.1∼1.3 nm have been experimentally synthesized via a topochemical transformation process. These films exhibit room-temperature ferromagnetism along with semiconducting behavior.325325. P. Chen, K. Xu, X. Li, Y. Guo, D. Zhou, J. Zhao, X. Wu, C. Wu, and Y. Xie, Chem. Sci. 5(6), 2251 (2014). https://doi.org/10.1039/C3SC53303D Besides the 2D ternary sulfide halides and oxyhalides, intrinsic magnets have also been observed in nitride halides, such as FeNF, MnNF, MnNCl, and MnNBr,26,13226. C. Wang, X. Zhou, L. Zhou, N.-H. Tong, Z.-Y. Lu, and W. Ji, Sci. Bull. 64(5), 293 (2019). https://doi.org/10.1016/j.scib.2019.02.011132. J. Pan, J. Yu, Y.-F. Zhang, S. Du, A. Janotti, C.-X. Liu, and Q. Yan, npj Computat. Mater. 6, 152 (2020). https://doi.org/10.1038/s41524-020-00419-y and the corresponding Curie temperatures are 398, 238, 261, and 492 K, respectively.

Since the 3D AMnBi family (A = K, Rb, Cs) with layered structure have strong AFM coupling between the Mn layers and weak interlayer coupling, AFM ordering is also anticipated at their 2D limit.326326. Z. Zhu, C. Liao, S. Li, X. Zhang, W. Wu, Z.-M. Yu, R. Yu, W. Zhang, and S. A. Yang, arXiv preprint arXiv:2003.10671 (2020). According to DFT calculations, AFM state is indeed favored for all of the 2D KMnBi, RbMnBi, and CsMnBi as the ground state. The strong Coulomb interaction arising from d orbitals of Mn atom results in their magnetic state. The easy magnetic axis is along the z direction with MAE values of 0.86∼1.1 meV. The Néel temperature is about 302–307 K, which is higher than that of the value of 2D FePS3 (118 K). Moreover, the mobilities for both electron and hole carriers are in the order of 103 cm2/(V·s), which is higher than 2D MoS2 at room temperature.327327. X. Li, T. Gao, and Y. Wu, Sci. China Inform. Sci. 59(6), 061405 (2016). https://doi.org/10.1007/s11432-016-5559-z Two-dimensional K2CoS2 is also an in-plane antiferromagnetic insulator,328328. A. B. Sarkar, B. Ghosh, B. Singh, S. Bhowmick, H. Lin, A. Bansil, and A. Agarwal, arXiv preprint arXiv:2005.12868 (2020). and MC simulations predicted its transition temperature to be TN ≈ 15 K. Remarkably, bulk K2CoS2 also hosts an in-plane AFM state, and its magnetic ordering can persist even in ultrathin films down to monolayer limit.

F. 2D f-electron magnets

Up to now, most reported 2D magnets are based on d electrons. Generally speaking, d electrons are more localized and have stronger correlation effect than s and p electrons, which is the basic requirement of magnetic state. Compared to the d-electron based materials, f electrons are even more localized; thus, the direct overlap of f orbitals between neighboring rare earth atoms as well as the hybridization between f orbitals and p orbitals of neighbor anions, are mostly negligible. As a result, the direct exchange and superexchange interactions mediated by anions are usually very weak between rare earth magnetic anions, which is the most serious drawback for finding high-temperature f magnetism. However, the f-electron based 2D materials still have many advantages for future spintronic applications. Especially, f electrons usually have much stronger spin-orbit coupling than d electrons, which in turn leads to stronger magnetocrystalline anisotropy. Hence, it is still meaningful to design 2D f-electron magnets with high TC. To this end, a few pioneer works have been reported.

In the 2D f-electron magnets, the most attractive element is gadolinium (Gd), which has half-filled and well-localized 4f subshell leading to ferromagnetic behavior with high saturation magnetization. Experimentally, Ormaza et al.329329. M. Ormaza, L. Fernández, M. Ilyn, A. Magaña, B. Xu, M. J. Verstraete, M. Gastaldo, M. A. Valbuena, P. Gargiani, A. Mugarza, A. Ayuela, L. Vitali, M. Blanco-Rey, F. Schiller, and J. E. Ortega, Nano Lett. 16(7), 4230 (2016). https://doi.org/10.1021/acs.nanolett.6b01197 reported that single-layer GdAg2 grown on Ag(111) is ferromagnetic with a Curie temperature of 85 K [Fig. 14(a)]. All the bands are spin-polarized owing to the presence of half-filled Gd 4f orbitals. The exchange interaction between Gd atoms is mediated by s, p–d Ag–Gd hybrid bands, similar as the effective s–d hybrid bands in pure Gd solid.329,330329. M. Ormaza, L. Fernández, M. Ilyn, A. Magaña, B. Xu, M. J. Verstraete, M. Gastaldo, M. A. Valbuena, P. Gargiani, A. Mugarza, A. Ayuela, L. Vitali, M. Blanco-Rey, F. Schiller, and J. E. Ortega, Nano Lett. 16(7), 4230 (2016). https://doi.org/10.1021/acs.nanolett.6b01197330. A. Correa, B. Xu, M. J. Verstraete, and L. Vitali, Nanoscale 8(45), 19148 (2016). https://doi.org/10.1039/C6NR06398E Twofold degenerate Weyl nodal lines in a 2D single-layer Gd-Ag compound were observed by combining angle-resolved photoemission spectroscopy measurements and theoretical calculations.331331. B. Feng, R.-W. Zhang, Y. Feng, B. Fu, S. Wu, K. Miyamoto, S. He, L. Chen, K. Wu, K. Shimada, T. Okuda, and Y. Yao, Phys. Rev. Lett. 123(11), 116401 (2019). https://doi.org/10.1103/PhysRevLett.123.116401 Lei et al.332332. S. Lei, J. Lin, Y. Jia, M. Gray, A. Topp, G. Farahi, S. Klemenz, T. Gao, F. Rodolakis, J. L. McChesney, C. R. Ast, A. Yazdani, K. S. Burch, S. Wu, N. P. Ong, and L. M. Schoop, Sci. Adv. 6(6), eaay6407 (2020). https://doi.org/10.1126/sciadv.aay6407 demonstrated that GdTe3 can be exfoliated to ultrathin flakes. The obtained monolayer GdTe3 flake is an antiferromagnet, exhibiting a relatively high carrier mobility.

FIG. 14. (a) STM image, remanent magnetization at zero applied field, and angle-resolved photoemission of a GdAg2 monolayer alloy. (b) Temperature-dependent spin moments of three different K2N AXenes phases. (c) 3D band structure of the spin-down channel around the Fermi level. (d) PDOS of N and Y atoms for 1T-YN2. (e) PDOS of s and p orbitals of N atom for 1T-YN2. (f) Schematic diagram for the origin of magnetic moment of 1T-YN2 monolayer. Panel (a) reproduced with permission from Ormaza et al., Nano Lett. 16, 4230 (2016). Copyright 2016 American Chemical Society.329329. M. Ormaza, L. Fernández, M. Ilyn, A. Magaña, B. Xu, M. J. Verstraete, M. Gastaldo, M. A. Valbuena, P. Gargiani, A. Mugarza, A. Ayuela, L. Vitali, M. Blanco-Rey, F. Schiller, and J. E. Ortega, Nano Lett. 16(7), 4230 (2016). https://doi.org/10.1021/acs.nanolett.6b01197 Panel (b) reproduced with permission from Jiang et al., J. Phys. Chem. Lett. 10, 7753 (2019). Copyright 2019 American Chemical Society.341341. X. Jiang, Q. Liu, J. Xing, and J. Zhao, J. Phys. Chem. Lett. 10(24), 7753 (2019). https://doi.org/10.1021/acs.jpclett.9b03030 Panels (c)–(f) reproduced with permission from Liu et al., Nano Res. 10, 1972 (2017). Copyright 2017 Springer Nature.66. Z. Liu, J. Liu, and J. Zhao, Nano Res. 10(6), 1972 (2017). https://doi.org/10.1007/s12274-016-1384-3

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Rare earth metal functionalized silicene MSi2 (M = Eu, Gd) were successfully synthesized by the reaction of M with Si(111) substrate using MBE technique. Strong magnetic response of transport was reported in EuSi2 and GdSi2 monolayers, suggesting indirect exchange interaction between localized f-shells of Eu/Gd and p orbitals of silicene. The extended pz states of silicene can mediate the long-range magnetic interactions.333333. O. E. Parfenov, A. M. Tokmachev, D. V. Averyanov, I. A. Karateev, I. S. Sokolov, A. N. Taldenkov, and V. G. Storchak, Mater. Today 29, 20 (2019). https://doi.org/10.1016/j.mattod.2019.03.017 In addition, 4f-electron based EuGe2 and GdGe2334334. A. M. Tokmachev, D. V. Averyanov, A. N. Taldenkov, O. E. Parfenov, I. A. Karateev, I. S. Sokolov, and V. G. Storchak, Mater. Horiz. 6(7), 1488 (2019). https://doi.org/10.1039/C9MH00444K were also synthesized by direct reaction between these elements, with thickness from bulk down to monolayer. The common pattern is a transformation from 3D antiferromagnetism to 2D ferromagnetism, as revealed by magnetization and electron transport measurements.

Theoretically, high-temperature f-electron FM semiconductor has been found in GdI2 monolayer.129129. B. Wang, X. Zhang, Y. Zhang, S. Yuan, Y. Guo, S. Dong, and J. Wang, Mater. Horiz. 7, 1623 (2020). https://doi.org/10.1039/D0MH00183J The highly localized 4f electrons often lead to weak direct exchange and superexchange interactions. However, due to the coexistence of spin-polarized 5d orbitals and 4f orbitals in Gd2+ cation, the strong direct interaction between these two orbitals is found to determine the FM ground state of GdI2 monolayer, whereas there still exists Gd 5d–I 5p–Gd 5d superexchange interaction. As a result, high TC (241 K), large magnetization (8 μB/f.u.), and large magnetic anisotropy energy (0.553 meV/Gd) were observed in GdI2 monolayer. According to a recent DFT study, Gd2B2 monolayer is a ferromagnetic metal, and its ferromagnetic state can sustain above room temperature as high as TC = 550 K with a huge magnetic moment of μ = 7.30 μB per Gd atom.335335. T. Gorkan, E. Vatansever, U. Akɪncɪ, G. Gökoglu, E. Aktürk, and S. Ciraci, J. Phys. Chem. C 124, 12816 (2020). https://doi.org/10.1021/acs.jpcc.0c03304

In addition to the 4f systems, Zhang et al.336336. S. Li, Z. Wang, M. Zhou, F. Zheng, X. Shao, and P. Zhang, J. Phys. D: Appl. Phys. 53(18), 185301 (2020). https://doi.org/10.1088/1361-6463/ab740c firstly reported a potential 5f-electron 2D magnet, i.e., hexagonal UI3 monolayer, using DFT calculations and MC simulations. Non-SOC calculations revealed that UI3 monolayer is a Weyl semi-metal, while it becomes a semiconductor with a bandgap of 0.18 eV after inclusion of SOC effect. The projected density of states showed that the magnetism comes from f electrons of U atom. Noticeably, its exchange parameter and anisotropic energy are one order of magnitude larger than those of CrI3 monolayer. Hence, the estimated Curie temperature was 110 K.336336. S. Li, Z. Wang, M. Zhou, F. Zheng, X. Shao, and P. Zhang, J. Phys. D: Appl. Phys. 53(18), 185301 (2020). https://doi.org/10.1088/1361-6463/ab740c

G. 2D p-electron magnets

Among the 2D magnets discussed above, a common feature is that the high-spin states are guaranteed by the magnetic metal elements with partially filled 3d or 4f subshells. Apart from these conventional classes of 2D d/f ferromagnets, robust magnetic coupling has also been observed in many materials with partially occupied and localized/delocalized p orbitals, namely, p-electron magnets. Similar to d and f orbitals, the partially occupied p orbitals with certain localized character are mainly responsible for the magnetism. It is also explained by the crystal symmetry protected flat bands model. Compared to the 2D d/f-electron magnets, p orbitals in the superexchange interaction are more delocalized, which is beneficial for the long-distance spin coupling. Thus, these 2D p-electron magnetic materials are likely to possess higher Fermi velocity and longer spin coherence length due to greater delocalization of p orbitals and smaller SOC strength, which are prominent advantages for high-speed and long-distance spin transport.

According to the origin of magnetism, 2D p-electron magnets can be divided into two categories—d0 magnetism and dn magnetism with paired spin-antiparallel d electron. Clearly, d0 magnetism would be observed in many 2D materials without transition metal, rare earth, or actinide elements. First, these novel d0 magnetism may originate from their hosting flat bands, which resulted in high density of states in the vicinity of the Fermi levels. Both theoretical and experimental studies proposed that zigzag graphene nanoribbons with localized edge states are room-temperature antiferromagnets.337–339337. Y.-W. Son, M. L. Cohen, and S. G. Louie, Nature 444(7117), 347 (2006). https://doi.org/10.1038/nature05180338. G. Z. Magda, X. Jin, I. Hagymási, P. Vancsó, Z. Osváth, P. Nemes-Incze, C. Hwang, L. P. Biró, and L. Tapasztó, Nature 514(7524), 608 (2014). https://doi.org/10.1038/nature13831339. M. Slota, A. Keerthi, W. K. Myers, E. Tretyakov, M. Baumgarten, A. Ardavan, H. Sadeghi, C. J. Lambert, A. Narita, and K. Müllen, Nature 557(7707), 691 (2018). https://doi.org/10.1038/s41586-018-0154-7 The intrinsic magnetic ordering survives at room temperature in a novel B5N5 monolayer allotrope with decorated bounce lattice, which is also a 2D antiferromagnetic insulator. The antiferromagnetism arises from the nearly flat bands at the vicinity of the Fermi energy.340340. D. Zhang, Q. Xiong, and K. Chang, Nanoscale Adv. 2, 4421 (2020). https://doi.org/10.1039/D0NA00270D

Second, d0 magnetism has been found in a few artificially designed 2D materials with nonstoichiometric compositions.6,3416. Z. Liu, J. Liu, and J. Zhao, Nano Res. 10(6), 1972 (2017). https://doi.org/10.1007/s12274-016-1384-3341. X. Jiang, Q. Liu, J. Xing, and J. Zhao, J. Phys. Chem. Lett. 10(24), 7753 (2019). https://doi.org/10.1021/acs.jpclett.9b03030 The periodic nonstoichiometric compound refers to the order compound with either cation deficient or electron deficient rather than the atomic defects, such as experimentally obtained 2D Na2Cl and Na3Cl342342. G. Shi, L. Chen, Y. Yang, D. Li, Z. Qian, S. Liang, L. Yan, L. H. Li, M. Wu, and H. Fang, Nat. Chem. 10(7), 776 (2018). https://doi.org/10.1038/s41557-018-0061-4 and theoretically predicted K2N341341. X. Jiang, Q. Liu, J. Xing, and J. Zhao, J. Phys. Chem. Lett. 10(24), 7753 (2019). https://doi.org/10.1021/acs.jpclett.9b03030 and YN2.66. Z. Liu, J. Liu, and J. Zhao, Nano Res. 10(6), 1972 (2017). https://doi.org/10.1007/s12274-016-1384-3 Such unconventional compounds may lead to long-range ordered unpaired p electrons in the magnetic lattice. By carefully considering the compositions and electronic configurations, a series of p-state intrinsic ferromagnetic A2N compounds of alkali metal (A) and nitrogen (N), namely, AXenes, have been proposed.341341. X. Jiang, Q. Liu, J. Xing, and J. Zhao, J. Phys. Chem. Lett. 10(24), 7753 (2019). https://doi.org/10.1021/acs.jpclett.9b03030 Taking 2D K2N as an example, all of the three predicted phases (H, T, and I) are half metals with high Curie temperature of 480∼1180 K [Fig. 14(b)]. As expected, the ferromagnetism in all three phases is mainly contributed by N atoms, with on-site moment of 0.81, 0.72, and 0.79 μB, respectively. Meanwhile, their high Curie temperatures arise from the coexistence of N–K–N superexchange and the carrier-mediated interaction mechanism. Very recently, Jin et al.343343. L. Jin, X. Zhang, Y. Liu, X. Dai, X. Shen, L. Wang, and G. Liu, Phys. Rev. B 102, 125118 (2020). https://doi.org/10.1103/PhysRevB.102.125118 further found that K2N monolayer with D3h point group shows two nodal lines in its low-energy band structures, and these nodal lines are robust against weak SOC. Such feasible nonstoichiometric strategy has also attained long-range p electron magnetic ordering in 2D C3Ca2 and Na2C with Honeycomb-Kagome lattice.344,345344. W.-x. Ji, B.-m. Zhang, S.-f. Zhang, C.-w. Zhang, M. Ding, P. Li, and P.-j. Wang, J. Mater. Chem. C 5(33), 8504 (2017). https://doi.org/10.1039/C7TC02700A345. W.-X. Ji, B.-M. Zhang, S.-F. Zhang, C.-W. Zhang, M. Ding, P.-J. Wang, and R. Zhang, Nanoscale 10(28), 13645 (2018). https://doi.org/10.1039/C8NR02761G First-principles and tight-binding calculations revealed that both of them are intrinsic Dirac half-metals. Specifically, 2D C3Ca2 has a high-spin ferromagnetic configuration of 8 μB per unit cell with a Curie temperature of 30.7 K, which is mainly contributed by the 2p orbitals of carbon atoms. The mechanism of magnetism could be understood by the double exchange between carbon anions using Ca2+ cations as bridges. In a similar manner, ferromagnetism of 2D Na2C is also mainly contributed by the unpaired 2p electrons of carbon with an estimated Curie temperature of 382 K. The origin of such 2p magnetism could be explained by the superexchange mechanism between C2− anions with Na+ cations as bridges. Indeed, the calculated Fermi velocities reach up to ∼105 ms−1, which are promising for high-speed spintronic devices.

Novel 2D p-electron magnets with paired d electrons that have antiparallel spin orientation have been reported in a few transition metal compounds, such as MoN2, Y2N, MoN2, TcN2, TaN2, NbN2, and LaBr2. Using first-principles calculations, 1H-MoN2 monolayer was theoretically proposed to be a 2D p-electron intrinsically FM material with a high Curie temperature of 420 K,346346. F. Wu, C. Huang, H. Wu, C. Lee, K. Deng, E. Kan, and P. Jena, Nano Lett. 15(12), 8277 (2015). https://doi.org/10.1021/acs.nanolett.5b03835 while it can be exfoliated experimentally.347347. S. Wang, H. Ge, S. Sun, J. Zhang, F. Liu, X. Wen, X. Yu, L. Wang, Y. Zhang, H. Xu, J. C. Neuefeind, Z. Qin, C. Chen, C. Jin, Y. Li, D. He, and Y. Zhao, J. Am. Chem. Soc. 137(14), 4815 (2015). https://doi.org/10.1021/jacs.5b01446 Liu et al. found that 2D Y2N with octahedral coordination is a novel p-state Dirac half metal,66. Z. Liu, J. Liu, and J. Zhao, Nano Res. 10(6), 1972 (2017). https://doi.org/10.1007/s12274-016-1384-3 as shown in Fig. 14(c). From the PDOS in Figs. 14(d) and 14(e), one can clearly see that N atoms instead of Y atoms contribute to the Dirac states. More interestingly, the half-metallic gap is 1.53 eV, the Fermi velocity is 3.74 × 105 m/s, and the Curie temperature estimated by mean-field approximation reaches over 332 K. Motivated by these studies, 2D p-electron intrinsic magnets have also been explored by first-principles computational search of thirty possible monolayer structures of transition metal dinitride. Among them, 1H-MoN2 and 1H-TcN2 are 2D p-state intrinsically ferromagnetic metals, while monolayer 1T-TaN2 and 1T-NbN2 are 2D p-state intrinsically ferromagnetic half-metals.124,348124. J. Liu, Z. Liu, T. Song, and X. Cui, J. Mater. Chem. C 5(3), 727 (2017). https://doi.org/10.1039/C6TC04490E348. R. Li, B. Yang, F. Li, Y. Wang, X. Du, and Y. Yan, J. Phys.: Condens. Matter 31(33), 335801 (2019). https://doi.org/10.1088/1361-648X/ab1fbb For all these materials, the robust FM ground state originates from the strong N–N direct exchange interaction.

Taking 1T-YN2 monolayer as an example, we discuss the origin of paired d electrons and unpaired p electrons induced magnetism in Fig. 14(f).66. Z. Liu, J. Liu, and J. Zhao, Nano Res. 10(6), 1972 (2017). https://doi.org/10.1007/s12274-016-1384-3 The ground state electronic configurations of neutral Y and N atoms are 4d15s2 and 3s23p3, respectively. In YN2 monolayer, one of the two 5s electrons in Y atom occupies 4d orbital of Y and the other one transfers to N-2p orbital, resulting in 4d25s0 electronic configurations of Y2+ cation. Consequently, Y-4d orbitals are occupied by two spin-antiparallel electrons, exhibiting nearly zero magnetic moment. Meanwhile, 3p states of the two N atoms are occupied by a total of eleven 3p electrons via gaining one Y-5s electron. Following the eight-electron rule and assuming a nearly electron-free gas model, one can conclude that these eleven 3p electrons would exhibit an electronic shell configuration like: ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑ ↑. In other words, the three unpaired electrons would result in a magnetic moment of 3 μB per YN2 formula unit, as obtained from spin-polarized DFT calculations.

H. 2D organic magnets

Apart from the rich family of 2D inorganic magnets, 2D organic magnetic materials have also attracted considerable attention due to their molecular diversity, flexibility in synthesis, easy processing, low cost, well-defined geometry, and potential applications in quantum Hall effect, magnetic storage, and spintronics. Research of the two fundamental physical concepts, i.e., exchange interaction and spin orbit coupling, represents the important branches of 2D organic magnets. Generally speaking, the magnetic properties of two conceptual classes of 2D organic materials have been discussed extensively in recent literature. One class of 2D organic materials is 2D metal organic frameworks (MOF), which is a kind of long-range network constructed by organic linkers and metal ion centers. The magnetism can be implemented by incorporating metal ions as the magnetic carriers. Another class of 2D organic magnets is covalent organic frameworks (COFs), which are formed by covalent bonding of the atoms of light elements (H, B, C, N and O). Without magnetic metal ions, the magnetism in 2D COF can be implemented by incorporating open-shell organic ligands. In addition, both ordered 2D MOF and COF conformations render the connection between magnetic moment carriers within an interacting distance.101,349–352101. J. Zhou and Q. Sun, J. Am. Chem. Soc. 133(38), 15113 (2011). https://doi.org/10.1021/ja204990j349. M. Kurmoo, Chem. Soc. Rev. 38(5), 1353 (2009). https://doi.org/10.1039/b804757j350. S. Yang, W. Li, C. Ye, G. Wang, H. Tian, C. Zhu, P. He, G. Ding, X. Xie, and Y. Liu, Adv. Mater. 29(16), 1605625 (2017). https://doi.org/10.1002/adma.201605625351. A. Du, S. Sanvito, and S. C. Smith, Phys. Rev. Lett. 108(19), 197207 (2012). https://doi.org/10.1103/PhysRevLett.108.197207352. E. Kan, W. Hu, C. Xiao, R. Lu, K. Deng, J. Yang, and H. Su, J. Am. Chem. Soc. 134(13), 5718 (2012). https://doi.org/10.1021/ja210822c The key electronic and magnetic properties of 2D MOF and COF are listed in Table V for discussion.

TABLE V. A list of 2D organic magnets with their compositions and representative electronic and magnetic properties, including the magnetic ground state (GS), the values of Hubbard U term, energy gap (Eg), magnetic moment on per transition metal (Ms), Curie temperature (TC), and magnetic anisotropy energy per unit cell (MAE).

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Sci. 10(44), 10381 (2019). https://doi.org/10.1039/C9SC03816G[email protected]AFM30.163.12––385385. L.-C. Zhang, L. Zhang, G. Qin, Q.-R. Zheng, M. Hu, Q.-B. Yan, and G. Su, Chem. Sci. 10(44), 10381 (2019). https://doi.org/10.1039/C9SC03816G[email protected]Dimerized30.531.96––385385. L.-C. Zhang, L. Zhang, G. Qin, Q.-R. Zheng, M. Hu, Q.-B. Yan, and G. Su, Chem. Sci. 10(44), 10381 (2019). https://doi.org/10.1039/C9SC03816G[email protected]Dimerized30.730.96––385385. L.-C. Zhang, L. Zhang, G. Qin, Q.-R. Zheng, M. Hu, Q.-B. Yan, and G. Su, Chem. Sci. 10(44), 10381 (2019). https://doi.org/10.1039/C9SC03816G3d@T4PT[email protected]FMi––21.8–386386. T. Umbach, M. Bernien, C. F. Hermanns, A. Krüger, V. Sessi, I. Fernandez-Torrente, P. Stoll, J. I. Pascual, K. Franke, and W. Kuch, Phys. Rev. Lett. 109(26), 267207 (2012). https://doi.org/10.1103/PhysRevLett.109.267207Ni2C24S6H12FM3DHM1630–387387. L. Wei, X. Zhang, and M. Zhao, Phys. Chem. Chem. Phys. 18(11), 8059 (2016). https://doi.org/10.1039/C6CP00368K[email protected][email protected]FM–HM1325–8181. H. Sun, B. Li, and J. Zhao, J. Phys.: Condens. Matter 28(42), 425301 (2016). https://doi.org/10.1088/0953-8984/28/42/425301[email protected]FM–HM1200–8181. H. Sun, B. Li, and J. Zhao, J. Phys.: Condens. Matter 28(42), 425301 (2016). https://doi.org/10.1088/0953-8984/28/42/425301[email protected]FM–HM1325–8181. H. Sun, B. Li, and J. Zhao, J. Phys.: Condens. Matter 28(42), 425301 (2016). https://doi.org/10.1088/0953-8984/28/42/425301[email protected]FM–0.06363019388388. J. Xing, P. Wang, Z. Jiang, X. Jiang, Y. Wang, and J. Zhao, APL Mater. 8(7), 071105 (2020). https://doi.org/10.1063/5.0010822[email protected][email protected]AFM3–0.8––391391. E. Kan, X. Wu, C. Lee, J. H. Shim, R. Lu, C. Xiao, and K. Deng, Nanoscale 4(17), 5304 (2012). https://doi.org/10.1039/c2nr31074k[email protected]FM3Metal2.9279<1391391. E. Kan, X. Wu, C. Lee, J. H. Shim, R. Lu, C. Xiao, and K. 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The rapid development of 2D organic magnets benefits from the synthesis of high-quality and highly stable 2D MOFs.353–356353. D. Sheberla, L. Sun, M. A. Blood-Forsythe, S. l. Er, C. R. Wade, C. K. Brozek, A. n. Aspuru-Guzik, and M. Dinca˘, J. Am. Chem. Soc. 136(25), 8859 (2014). https://doi.org/10.1021/ja502765n354. D. Grumelli, B. Wurster, S. Stepanow, and K. Kern, Nat. Commun. 4(1), 2904 (2013). https://doi.org/10.1038/ncomms3904355. A. J. Clough, J. W. Yoo, M. H. Mecklenburg, and S. C. Marinescu, J. Am. Chem. Soc. 137(1), 118 (2015). https://doi.org/10.1021/ja5116937356. T. Kambe, R. Sakamoto, K. Hoshiko, K. Takada, M. Miyachi, J. H. Ryu, S. Sasaki, J. Kim, K. Nakazato, and M. Takata, J. Am. Chem. Soc. 135(7), 2462 (2013). https://doi.org/10.1021/ja312380b So far, the majority of magnetic frameworks in 2D MOFs contain paramagnetic metal centers, in particular, the open-shell 3d and 5d transition metals. These metal ions, which may exist in different oxidation states, allow variation of the two important parameters—spin quantum number and magnetic anisotropy. In addition, the diversity of organic molecule frameworks offers many opportunities to anchor the magnetic atoms, such as phthalocyanine (Pc), polyporphyrin (poly-Pp), benzenehexathiolate (BHT), and 5,5′-bis(4-pyridyl)(2,2′-bipirimidine) (PBP). These organic frameworks act as the medium to couple metal carriers. In addition, the organic ligands impose a coordination environment on the metal ions, namely, ligand field, which is important for determining the magnetic behavior. According to the symmetry of typical molecular architectures, the possible coordination numbers of central metal ions are 2, 3, 4, and 6.

Four is the most common coordination number for transition metal atoms in 2D organic magnets, especially Pc, Pp, and BHT frameworks. As an 18-electron conjugated system, Pc framework is a macrocyclic compound composed of an inner porphyrazine ring that connects four isoindole groups, giving rise to the characteristic cross-like shape. Pc framework has a cavity with a diameter of about 2.70 Å in the center of the large conjugated ring. Transition metal species embedded in the cavity can chelate with the Pc framework through coordination bonds and form metal phthalocyanine sheet ([email protected]) with appreciable thermal stability. Both experimental and theoretical reports argued that a variety of [email protected] sheets are good conductors or semiconductors.101,357–360101. J. Zhou and Q. Sun, J. Am. Chem. Soc. 133(38), 15113 (2011). https://doi.org/10.1021/ja204990j357. B. Białek, I. G. Kim, and J. I. Lee, Surf. Sci. 526(3), 367 (2003). https://doi.org/10.1016/S0039-6028(03)00002-5358. D. M. Sedlovets, M. V. Shuvalov, Y. V. Vishnevskiy, V. T. Volkov, I. I. Khodos, O. V. Trofimov, and V. I. Korepanov, Mater. Res. Bull. 48(10), 3955 (2013). https://doi.org/10.1016/j.materresbull.2013.06.015359. Z. Honda, Y. Sakaguchi, M. Tashiro, M. Hagiwara, T. Kida, M. Sakai, T. Fukuda, and N. Kamata, Appl. Phys. Lett. 110(13), 133101 (2017). https://doi.org/10.1063/1.4979030360. P. Wang, X. Jiang, J. Hu, X. Huang, and J. Zhao, J. Mater. Chem. C 4(11), 2147 (2016). https://doi.org/10.1039/C5TC04402B As listed in Table V, 3d and 5d transition metal substituted Pc frameworks have attracted much attention in the field of 2D magnetism.

Experimentally, Able et al. reported that 2D polymeric arrays of [email protected] can be obtained by co-evaporation of Fe and 1,2,4,5-tetracyanobenzene (TCNB) with 2:1 stoichiometry in ultrahigh vacuum condition onto Au(111), Ag(111) and even insulating NaCl substrates.361361. M. Abel, S. Clair, O. Ourdjini, M. Mossoyan, and L. Porte, J. Am. Chem. Soc. 133(5), 1203 (2011). https://doi.org/10.1021/ja108628r [email protected] film can be synthesized through the reaction of pyromellitic acid tetranitrile (PMTN) with copper in a CVD set-up.358358. D. M. Sedlovets, M. V. Shuvalov, Y. V. Vishnevskiy, V. T. Volkov, I. I. Khodos, O. V. Trofimov, and V. I. Korepanov, Mater. Res. Bull. 48(10), 3955 (2013). https://doi.org/10.1016/j.materresbull.2013.06.015 As reported by Honda et al.,359359. Z. Honda, Y. Sakaguchi, M. Tashiro, M. Hagiwara, T. Kida, M. Sakai, T. Fukuda, and N. Kamata, Appl. Phys. Lett. 110(13), 133101 (2017). https://doi.org/10.1063/1.4979030 XRD analysis, TEM characterization, and magnetization measurements of 2D [email protected] sheets revealed the existence of antiferromagnetic exchange interactions between neighboring Cu2+ ions.

According to the linking way, there are two kinds of [email protected] structures. As displayed in Figs. 15(a) and 15(b), they possess tetragonal symmetry with space group of P4/mmm ([email protected]) and six-fold symmetry within a Kagome lattice ([email protected]), respectively. Among them, [email protected] and [email protected] have been proven to be stable antiferromagnetic semiconductors, while [email protected] and [email protected] are ferromagnetic half-metals. MC simulations within Ising model or Heisenberg model have revealed phase transition between FM and PM states at a critical temperature of 150 K and 125 K for [email protected] and [email protected], respectively.101,362101. J. Zhou and Q. Sun, J. Am. Chem. Soc. 133(38), 15113 (2011). https://doi.org/10.1021/ja204990j362. H. Chen, H. Shan, A. Zhao, and B. Li, Chinese J. Chem. Phys. 32(5), 563 (2019). https://doi.org/10.1063/1674-0068/cjcp1810227 However, Fe, Co and Cu-based systems exhibit different magnetic couplings under tetragonal and hexagonal lattices. The magnetic coupling in [email protected] and [email protected] belongs to weak FM and weak AFM, respectively. In [email protected] and [email protected], dxz and dyz orbitals of metal atoms hybridize strongly with p electrons of Pc in the proximity of Fermi level, thereby leading to robust long-range ferromagnetic ordering.101,362101. J. Zhou and Q. Sun, J. Am. Chem. Soc. 133(38), 15113 (2011). https://doi.org/10.1021/ja204990j362. H. Chen, H. Shan, A. Zhao, and B. Li, Chinese J. Chem. Phys. 32(5), 563 (2019). https://doi.org/10.1063/1674-0068/cjcp1810227 In contrast, the other 2D [email protected] frameworks have larger bandgaps so that their magnetic couplings are relatively weaker.

FIG. 15. Geometric structures of (a) [email protected], (b) [email protected], (c) Mo2@Pc, (d) [email protected], (e) [email protected], (f) [email protected], (g) [email protected], (h) [email protected], (i) [email protected], (j) [email protected], (k) [email protected], and (l) [email protected] and [email protected] Panel (a) reproduced from Honda et al., Appl. Phys. Lett. 110, 133101 (2017), with the permission of AIP Publishing.359359. Z. Honda, Y. Sakaguchi, M. Tashiro, M. Hagiwara, T. Kida, M. Sakai, T. Fukuda, and N. Kamata, Appl. Phys. Lett. 110(13), 133101 (2017). https://doi.org/10.1063/1.4979030 Panel (b) reproduced with permission from Chen et al., Chinese J. Chem. Phys. 32, 563 (2019). Copyright 2019 Chinese Physics Society.362362. H. Chen, H. Shan, A. Zhao, and B. Li, Chinese J. Chem. Phys. 32(5), 563 (2019). https://doi.org/10.1063/1674-0068/cjcp1810227 Panel (c) reproduced with permission from Zhu et al., J. Phys. Chem. A 118, 304 (2014). Copyright 2014 American Chemical Society.366366. G. Zhu, M. Kan, Q. Sun, and P. Jena, J. Phys. Chem. A 118(1), 304 (2014). https://doi.org/10.1021/jp4109255 Panel (d) reproduced with permission from Li et al., Chem. Sci. 8, 2859 (2017). Licensed under a Creative Commons Attribution (CC-BY-3.0).367367. W. Li, L. Sun, J. Qi, P. Jarillo-Herrero, M. Dincă, and J. Li, Chem. Sci. 8(4), 2859 (2017). https://doi.org/10.1039/C6SC05080H Panel (e) reproduced with permission from Singh et al., J. Phys. Chem. C 119, 25657 (2015). Copyright 2015 American Chemical Society.7979. H. K. Singh, P. Kumar, and U. V. Waghmare, J. Phys. Chem. C 119(45), 25657 (2015). https://doi.org/10.1021/acs.jpcc.5b09763 Panels (f) and (g) reproduced with permission from Sun et al., J. Mater. Chem. C 3, 6901 (2015). Copyright 2015 Royal Society of Chemistry.368368. Q. Sun, Y. Dai, Y. Ma, X. Li, W. Wei, and B. Huang, J. Mater. Chem. C 3(26), 6901 (2015). https://doi.org/10.1039/C5TC01493J Panel (h) reproduced with permission from Chakravarty et al., J. Phys. Chem. C 120, 28307 (2016). Copyright 2016 American Chemical Society.372372. C. Chakravarty, B. Mandal, and P. Sarkar, J. Phys. Chem. C 120(49), 28307 (2016). https://doi.org/10.1021/acs.jpcc.6b09416 Panel (i) reproduced with permission from Zhang et al., Nano Lett. 17, 6166 (2017). Copyright 2017 American Chemical Society.375375. X. Zhang, Y. Zhou, B. Cui, M. Zhao, and F. Liu, Nano Lett. 17(10), 6166 (2017). https://doi.org/10.1021/acs.nanolett.7b02795 Panel (j) reproduced with permission from Li et al., J. Phys. Chem. Lett. 10, 2439 (2019). Copyright 2019 American Chemical Society.77. X. Li and J. Yang, J. Phys. Chem. Lett. 10(10), 2439 (2019). https://doi.org/10.1021/acs.jpclett.9b00769 Panel (k) reproduced with permission from Ma et al., J. Phys. Chem. A 117, 5171 (2013). Copyright 2013 American Chemical Society.378378. Y. Ma, Y. Dai, W. Wei, L. Yu, and B. Huang, J. Phys. Chem. A 117(24), 5171 (2013). https://doi.org/10.1021/jp402637f Panel (l) left reproduced with permission from Wang et al., Rev. Lett. 110, 196801 (2013). Copyright 2013 American Physical Society.383383. Z. Wang, Z. Liu, and F. Liu, Phys. Rev. Lett. 110(19), 196801 (2013). https://doi.org/10.1103/PhysRevLett.110.196801 Panel (l) right reproduced with permission from Zhang et al., Chem. Sci. 10, 10381 (2019). Licensed under a Creative Commons Attribution (CC BY-NC 3.0).385385. L.-C. Zhang, L. Zhang, G. Qin, Q.-R. Zheng, M. Hu, Q.-B. Yan, and G. Su, Chem. Sci. 10(44), 10381 (2019). https://doi.org/10.1039/C9SC03816G

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During 2002 and 2006, Białek's group investigated the electronic structures of a series of [email protected] (M = Fe, Co, Ni, and Cu) using the all-electron full-potential linearized augmented plane wave method.357,363–365357. B. Białek, I. G. Kim, and J. I. Lee, Surf. Sci. 526(3), 367 (2003). https://doi.org/10.1016/S0039-6028(03)00002-5363. B. Białek, I. G. Kim, and J. I. Lee, Thin Solid Films 513(1–2), 110 (2006). https://doi.org/10.1016/j.tsf.2006.01.050364. B. Białek, I. G. Kim, and J. I. Lee, Thin Solid Films 436(1), 107 (2003). https://doi.org/10.1016/S0040-6090(03)00521-2365. B. Białek, I. G. Kim, and J. I. Lee, Synth. Met. 129(2), 151 (2002). https://doi.org/10.1016/S0379-6779(02)00042-5 They found that [email protected] and [email protected] prefer long-range FM and AFM orderings with on-site magnetic moment of about 1.95 and 1.01 μB per Fe and Co atom, respectively. The result of [email protected] is consistent with that of Zhou et al.101101. J. Zhou and Q. Sun, J. Am. Chem. Soc. 133(38), 15113 (2011). https://doi.org/10.1021/ja204990j According to the spin-polarized density of state, [email protected] behaves as a half-metal and the other three systems possess moderate bandgaps in the range of 0.56 to 1.45 eV.

In addition, 5d TM single atoms and dimers adsorbed on the central hollow site of 2D Pc have been investigated using first-principles calculations.360360. P. Wang, X. Jiang, J. Hu, X. Huang, and J. Zhao, J. Mater. Chem. C 4(11), 2147 (2016). https://doi.org/10.1039/C5TC04402B The on-site magnetic moments of [email protected] and [email protected] are approximately identical (c.a. 2.4 μB). The calculations of exchange energy indicated that the magnetic ground state of [email protected] system is antiferromagnetic. Attractively, [email protected] exhibits stable FM state with a high Curie temperature of about 626 K and a perpendicular MAE of about 20.7 meV. When a homonuclear dimer is adsorbed on Pc framework (denoted as TM2@Pc), the MAE can be greatly enhanced,360360. P. Wang, X. Jiang, J. Hu, X. Huang, and J. Zhao, J. Mater. Chem. C 4(11), 2147 (2016). https://doi.org/10.1039/C5TC04402B i.e., 26.9, 40.7, and 47.2 meV for Ta2@Pc, Os2@Pc, and Re2@Pc, respectively. Among those systems, Os2@Pc and Ir2@Pc are FM with TC of 52 and 91 K, respectively. For 4d transition metals, Mo dimer embedded in Pc with another kind of atomic arrangement shown in Fig. 15(c) has been discussed by Sun's group.366366. G. Zhu, M. Kan, Q. Sun, and P. Jena, J. Phys. Chem. A 118(1), 304 (2014). https://doi.org/10.1021/jp4109255 In this 2D material, each Mo atom has a magnetic moment of about 0.88 μB, and the entire Mo2@Pc system adopts AFM ground state. Using DFT calculations with the hybrid HSE06 functional, a direct gap of about 0.93 eV was obtained.

By replacing Pc with octaamino-substituted phthalocyanines (OIPc) and square planar Ni2+ ions, a new kind of square 2D MOFs with two different 4-coordinated transition metal centers in each unit cell has been predicted.367367. W. Li, L. Sun, J. Qi, P. Jarillo-Herrero, M. Dincă, and J. Li, Chem. Sci. 8(4), 2859 (2017). https://doi.org/10.1039/C6SC05080H The OIPc organic molecule enables strong conjugation of π electrons, having a critical impact on the magnetic properties of the 2D lattices [Fig. 15(d)]. Among these charge neutral 2D MOFs candidates, [email protected] exhibits a half-metallic and ferromagnetic ground state. The large exchange energy of [email protected] results from the unique strong hybridization between d/π orbitals of Mn, Pc ring, and Ni-bisphenylenediimine nodes. This picture is consistent with the [email protected] mentioned above. In addition, CrNi, FeNi, CoNi, and CuNi-based systems are all narrow-band-gap semiconductors (0.28∼0.35 eV) with weak AFM coupling.367367. W. Li, L. Sun, J. Qi, P. Jarillo-Herrero, M. Dincă, and J. Li, Chem. Sci. 8(4), 2859 (2017). https://doi.org/10.1039/C6SC05080H

The porphyrin (Pp) ligand consisting of four pyrroles, is a planar, dianionic macrocycle with four nitrogen donors in a square planar arrangement with a hole size of around 2.0 Å in radius. Using Pp molecule as building block, a series of stable four-coordination 2D periodic metal porphyrin frameworks ([email protected]) have been proposed in recent years,79,8079. H. K. Singh, P. Kumar, and U. V. Waghmare, J. Phys. Chem. C 119(45), 25657 (2015). https://doi.org/10.1021/acs.jpcc.5b0976380. J. Tan, W. Li, X. He, and M. Zhao, RSC Adv. 3(19), 7016 (2013). https://doi.org/10.1039/c3ra40502h which are formed by embedding transition metal atoms in poly-Pp framework. Based on different bridged ligands, the Pp frameworks can be labeled as Pp, Pp0, and Pp45, which are shown in Figs. 15(e), 15(f), and 15(g), respectively. Benefiting from the abundant combinations of metal atoms, Pp frameworks, and bridged ligands, many 2D MOFs with diverse magnetic ground states can be designed.

When Fe and Cu atoms are embedded in Pp and Pp0 frameworks, AFM ground state is more favorable than FM ground state. For the other TM elements, magnetic coupling of ground state is sensitive to the organic frameworks and transition metals. As summarized in Table V, [email protected], [email protected], and [email protected] are FM; [email protected] and [email protected] are AFM; while [email protected], [email protected], and [email protected] are PM. In [email protected]8080. J. Tan, W. Li, X. He, and M. Zhao, RSC Adv. 3(19), 7016 (2013). https://doi.org/10.1039/c3ra40502h and [email protected] sheets,7979. H. K. Singh, P. Kumar, and U. V. Waghmare, J. Phys. Chem. C 119(45), 25657 (2015). https://doi.org/10.1021/acs.jpcc.5b09763 robust FM ordering is obtained with considerable TC of 187 and 197 K, respectively. Interestingly, half-metallicity can be achieved in these 2D systems as the Fermi level is lifted up via electron doping.8080. J. Tan, W. Li, X. He, and M. Zhao, RSC Adv. 3(19), 7016 (2013). https://doi.org/10.1039/c3ra40502h The magnetic coupling in Mn, Fe, Co, and Cu-based [email protected] systems are all AFM with on-site magnetic moment of 3.8, 2, 1 and 1.4 μB, respectively. For [email protected] and [email protected] nanosheets, the interactions between the local magnetic moments are almost negligible due to the large lattice constant, thereby exhibiting PM feature. Among the metal-embedded Pp0 frameworks, only [email protected] framework exhibits half-metallic nature as well as long-range FM coupling with room-temperature TC of about 320 K, whereas 2D [email protected], [email protected], and [email protected] MOFs prefer weak antiferromagnetic coupling and [email protected] exhibits PM behavior.368368. Q. Sun, Y. Dai, Y. Ma, X. Li, W. Wei, and B. Huang, J. Mater. Chem. C 3(26), 6901 (2015). https://doi.org/10.1039/C5TC01493J In Pp45 frameworks incorporated with 3d TM atoms, the inter-spin coupling is identified to be PM, mainly arising from their long spin coherence length. Meanwhile, different magnetic coupling states and large perpendicular magnetic anisotropy (PMA) in Pp45 frameworks are induced by various 5d TM atoms.369369. P. Wang, X. Jiang, J. Hu, and J. Zhao, Adv. Sci. 4(10), 1700019 (2017). https://doi.org/10.1002/advs.201700019

Moreover, the magnetic moment and magnetic anisotropy can be modified by replacing the peripheral H atoms of Pp framework by methyl (-CH3), hydroxyl (-OH), and amino (-NH2) radicals, denoted as [email protected], [email protected], and [email protected], respectively. Among them, [email protected] based systems prefer AFM coupling, and the coupling strength is gradually strengthened with the electron donating capacity increasing, which is ascribed to the functional radicals. The on-site magnetic moment and PMA can be tailored in range of 2.3∼2.7 μB and 24∼36.7 meV, respectively.369369. P. Wang, X. Jiang, J. Hu, and J. Zhao, Adv. Sci. 4(10), 1700019 (2017). https://doi.org/10.1002/advs.201700019 In contrast, [email protected] based systems prefer FM state with exchange energy over 180 meV, and the coupling strength changes slightly with functional radical. Amazingly, MAE of [email protected] framework can be greatly enhanced from 23.9 to 60.8 meV when H atoms are replaced by NH2 radicals. Furthermore, MC simulations yielded an estimated TC of ∼200 K for [email protected], suggesting that its ferromagnetism can be retained at relatively high temperature.

A group of stable 2D tetra-coordination polymer complexes linked by conjugated benzenehexathiolate following two different Kagome frameworks (M3@BHT-1 and M3@BHT-2) were also experimentally prepared or theoretically designed, and parts of them showed magnetic behavior. In them, the metal ions (M = Mg, Zn, Ni, Cu) with sixfold symmetry were successfully synthesized by the coordination reaction between benzenehexathiol (BHT) and metal acetate [M-(OAc)2], and the system with Co ions was calculated by first-principles method.355,356,370355. A. J. Clough, J. W. Yoo, M. H. Mecklenburg, and S. C. Marinescu, J. Am. Chem. Soc. 137(1), 118 (2015). https://doi.org/10.1021/ja5116937356. T. Kambe, R. Sakamoto, K. Hoshiko, K. Takada, M. Miyachi, J. H. Ryu, S. Sasaki, J. Kim, K. Nakazato, and M. Takata, J. Am. Chem. Soc. 135(7), 2462 (2013). https://doi.org/10.1021/ja312380b370. X. Huang, P. Sheng, Z. Tu, F. Zhang, J. Wang, H. Geng, Y. Zou, C.-a. Di, Y. Yi, and Y. Sun, Nat. Commun. 6(1), 1 (2015). Since BHT is a polyphosphine ligand with three dithiolene donor groups (C6S66–), a series of M3@BHT complexes were studied using first-principles calculations by considering all 3d transition metal elements. Indeed, three kinds of systems, such as Mn3C12S12,371371. M. Zhao, A. Wang, and X. Zhang, Nanoscale 5(21), 10404 (2013). https://doi.org/10.1039/c3nr03323f M3C6S6 (M3@BHT-1),372372. C. Chakravarty, B. Mandal, and P. Sarkar, J. Phys. Chem. C 120(49), 28307 (2016). https://doi.org/10.1021/acs.jpcc.6b09416 and MMg2C12S12 (M-Mg2@BHT-2),373373. L. Tang, Q. Li, C. Zhang, F. Ning, W. Zhou, L. Tang, and K. Chen, J. Magn. Magn. Mater. 488, 165354 (2019). https://doi.org/10.1016/j.jmmm.2019.165354 have been reported to possess magnetic properties. Their structural models are depicted in Figs. 15(h) and 15(i). Among Mn3C12S12 and M3@BHT-1 systems with planar spin-frustrated Kagome lattice, Mn, Fe, and Co complexes have half-metallicity and FM ground state, whereas [email protected] is stabilized in AFM ground state and behaves as a semimetal.372372. C. Chakravarty, B. Mandal, and P. Sarkar, J. Phys. Chem. C 120(49), 28307 (2016). https://doi.org/10.1021/acs.jpcc.6b09416 A similar study was reported by Liu and Sun in 2015,374374. J. Liu and Q. Sun, Chemphyschem 16(3), 614 (2015). https://doi.org/10.1002/cphc.201402713 and they predicted 2D Mn3C12N12H12 sheet to exhibit stronger FM coupling with TC of 450 K. In 2D Mn3C12N12H12 sheet, the isoelectronic NH groups take the position of sulfur atoms, which result in smaller lattice constant and larger magnetic coupling strength. Furthermore, d-p hybridization not only makes the main contribution to the stable π-conjugated planar Kagome framework structure but also results in favorable FM magnetic coupling.

Based on DFT calculations, it was found that Cu3C6H6 monolayer ([email protected]) is a FM metal with an altralow TC of about 4 K,375375. X. Zhang, Y. Zhou, B. Cui, M. Zhao, and F. Liu, Nano Lett. 17(10), 6166 (2017). https://doi.org/10.1021/acs.nanolett.7b02795 while 2D Mg3C6S6 is a nonmagnetic semiconductor.376376. L. Tang, L. Tang, D. Wang, H. Deng, and K. Chen, J. Phys.: Condens. Matter 30(46), 465301 (2018). https://doi.org/10.1088/1361-648X/aae618 The atomic model is shown in Fig. 15(i). When one of the Mg atoms in nonmagnetic Mg3C6S6 is substituted by a 3d transition metal atom (i.e., Sc∼Co), intrinsically magnetic and semiconducting properties can be observed. Among these 2D systems, FM state is more stable than PM state for V-Mg2@BHT-2 with rather high TC of 471 K.373373. L. Tang, Q. Li, C. Zhang, F. Ning, W. Zhou, L. Tang, and K. Chen, J. Magn. Magn. Mater. 488, 165354 (2019). https://doi.org/10.1016/j.jmmm.2019.165354 The π-d coupling between central metal atom and organic ligands effectively regulates the spin-polarized state of these systems and the coupling strength is greatly influenced by the magnetic moment of TM atoms and interatomic distance.

Apart from the above systems, magnetic MOFs have also been identified in other 2D materials with tetra-coordination, such as TM3HITP2 (HITP = 2, 3, 6, 7, 10, 11-hexaiminotriphenylene),377377. L. Dong, Y. Kim, D. Er, A. M. Rappe, and V. B. Shenoy, Phys. Rev. Lett. 116(9), 096601 (2016). https://doi.org/10.1103/PhysRevLett.116.096601 [email protected] (DPP = diketopyrrolopyrrole),125125. X. Li and J. Yang, J. Am. Chem. Soc. 141(1), 109 (2019). https://doi.org/10.1021/jacs.8b11346 [email protected] (TCNQ = 7,7,8,8-tetracyanoquinodimethane),378378. Y. Ma, Y. Dai, W. Wei, L. Yu, and B. Huang, J. Phys. Chem. A 117(24), 5171 (2013). https://doi.org/10.1021/jp402637f TM-naphthalene,8282. B. Mandal and P. Sarkar, Phys. Chem. Chem. Phys. 17(26), 17437 (2015). https://doi.org/10.1039/C5CP01359C [email protected],379379. A. Pimachev, R. D. Nielsen, A. Karanovich, and Y. Dahnovsky, Phys. Chem. Chem. Phys. 21(46), 25820 (2019). https://doi.org/10.1039/C9CP04509K and [email protected] (PTC = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12-perthiolated coronene).380380. R. Dong, Z. Zhang, D. C. Tranca, S. Zhou, M. Wang, P. Adler, Z. Liao, F. Liu, Y. Sun, W. Shi, Z. Zhang, E. Zschech, S. C. B. Mannsfeld, C. Felser, and X. Feng, Nat. Commun. 9(1), 2637 (2018). https://doi.org/10.1038/s41467-018-05141-4 In 2014 and 2015, the experimentally synthesized Ni3(HITP)2 and Cu3(HITP)2 were reported to be semiconductors with high electrical conductivity.353,381353. D. Sheberla, L. Sun, M. A. Blood-Forsythe, S. l. Er, C. R. Wade, C. K. Brozek, A. n. Aspuru-Guzik, and M. Dinca˘, J. Am. Chem. Soc. 136(25), 8859 (2014). https://doi.org/10.1021/ja502765n381. M. G. Campbell, D. Sheberla, S. F. Liu, T. M. Swager, and M. Dincă, Angew. Chem. Int. Ed. 54(14), 4349 (2015). https://doi.org/10.1002/anie.201411854 Later, QAH effect in TM3(HIPT)2 was theoretically predicted by Dong et al.377377. L. Dong, Y. Kim, D. Er, A. M. Rappe, and V. B. Shenoy, Phys. Rev. Lett. 116(9), 096601 (2016). https://doi.org/10.1103/PhysRevLett.116.096601 In their study, Ta3(HITP)2, Re3(HITP)2, and Ir3(HITP)2 monolayers are ferromagnetic narrow-band-gap semiconductors with magnetic moment of 1 μB per TM atom. When all N atoms in TM3(HITP)2 are substituted by O atoms, the resulted Ta3(C18H12O6)2 and Ir3(C18H12O6)2 systems retain FM ground state. Meanwhile, QAH effect could be successfully realized at much higher temperature by chemical modification in Ta3(C18H12O6)2. The magnetic moment of Ta ion is greatly enhanced to 3 μB as compared to that of Ta3(HITP)2 (1 μB).377377. L. Dong, Y. Kim, D. Er, A. M. Rappe, and V. B. Shenoy, Phys. Rev. Lett. 116(9), 096601 (2016). https://doi.org/10.1103/PhysRevLett.116.096601 The ground state of 2D V(Cr)-diketopyrrolopyrrole (DPP), as shown in Fig. 15(j), was theoretically predicted to be ferrimagnetic with an exchange energy more than 426 meV (328 meV).77. X. Li and J. Yang, J. Phys. Chem. Lett. 10(10), 2439 (2019). https://doi.org/10.1021/acs.jpclett.9b00769 The robust ferrimagnetic ordering originates from strong d-p direct exchange interactions between conjugated electron acceptors and electron providers.125125. X. Li and J. Yang, J. Am. Chem. Soc. 141(1), 109 (2019). https://doi.org/10.1021/jacs.8b11346 TM-7,7,8,8-tetracyanoquinodimethane ([email protected]), [email protected], [email protected], and [email protected] exhibit long-range AFM coupling [Fig. 15(k)], while [email protected] is PM according to DFT calculations.378378. Y. Ma, Y. Dai, W. Wei, L. Yu, and B. Huang, J. Phys. Chem. A 117(24), 5171 (2013). https://doi.org/10.1021/jp402637f For a simple 2D MOF composed of substituted naphthalene moieties and transition metals, FM coupling can be achieved in Cr- and Mn-based systems with high on-site magnetic moment of about 4 μB. Except that Mn complex is metallic, Cr, Fe, and Co complexes are all half-metallic in nature. Furthermore, Fe and Cr complexes exhibit remarkable 100% spin-filtering efficiency. Therefore, TCNQ and TM-naphthalene could serve as ideal building blocks for the candidate materials of spintronic devices.8282. B. Mandal and P. Sarkar, Phys. Chem. Chem. Phys. 17(26), 17437 (2015). https://doi.org/10.1039/C5CP01359C Another 2D ferromagnetic MOF, i.e., [email protected] [PTC = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)-perthiolated coronene] compound was synthesized from reaction of PTC with ammoniacal solutions of iron acetate [Fe(OAc)2] and exhibited a high electrical conductivity of about 10 S/cm at 300 K through the measured I–V curves, which decreased upon cooling and suggested typical feature of semiconductor.380380. R. Dong, Z. Zhang, D. C. Tranca, S. Zhou, M. Wang, P. Adler, Z. Liao, F. Liu, Y. Sun, W. Shi, Z. Zhang, E. Zschech, S. C. B. Mannsfeld, C. Felser, and X. Feng, Nat. Commun. 9(1), 2637 (2018). https://doi.org/10.1038/s41467-018-05141-4

Reducing the coordination number of transition metal centers from 4 to 3, there are still many 2D MOFs with intrinsic magnetism through rational design, such as [email protected] (M2C18H12, M= Co, Ni and Mn),382,383382. Y. Ma, Y. Dai, X. Li, Q. Sun, and B. Huang, Carbon 73, 382 (2014). https://doi.org/10.1016/j.carbon.2014.02.080383. Z. Wang, Z. Liu, and F. Liu, Phys. Rev. Lett. 110(19), 196801 (2013). https://doi.org/10.1103/PhysRevLett.110.196801 indium-phenylene ([email protected]),384384. Z. Liu, Z. Wang, J. Mei, Y. Wu, and F. Liu, Phys. Rev. Lett. 110(10), 106804 (2013). https://doi.org/10.1103/PhysRevLett.110.106804 [email protected] [PBP = 5,5′-bis(4-pyridyl)(2,2′-bipirimidine],385385. L.-C. Zhang, L. Zhang, G. Qin, Q.-R. Zheng, M. Hu, Q.-B. Yan, and G. Su, Chem. Sci. 10(44), 10381 (2019). https://doi.org/10.1039/C9SC03816G bilayer [email protected] [T4PT = 2,4,6-tris(4-pyridyl)-1,3,5-triazine],386386. T. Umbach, M. Bernien, C. F. Hermanns, A. Krüger, V. Sessi, I. Fernandez-Torrente, P. Stoll, J. I. Pascual, K. Franke, and W. Kuch, Phys. Rev. Lett. 109(26), 267207 (2012). https://doi.org/10.1103/PhysRevLett.109.267207 and Ni-thiophene (Ni2C24S6H12).387387. L. Wei, X. Zhang, and M. Zhao, Phys. Chem. Chem. Phys. 18(11), 8059 (2016). https://doi.org/10.1039/C6CP00368K Among these compounds, [email protected] framework has already been synthesized on Au(111) substrate by molecular self-assembly.354354. D. Grumelli, B. Wurster, S. Stepanow, and K. Kern, Nat. Commun. 4(1), 2904 (2013). https://doi.org/10.1038/ncomms3904 [email protected] and [email protected] (M=Co, Ni, and Mn) share the same geometry, as shown in Fig. 15(l). Except for [email protected] and [email protected], most of the above mentioned three-coordinated 2D MOFs possess amazing half-metallic Dirac point and are novel topologically nontrivial materials. Meanwhile, [email protected], [email protected], [email protected], [email protected], and Ni2C24S6H12 have been reported as 2D ferromagnets. [email protected] is the first ferromagnetic 2D MOF with the Shastry-Sutherland lattice [Fig. 15(m)], and its TC was predicted to be about 105 K, while [email protected] and [email protected] (TM = Cr, Co, Ni) were found to be AFM and magnetic-dimerized, respectively.385385. L.-C. Zhang, L. Zhang, G. Qin, Q.-R. Zheng, M. Hu, Q.-B. Yan, and G. Su, Chem. Sci. 10(44), 10381 (2019). https://doi.org/10.1039/C9SC03816G

Other 2D MOFs with even lower coordination of two have been theoretically designed. One kind of two-coordinated organometallic framework composed by (1,3,5)-benzenetricarbonitrile (TCB) molecules and noble metals (Au, Ag, and Cu) have been shown as FM half-metals with TC as high as 325 K. Besides, TCB-Re exhibits intrinsically ferromagnetic ordering with a high TC of 613 K predicted by MFT and a considerable MAE of 19 meV/atom.388388. J. Xing, P. Wang, Z. Jiang, X. Jiang, Y. Wang, and J. Zhao, APL Mater. 8(7), 071105 (2020). https://doi.org/10.1063/5.0010822 In these organometallic frameworks, the strong electronegativity of C–N groups drives the charge transfer from metal atoms to the organic molecules, forming the local magnetic centers. These magnetic centers experience strong FM and AFM couplings through d–p covalent bonding.8181. H. Sun, B. Li, and J. Zhao, J. Phys.: Condens. Matter 28(42), 425301 (2016). https://doi.org/10.1088/0953-8984/28/42/425301

In addition, many researchers have also observed 2D magnetic MOFs with hexa-coordination. Experimentally, 2D Cu-TP-1 has been synthesized under solvothermal conditions from the Cu2+ and 2-tetrazole pyrimidine (C5H5N6, H-TP). According to the field cooled (FC) and zero field cooled (ZFC) measurements, the system exhibited an antiferromagnetically coupled Cu–Cu interaction down to 8 K with a Weiss temperature around 108 K.389389. P. Pachfule, R. Das, P. Poddar, and R. Banerjee, Cryst. Growth Des. 10(6), 2475 (2010). https://doi.org/10.1021/cg1003726 Another polynuclear Cu compound showed predominant ferromagnetic coupling even at 300 K.390390. X. Zhu, J. Zhao, B. Li, Y. Song, Y. Zhang, and Y. Zhang, Inorg. Chem. 49(3), 1266 (2010). https://doi.org/10.1021/ic902404b Theoretically, Kan et al.391391. E. Kan, X. Wu, C. Lee, J. H. Shim, R. Lu, C. Xiao, and K. Deng, Nanoscale 4(17), 5304 (2012). https://doi.org/10.1039/c2nr31074k found that one kind of freestanding organometallic sheets (Ps) can be assembled by 3d TM atoms and benzene molecules. Among them, [email protected] and [email protected] are FM systems with TC of 279 K and 96 K based on MFT, respectively, while [email protected], [email protected], and [email protected] exhibit AFM ordering.391391. E. Kan, X. Wu, C. Lee, J. H. Shim, R. Lu, C. Xiao, and K. Deng, Nanoscale 4(17), 5304 (2012). https://doi.org/10.1039/c2nr31074k In these frameworks, their magnetic coupling can be explained by maximization of the virtual hopping between separated magnetic centers caused by the half-occupied dxz and dyz bands. In addition, another hexa-coordinate compound, i.e., Mn2C6S12, has also been predicted. It is a honeycomb structure and possesses stable FM state at room temperature along with spin-polarized Dirac cone. Interestingly, the exchange interaction between Mn ions is achieved by the conduction electrons of C atoms acting as the intermediate.392392. A. Wang, X. Zhang, Y. Feng, and M. Zhao, J. Phys. Chem. Lett. 8(16), 3770 (2017). https://doi.org/10.1021/acs.jpclett.7b01187

Due to large magnetic moments and remarkable magnetic anisotropy in the lanthanide ions, a series of 2D lanthanide-MOFs displayed strong magnetic interactions. Using hydrothermal method, a new 2D Dy3+ MOF was synthesized from 4-hydroxypyridine-2,6-dicarboxylic acid and showed intramolecular ferromagnetic interaction and two-step thermal magnetic relaxation.393393. C. Liu, J. Xiong, D. Zhang, B. Wang, and D. Zhu, RSC Adv. 5(127), 104854 (2015). https://doi.org/10.1039/C5RA23638J Another dysprosium layered compound from reaction with 2-(3-pyridyl) pyrimidine-4-carboxylic acid also presented FM interactions between Dy3+ ions and slowed magnetic relaxation behavior.394394. D. Yin, Q. Chen, Y. Meng, H. Sun, Y. Zhang, and S. Gao, Chem. Sci. 6(5), 3095 (2015). https://doi.org/10.1039/C5SC00491H

Another important member of 2D organic materials is COFs, which have been investigated widely as catalysts, energy storage and gas adsorption materials, and so on. Two-dimensional COFs are crystalline porous polymers formed by molecular building units and organic linkers via covalent bond without any transition metal.395,396395. X. Li, P. Yadav, and K. P. Loh, Chem. Soc. Rev. 49(14), 4835 (2020). https://doi.org/10.1039/D0CS00236D396. S. B. Alahakoon, S. D. Diwakara, C. M. Thompson, and R. A. Smaldone, Chem. Soc. Rev. 49(5), 1344 (2020). https://doi.org/10.1039/C9CS00884E Due to their transition metal free nature, it is hardly to found 2D magnets in COFs. However, some pioneer studies have proven that they can exhibit magnetic properties in the presence of some special atomic arrangements. In a theoretical study by Yang et al.,352352. E. Kan, W. Hu, C. Xiao, R. Lu, K. Deng, J. Yang, and H. Su, J. Am. Chem. Soc. 134(13), 5718 (2012). https://doi.org/10.1021/ja210822c single-layer organic porous sheets dimethylmethylene-bridged triphenylamine (DTPA) is a ferromagnetic half-metal with a bandgap in semiconducting channel of about 1 eV. In comparison with the boron-doped (FM) and pure graphene nanoflakes (GFs) (AFM), both of which possess similar molecular architecture with DTPA, the FM state can be explained by half-occupied π orbital and allowed virtual hopping for FM configurations. Graphitic carbon nitride (g-C4N3) as a novel material with FM ground state and intrinsic half-metallicity has also been theoretically predicted by Du et al.351351. A. Du, S. Sanvito, and S. C. Smith, Phys. Rev. Lett. 108(19), 197207 (2012). https://doi.org/10.1103/PhysRevLett.108.197207 According the analysis of orbital-resolved DOS, the p orbitals of N atoms rather than C atoms make the main contributions to the half-metallicity and magnetism of g-C4N3. A 2D COF with D6h symmetry, C3N, was shown to have an intrinsic indirect bandgap of 0.39 eV under FM ground state from both experimental and theoretical studies.350350. S. Yang, W. Li, C. Ye, G. Wang, H. Tian, C. Zhu, P. He, G. Ding, X. Xie, and Y. Liu, Adv. Mater. 29(16), 1605625 (2017). https://doi.org/10.1002/adma.201605625 No doubt, the above studies open a door for fundamental research and potential applications toward realistic metal-free spintronics.

IV. MODIFICATIONS

Section:

In the above discussions, we mainly focused on the database of 2D magnets and their dominant magnetic exchange interactions. For practical applications, we have to address the other issues, such as how to enhance the critical transition temperature (TC or TN) to room temperature in these existing 2D magnetic materials by post-treating with various manipulations. We have already shown that the magnetic ground state and exchange coupling strength are very sensitive to symmetry, charge distributions, Fermi level, valence states, orbital occupation, orbital hybridizations, energy level, hopping paths, and so on. According to these target parameters, many strategies have been proposed, including strain engineering, intercalation, external electronic/magnetic field, interfacial engineering, defect engineering, Janus structuring, and optical controlling. A schematic diagram of these modification mechanisms is displayed in Fig. 16.

FIG. 16. The schematic diagram of the modification mechanisms of Curie temperature of 2D magnets. Many strategies have been included, such as strain engineering, intercalation, external electronic/magnetic field, interfacial engineering, defect engineering, Janus structuring, and optical controlling.

• PPT
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• High resolution

A. Strain engineering

Strain engineering is a simple and efficient means for tailoring the magnetic properties. Experimentally, the strain effect on 2D magnets is inevitable during the synthesis processes. After exfoliation, 2D magnets (e.g., 2D CrI32828. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391) could be transferred on SiO2 substrate and other 2D materials. In addition, there are also direct MBE/CVD growth of VSe2, MnSe2, and MnSe on Si(111)/SiO2 substrates.34,3534. M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan, and M. Batzill, Nature Nanotechnol. 13(4), 289 (2018). https://doi.org/10.1038/s41565-018-0063-935. J. Li, B. Zhao, P. Chen, R. Wu, B. Li, Q. Xia, G. Guo, J. Luo, K. Zang, Z. Zhang, H. Ma, G. Sun, X. Duan, and X. Duan, Adv. Mater. 30(36), 1801043 (2018). https://doi.org/10.1002/adma.201801043 As a consequence, the lattice mismatch of substrate with 2D magnets would cause certain lattice strain. Even so, one should note that we mainly discussed 2D van der Waals materials in this review. Strain from the neighboring layers could be either non-uniform or quite small, despite the large lattice mismatch.

The effect of in-plane biaxial strain on the TC of 2D magnetic materials has been thoroughly investigated, especially on the experimentally reported systems. From the structural point of view, biaxial tensile strain would immediately increase the bond lengths and widen the bond angle between the magnetic atoms, while compressive strain would reduce the bond length and narrow the bond angle. These two factors undoubtedly affect orbital hybridization and change the magnetic exchange parameters, which are described by the distance and angle dependent GKA rules.126–128126. J. B. Goodenough, Phys. Rev. 100(2), 564 (1955). https://doi.org/10.1103/PhysRev.100.564127. J. Kanamori, J. Appl. Phys. 31(5), S14 (1960). https://doi.org/10.1063/1.1984590128. P. W. Anderson, Phys. Rev. 115(1), 2 (1959). https://doi.org/10.1103/PhysRev.115.2 Taking monolayer CrSi(Ge)Te3 as an example, herein we further explain the strain effect. As shown in Fig. 17(a), the direct AFM interaction is short-ranged and decreases rapidly with the increase of Cr–Cr distance, while the superexchange FM interaction is comparatively long-ranged and decreases relatively slowly with the increase of Cr–Te–Cr distance. Under biaxial tensile strain, the Cr–Te–Cr angle gradually approaches to normative 90°, and the FM exchange interaction is strengthened.397397. X. Chen, J. Qi, and D. Shi, Phys. Lett. A 379(1–2), 60 (2015). https://doi.org/10.1016/j.physleta.2014.10.042 These combined effects lead to increase of the energy difference between FM and AFM states. Moreover, the magnetic moment on Cr atoms increases monotonically with tensile strain.398,399398. X.-J. Dong, J.-Y. You, B. Gu, and G. Su, Phys. Rev. Appl. 12(1), 014020 (2019). https://doi.org/10.1103/PhysRevApplied.12.014020399. K. Wang, T. Hu, F. Jia, G. Zhao, Y. Liu, I. V. Solovyev, A. P. Pyatakov, A. K. Zvezdin, and W. Ren, Appl. Phys. Lett. 114(9), 092405 (2019). https://doi.org/10.1063/1.5083992 Thus, the calculated TC of CrSiTe3 by MFA dramatically increases from 22.5 K in strain-free state to 290 K under 8% strain. Figure 17(b) displays TC as a function of strain for CrGeTe3. Under 3% and 5% tensile strains, the TC can be enhanced to 326 and 421 K, respectively, in comparison to TC = 144 K for strain-free state. Under a compressive strain of 1%, the TC will decrease to 67 K.398398. X.-J. Dong, J.-Y. You, B. Gu, and G. Su, Phys. Rev. Appl. 12(1), 014020 (2019). https://doi.org/10.1103/PhysRevApplied.12.014020 The strain effect on the magnetic properties of VSe2 was investigated by DFT calculations.400400. S. Feng and W. Mi, Appl. Surf. Sci. 458, 191 (2018). https://doi.org/10.1016/j.apsusc.2018.07.070 Figures 17(c) and 17(d) show the energy difference and individual magnetic moment in strained VSe2, respectively. As the strain increases, the calculated magnetic moment of V atom increases from 0.77 to 1.18 μB. The TC is monotonously enhanced from 290 to 812 K under a strain of 6%. Similar results and underlying mechanisms have also been found in monolayer CrI3401401. Z. Wu, J. Yu, and S. Yuan, Phys. Chem. Chem. Phys. 21(15), 7750 (2019). https://doi.org/10.1039/C8CP07067A and Fe3GeTe2402402. X. Hu, Y. Zhao, X. Shen, A. V. Krasheninnikov, Z. Chen, and L. Sun, ACS Appl. Mater. Inter. 12(23), 26367 (2020). https://doi.org/10.1021/acsami.0c05530 sheets.

FIG. 17. (a) A schematic diagram of the nearest neighboring Cr–Cr direct AFM interaction and FM superexchange interaction mediated by the middle Te atom with Cr–Cr distance in monolayer CrSi(Ge)Te3. (b) Normalized magnetization as a function temperature. (c) Energy difference between FM and AFM states for monolayer VSe2 and the TC as a function of strain. (d) The calculated magnetic moments of V and Se atoms in ferromagnetic VSe2 monolayer as a function of strain. Panel (a) reproduced with permission from Chen et al., Phys. Lett. A 379, 60 (2015). Copyright 2015 Elsevier.397397. X. Chen, J. Qi, and D. Shi, Phys. Lett. A 379(1–2), 60 (2015). https://doi.org/10.1016/j.physleta.2014.10.042 Panel (b) reproduced with permission from Dong et al., Rev. Appl. 12, 014020 (2019). Copyright 2019 American Physical Society.398398. X.-J. Dong, J.-Y. You, B. Gu, and G. Su, Phys. Rev. Appl. 12(1), 014020 (2019). https://doi.org/10.1103/PhysRevApplied.12.014020 Panels (c) and (d) reproduced with permission from Feng et al., Surf. Sci. 458, 191 (2018). Copyright 2018 Elsevier.400400. S. Feng and W. Mi, Appl. Surf. Sci. 458, 191 (2018). https://doi.org/10.1016/j.apsusc.2018.07.070

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The applied strain also yields a pronounced transition of magnetic ground state from AFM to FM under tensile strain or FM to AFM under compressive strain.104,156,401,403–405104. L. Webster and J.-A. Yan, Phys. Rev. B 98(14), 144411 (2018). https://doi.org/10.1103/PhysRevB.98.144411156. F. Iyikanat, M. Yagmurcukardes, R. T. Senger, and H. Sahin, J. Mater. Chem. C 6(8), 2019 (2018). https://doi.org/10.1039/C7TC05266A401. Z. Wu, J. Yu, and S. Yuan, Phys. Chem. Chem. Phys. 21(15), 7750 (2019). https://doi.org/10.1039/C8CP07067A403. Z.-W. Lu, S.-B. Qiu, W.-Q. Xie, X.-B. Yang, and Y.-J. Zhao, J. Appl. Phys. 127(3), 033903 (2020). https://doi.org/10.1063/1.5126246404. Z. Guan, N. Luo, S. Ni, and S. Hu, Mater. Adv. 1(2), 244 (2020). https://doi.org/10.1039/D0MA00085J405. E. Vatansever, S. Sarikurt, F. Ersan, Y. Kadioglu, O. Ü. Aktürk, Y. Yüksel, C. Ataca, E. Aktürk, and Ü. Akıncı, J. Appl. Phys. 125(8), 083903 (2019). https://doi.org/10.1063/1.5078713 Depending on their ground states, the critical strains for phase transition in 2D CrTe3, RuCl3, and CrI3 are 3%, 2%, and –5%, respectively. However, the tensile strain induced TC enhancement and magnetic transition are not found in the ferromagnetic NiX3 (X = I, Br, Cl) sheets. In these materials, compressive strain will enhance their TC and induce a FM to AFM transition (8%). In fact, this is still consistent with GKA rules. In NiX3 (X = I, Br, Cl), the intrinsic angle of Ni–X–Ni is about 95°, which deviates from 90°. The tensile strain would further enlarge the Ni–X–Ni angle, which weakens FM coupling and strengthens AFM coupling.406406. Z. Li, B. Zhou, and C. Luan, RSC Adv. 9(61), 35614 (2019). https://doi.org/10.1039/C9RA06474E

In addition to the magnetic coupling parameters and TC, MAE is another significant magnetic characteristic that can be successfully modulated by strain engineering. According to the second-order perturbation theory, the value of MAE is very sensitive to strain, and no consistent mechanism has been found. For example, MAE increases with compressive strain in monolayer 1T-FeCl2 because of the enhanced positive contribution to MAE from the SOC interaction between dx2-y2 (dxy) and dyz (dxz) orbitals of Fe atom.407407. H. Zheng, J. Zheng, C. Wang, H. Han, and Y. Yan, J. Magn. Magn. Mater. 444, 184 (2017). https://doi.org/10.1016/j.jmmm.2017.08.005 Han et al. reported that MAE of monolayer CrSI is mainly contributed by spin-polarized p-orbitals of nonmetal I atoms. The compressive strain enhances the MAE value to 0.52 meV/atom, which originates from the positive contribution of matrix element difference between spin-up px and py orbitals as well as spin-up py and pz orbitals of I atoms.408408. R. Han and Y. Yan, Phys. Chem. Chem. Phys. 21(37), 20892 (2019). https://doi.org/10.1039/C9CP03535D

B. Intercalation

Owing to the existence of VDW gap and weak interlayer interaction, 2D materials are ideal host materials for various intercalant species, including small ions, atoms, and molecules. Chemical intercalation and electrochemical intercalation are two common methods to prepare intercalated systems.409–416409. S. C. Ganguli, H. Singh, I. Roy, V. Bagwe, D. Bala, A. Thamizhavel, and P. Raychaudhuri, Phys. Rev. B 93(14), 144503 (2016). https://doi.org/10.1103/PhysRevB.93.144503410. T. H. Bointon, I. Khrapach, R. Yakimova, A. V. Shytov, M. F. Craciun, and S. Russo, Nano Lett. 14(4), 1751 (2014). https://doi.org/10.1021/nl4040779411. J. Seel and J. Dahn, J. Electrochem. Soc. 147(3), 892 (2000). https://doi.org/10.1149/1.1393288412. D. Voiry, H. Yamaguchi, J. Li, R. Silva, D. C. Alves, T. Fujita, M. Chen, T. Asefa, V. B. Shenoy, and G. Eda, Nat. Mater. 12(9), 850 (2013). https://doi.org/10.1038/nmat3700413. K. J. Koski, C. D. Wessells, B. W. Reed, J. J. Cha, D. Kong, and Y. Cui, J. Am. Chem. Soc. 134(33), 13773 (2012). https://doi.org/10.1021/ja304925t414. H. Yuan, H. Wang, and Y. Cui, Acc. Chem. Res. 48(1), 81 (2015). https://doi.org/10.1021/ar5003297415. J. P. Motter, K. J. Koski, and Y. Cui, Chem. Mater. 26(7), 2313 (2014). https://doi.org/10.1021/cm500242h416. N. I. Kovtyukhova, Y. Wang, R. Lv, M. Terrones, V. H. Crespi, and T. E. Mallouk, J. Am. Chem. Soc. 135(22), 8372 (2013). https://doi.org/10.1021/ja403197h For example, Zhao et al. showed that self-intercalation of native atoms into bilayer transition metal dichalcogenides during growth generates a class of ultrathin, covalently bonded materials.417417. X. Zhao, P. Song, C. Wang, A. C. Riis-Jensen, W. Fu, Y. Deng, D. Wan, L. Kang, S. Ning, and J. Dan, Nature 581(7807), 171 (2020). https://doi.org/10.1038/s41586-020-2241-9 To date, intercalation has been proven as a powerful approach to induce local spin and long-range magnetic ordering in the 2D non-magnetic materials.417–422417. X. Zhao, P. Song, C. Wang, A. C. Riis-Jensen, W. Fu, Y. Deng, D. Wan, L. Kang, S. Ning, and J. Dan, Nature 581(7807), 171 (2020). https://doi.org/10.1038/s41586-020-2241-9418. E. Morosan, H. Zandbergen, L. Li, M. Lee, J. Checkelsky, M. Heinrich, T. Siegrist, N. P. Ong, and R. Cava, Phys. Rev. B 75(10), 104401 (2007). https://doi.org/10.1103/PhysRevB.75.104401419. W. J. Hardy, C.-W. Chen, A. Marcinkova, H. Ji, J. Sinova, D. Natelson, and E. Morosan, Phys. Rev. B 91(5), 054426 (2015). https://doi.org/10.1103/PhysRevB.91.054426420. C. Zhang, Y. Yuan, M. Wang, P. Li, J. Zhang, Y. Wen, S. Zhou, and X.-X. Zhang, Phys. Rev. Mater. 3(11), 114403 (2019). https://doi.org/10.1103/PhysRevMaterials.3.114403421. V. Pleshchev and N. Selezneva, Phys. Solid State 61(3), 339 (2019). https://doi.org/10.1134/S1063783419030259422. X. Zhang, Y. Sun, L. Ma, X. Zhao, and X. Yao, Nanotechnology 29(30), 305706 (2018). https://doi.org/10.1088/1361-6528/aac320 In the 2D intrinsic magnets, intercalation can further modulate the electronic structure, reduce the interlayer coupling, and change the valence state of magnetic ions by doping electron/hole.

Wang et al.423423. N. Wang, H. Tang, M. Shi, H. Zhang, W. Zhuo, D. Liu, F. Meng, L. Ma, J. Ying, and L. Zou, J. Am. Chem. Soc. 141(43), 17166 (2019). https://doi.org/10.1021/jacs.9b06929 successfully intercalated organic tetrabutyl ammonium (TBA) cations into Cr2Ge2Te6 [Fig. 18(a)] and obtained a hybrid superlattice of (TBA)Cr2Ge2Te6. Such electron doping leads to metallic behavior of (TBA)Cr2Ge2Te6 at low temperature. Meanwhile, the Curie temperature has been significantly elevated to 208 K [Fig. 18(b)]. For comparison, pristine Cr2Ge2Te6 is a FM semiconductor with TC of 67 K only. The underlying exchange coupling mechanism is illustrated in Fig. 18(c). A weak superexchange mechanism is found in Cr2Ge2Te6 semiconductor, while double exchange mechanism is dominated in FM metallic (TBA)Cr2Ge2Te6. Weber et al. demonstrated that Fe2.78GeTe2 can be topotactically intercalated with sodium in the presence of benzophenone to yield NaFe2.78GeTe2.424424. D. Weber, A. H. Trout, D. W. McComb, and J. E. Goldberger, Nano Lett. 19(8), 5031 (2019). https://doi.org/10.1021/acs.nanolett.9b01287 The measured Curie temperatures of both Fe2.78GeTe2 and NaFe2.78GeTe2 from SQUID magnetometry were about 150 K. Even though the Curie temperature has not been appreciably changed, positive evidence of room-temperature magnetism resulted from the presence of Fe2−xGe impurity was observed. Moreover, Qiu et al. have revealed sensitive dependence of Fe3GeTe2 TC on its environmental change by Ga implantation. The TC of bulk Fe3GeTe2 could increase up to 450 K by controlling the fluence of Ga irradiation, while the magnetic anisotropy could be inversed to in-plane direction.425425. M. Yang, Q. Li, R. V. Chopdekar, C. Stan, S. Cabrini, J. W. Choi, S. Wang, T. Wang, N. Gao, A. Scholl, N. Tamura, C. Hwang, F. Wang, and Z. Qiu, Adv. Quantum Technolog. 3(4), 2000017 (2020). https://doi.org/10.1002/qute.202000017

FIG. 18. (a) Side view plot of crystal structure of pristine Cr2Ge2Te6 and (TBA)Cr2Ge2Te6. Organic ion tetrabutyl ammonium is added into the van der Waals gap via electrochemical intercalated. (b) Temperature-dependent magnetic susceptibility of Cr2Ge2Te6 and (TBA)Cr2Ge2Te6. The Curie temperature is largely increased from 67 K in Cr2Ge2Te6 to 208 K in intercalated (TBA)Cr2Ge2Te6. (c) Schematic diagram of intercalation-induced magnetic exchange mechanism transition (from superexchange interaction to double exchange interaction). Reproduced with permission from Wang et al., J. Am. Chem. Soc. 141, 17166 (2019). Copyright 2019 American Chemical Society.423423. N. Wang, H. Tang, M. Shi, H. Zhang, W. Zhuo, D. Liu, F. Meng, L. Ma, J. Ying, and L. Zou, J. Am. Chem. Soc. 141(43), 17166 (2019). https://doi.org/10.1021/jacs.9b06929

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In a recent theoretical study, Guo et al.426426. Y. Guo, N. Liu, Y. Zhao, X. Jiang, Si Zhou, and J. Zhao, Chin. Phys. Lett. 37(10), 107506 (2020). https://doi.org/10.1088/0256-307X/37/10/107506 found that self-filling either Cr or I atoms into the vdW gap of stacked and twisted CrI3 bilayer sheets can significantly strengthen the interlayer FM coupling. The exchange energy increases with the intercalated Cr concentration, reaching about 40 meV per formula compared to the values of pristine CrI3 bilayer (2.95 meV/f.u. for the low-temperature stacked phase and −0.14 meV/f.u. for the high-temperature phase). Such strong ferromagnetism of self-intercalated CrI3 bilayer results from the mid-gap states due to eg-t2g hybridization, which is related to the additional electron hoping paths through intercalated atoms, bridging I atoms, and intralayered Cr atoms. On the other hand, the intercalated and intralayer Cr atoms show different oxidation states. In turn, double exchange interaction among them would take over superexchange interaction to determine the magnetic behavior. Thus, much higher TC with regard to that of pristine CrI3 bilayer (low-temperature phase) is highly anticipated.

C. Electric control magnetism

As the essential tools for electric control of magnetism, the effects of electrostatic/ion liquid gating and electric field on the magnetic properties of the recently emerged 2D magnets have been investigated. These studies offer exciting prospects of 2D magnets for processing and storing information in future spintronics. Due to the ultrathin nature of 2D magnets, electrostatic/ion liquid gating and electric field could largely modify the carrier concentration, electron population, orbital occupation, symmetry, and bandgap, which would further lead to the adjustment of magnetic ground state, exchange parameters, and magnetic anisotropy.

Jiang et al.427427. S. Jiang, L. Li, Z. Wang, K. F. Mak, and J. Shan, Nat. Nanotechnol. 13(7), 549 (2018). https://doi.org/10.1038/s41565-018-0135-x demonstrated control of the magnetic properties in both monolayer and bilayer CrI3 by electrostatic doping. The doping effect on the magnetic properties of monolayer CrI3 is illustrated in Fig. 19(a). From the saturation magnetization, coercive force, and Curie temperature, one can see strengthened/weakened magnetic ordering with hole/electron doping (–3 × 1013 to 3 × 1013). The TC of monolayer was finally modulated between 40 and 50 K. The doping effect on the magnetic properties of bilayer CrI3 is shown in Fig. 19(b). The AFM phase shrinks continuously with increasing electron doping density. As electron doping concentration increases to 2.5 × 1013 cm−2, the AFM ground state of bilayer CrI3 would transform into FM. Under different gate voltages, the spin-flip field and interlayer exchange constant are extracted in Fig. 19(c).427427. S. Jiang, L. Li, Z. Wang, K. F. Mak, and J. Shan, Nat. Nanotechnol. 13(7), 549 (2018). https://doi.org/10.1038/s41565-018-0135-x

FIG. 19. (a) Coercive force, saturation magnetization, and Curie temperature as a function of gate voltage and gate induced doping density of bilayer CrI3. (b) Doping density–magnetic field phase diagram of bilayer CrI3 at 4 K. (c) Interlayer exchange constant and spin-flip transition field as a function of gate voltage and gate induced doping density for bilayer CrI3. (d) Uniaxial magnetic anisotropy fields and TC for different gate voltage of few-layer Cr2Ge2Te6. (e) MAE of few-layer Cr2Ge2Te6 as a function of electron density. (f) Phase diagram of trilayer Fe3GeTe2 sample varies with the gate voltage and temperature. (g) The DOS of 0.5 hole and 0.5 electron doped CrI3 monolayer, and the dashed vertical lines refer to the shifting of Fermi level. (h) Relative energy of AFM and FM states under the variation of carrier concentration for CrI3 monolayer. (i) Relative energy of AFM and FM states under the variation of carrier concentration for 2D MnPSe3. Panels (a)–(c) reproduced with permission from Jiang et al., Nat. Nanotechnol. 13, 549 (2018). Copyright 2018 Springer Nature.427427. S. Jiang, L. Li, Z. Wang, K. F. Mak, and J. Shan, Nat. Nanotechnol. 13(7), 549 (2018). https://doi.org/10.1038/s41565-018-0135-x Panels (d) and (e) reproduced with permission from Verzhbitskiy et al., Nat. Electron. 3, 460 (2020). Copyright 2020 Springer Nature.431431. I. A. Verzhbitskiy, H. Kurebayashi, H. Cheng, J. Zhou, S. Khan, Y. P. Feng, and G. Eda, Nat. Electron. 3(8), 460 (2020). https://doi.org/10.1038/s41928-020-0427-7 Panel (f) reproduced with permission from Deng et al., Nature 563, 94 (2018). Copyright 2018 Springer Nature.5050. Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen, and Y. Zhang, Nature 563(7729), 94 (2018). https://doi.org/10.1038/s41586-018-0626-9 Panels (g) and (h) reproduced with permission from Wang et al., Europhys. Lett. 114, 47001 (2016). Copyright 2016 IOP.88. H. Wang, F. Fan, S. Zhu, and H. Wu, Europhys. Lett. 114(4), 47001 (2016). https://doi.org/10.1209/0295-5075/114/47001 Panel (i) reproduced with permission from Li et al., J. Am. Chem. Soc. 136, 11065 (2014). Copyright 2014 American Chemical Society.307307. X. Li, X. Wu, and J. Yang, J. Am. Chem. Soc. 136(31), 11065 (2014). https://doi.org/10.1021/ja505097m

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Two different gated bilayer CrI3 devices have been built by Huang et al.,428428. B. Huang, G. Clark, D. R. Klein, D. MacNeill, E. Navarro-Moratalla, K. L. Seyler, N. Wilson, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao, P. Jarillo-Herrero, and X. Xu, Nat. Nanotechnol. 13(7), 544 (2018). https://doi.org/10.1038/s41565-018-0121-3 and their magnetic behavior has been probed by MOKE microscopy. Under fixed magnetic fields, voltage-controlled switching between antiferromagnetic and ferromagnetic states was also found. Under zero magnetic fields, two distinct layered AFM states (“↑↓” and “↓↑”) exist on gate voltage, which are related to two initialization processes. However, tunability of the net magnetization with gate voltage disappeared when the bilayer device was warmed to about 40 K, revealing that the bilayer TN is unaffected within the range of applied gate voltage. Parallel to this study, dual-gate field-effect devices were also fabricated to investigate the electric field effect on the magnetic order of bilayer CrI3. In the AFM bilayer CrI3, the applied electric field creates an interlayer potential difference, which results in a large linear magnetoelectric effect. In addition, a reversible electrical switching of magnetic order has been observed near the AFM-FM spin-flip transition point.429429. S. Jiang, J. Shan, and K. F. Mak, Nat. Mater. 17(5), 406 (2018). https://doi.org/10.1038/s41563-018-0040-6

Similar to bilayer CrI3, both gating and electronic field are able to modulate the magnetic properties of few-layer Cr2Ge2Te6. Using ionic liquid and solid Si gates, the carrier density below 103 cm−2 was obtained in Cr2Ge2Te6 FET transistors.430430. Z. Wang, T. Zhang, M. Ding, B. Dong, Y. Li, M. Chen, X. Li, J. Huang, H. Wang, X. Zhao, Y. Li, D. Li, C. Jia, L. Sun, H. Guo, Y. Ye, D. Sun, Y. Chen, T. Yang, J. Zhang, S. Ono, Z. Han, and Z. Zhang, Nat. Nanotechnol. 13(7), 554 (2018). https://doi.org/10.1038/s41565-018-0186-z With such carrier density, Cr2Ge2Te6 transistors show remarkable enhancement of saturation magnetization and reduction of saturation field. However, Micro-area Kerr measurements with different gate doping demonstrated bipolar tunable magnetization loops below the Curie temperature. The unchanged TC may be attributed to a rebalance of the spin-polarized band structure while tuning its Fermi level. Using the electrical double layers transistors with a polymer gel based on ionic liquid, a higher electron-doped concentration (∼1014 cm−2) was achieved in few-layer Cr2Ge2Te6.431431. I. A. Verzhbitskiy, H. Kurebayashi, H. Cheng, J. Zhou, S. Khan, Y. P. Feng, and G. Eda, Nat. Electron. 3(8), 460 (2020). https://doi.org/10.1038/s41928-020-0427-7 Compared to the case of low carrier density, heavy electron doping not only enhances TC to 200 K, but also turns the magnetic easy axis from out-of-plane to in-plane direction [Figs. 19(d)–19(e)]. First-principles calculations further clarified the origin of doping induced magnetic ordering. The large carrier density would render carrier-mediated indirect exchange mechanism as prevailing over the superexchange mechanism in Cr2Ge2Te6. To understand the electric field effect, Xing et al. fabricated Hall-bar devices using the nanofabrication technique. The gate voltage dependence of channel resistances for 2D Cr2Ge2Te6 devices has been investigated and a giant modulation of the channel resistance via electric field effect has been revealed.9999. W. Xing, Y. Chen, P. M. Odenthal, X. Zhang, W. Yuan, T. Su, Q. Song, T. Wang, J. Zhong, S. Jia, X. C. Xie, Y. Li, and W. Han, 2D Mater. 4(2), 024009 (2017). https://doi.org/10.1088/2053-1583/aa7034

In contrast to these FM/AFM insulators, the itinerant magnetism possibly allows more effective tuning of TC by ionic gating. As we have discussed above, the exchange mechanism of 2D Fe3GeTe2 is mediated through conduction electrons. Thus, the extreme ionic gating induced electron doping could drastically modulate DOS at the Fermi level. A trilayer Fe3GeTe2 ionic field-effect transistor was set up by covering solid electrolyte (LiClO4) on both sides. The charge transfer between lithium ions and the Fe3GeTe2 film induces electron doping up to the order of 1014 cm−2 per layer. Such high doping level boosts TC of Fe3GeTe2 to room temperature [Fig. 19(f)].5050. Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen, and Y. Zhang, Nature 563(7729), 94 (2018). https://doi.org/10.1038/s41586-018-0626-9 The gate-induced room-temperature FM ordering was also observed in a four-layer sample.

On the theoretical side, one can mimic the gating effect of 2D materials by adding carriers into the unit cell and calculate the electronic structures by neutralizing with a homogeneous charge background.88. H. Wang, F. Fan, S. Zhu, and H. Wu, Europhys. Lett. 114(4), 47001 (2016). https://doi.org/10.1209/0295-5075/114/47001 For example, Wang et al.88. H. Wang, F. Fan, S. Zhu, and H. Wu, Europhys. Lett. 114(4), 47001 (2016). https://doi.org/10.1209/0295-5075/114/47001 have explained the correlation between the Curie temperature and carrier concentration of CrI3 monolayer. As discussed above, t2g valence bands and eg conduction bands of Cr atoms are separated by the insulating gap in CrI3 monolayer. As seen in Fig. 19(g), electron doping shifts the Fermi level into conduction bands, while hole doping moves the Fermi level into valence bands. In both situations, the spin-up channel in CrI3 monolayer becomes metallic, while the spin-down channel remains insulating. This phenomenon renders the transition of exchange coupling mechanism from weak superexchange semiconductor to itinerant FM half-metal, which strongly enhances the FM stability [Fig. 19(h)] as well as the Curie temperature. To be specific, the calculated TC increases from 75 K for pure CrI3 to 150 K (300 K) for half electron (hole) doped CrI3.88. H. Wang, F. Fan, S. Zhu, and H. Wu, Europhys. Lett. 114(4), 47001 (2016). https://doi.org/10.1209/0295-5075/114/47001 In 2D AFM semiconductor MnPSe3, doping concentrations of electron (hole) above 3 × 1013 (4 × 1013) carriers/cm2 would induce a transition from antiferromagnetic semiconductor to ferromagnetic half-metal. MC simulations suggested the Curie temperature of doped 2D MnPSe3 crystal reaches up to 206 K [Fig. 19(i)].307307. X. Li, X. Wu, and J. Yang, J. Am. Chem. Soc. 136(31), 11065 (2014). https://doi.org/10.1021/ja505097m In pristine monolayer VCl3 and VI3 sheets, the Curie temperatures are only 80 and 98 K, respectively. They can be also be enhanced up to room temperature by carrier doping.161161. J. He, S. Ma, P. Lyu, and P. Nachtigall, J. Mater. Chem. C 4(13), 2518 (2016). https://doi.org/10.1039/C6TC00409A The carrier density dependent total energy differences per MAX3 formula unit (M = V, Cr, Mn, Fe, Co, Ni; A = Si, Ge, Sn; X = S, Se, Te) between the AFM and FM phases were obtained from DFT-D2 calculations.290290. B. L. Chittari, D. Lee, N. Banerjee, A. H. MacDonald, E. Hwang, and J. Jung, Phys. Rev. B 101(8), 085415 (2020). https://doi.org/10.1103/PhysRevB.101.085415 In the case of FM semiconductors, the competition between antiferromagnetic and ferromagnetic ordering can be substantially altered for n doping in VSiTe3, VSnTe3, MnSiSe3, and FeSnTe3, and p doping for NiSiSe3, NiSTe3, and MnSnTe3, respectively. Hence, the associate TC can be also tailored. The investigated range of carrier density is 1013∼1014 carriers/cm2. Based on these experimental and theoretical results, we can infer that a higher electron/hole doped concentration injected into 2D magnetic semiconductors would modulate the magnetic exchange mechanism and enhance the TC to room temperature.

Using first-principles quantum transport approach, Dolui et al.432432. K. Dolui, M. D. Petrovic, K. Zollner, P. Plechac, J. Fabian, and B. K. Nikolic, Nano Lett. 20(4), 2288 (2020). https://doi.org/10.1021/acs.nanolett.9b04556 predicted that injecting unpolarized charge current parallel to the interface of bilayer-CrI3/monolayer-TaSe2 vdW heterostructure would induce a spin-orbit torque. Such effect will convert the first CrI3 layer from AFM to FM ordering in direct contact with TaSe2 without requiring any external magnetic field. This reversible current-driven nonequilibrium AFM-FM phase transition is due to the proximity effect, where evanescent wave functions from metallic TaSe2 is injected to the first monolayer of CrI3. During this process, the second monolayer of CrI3 remains insulating.

D. Magnetic field

It is natural to utilize external magnetic field to control the magnetic properties of 2D magnets. As known, different types of magnetism are defined as how the system respond to the external magnetic fields. On the one hand, external magnetic field induced Zeeman spin splitting is used to control magnetic ordering. On the other hand, the applied magnetic field will enforce reorientation of the spin direction and thus determine their magnetic ground state. The Curie temperature may depend strongly on the applied magnetic field in terms of both strength and direction. If the external field is parallel to the direction of spontaneous magnetization, TC typically increases with increasing external magnetic field. On the contrary, the magnetic ordering can be suppressed by applying an external magnetic field of opposite direction. For the perpendicular magnetic field direction, a complicated variation may arise because of the competition between the tendencies of both orderings.

For the recently reported 2D magnets, the effect of external magnetic field has been firstly investigated in atomic layers of Cr2Ge2Te6. Gong et al.3737. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature 546(7657), 265 (2017). https://doi.org/10.1038/nature22060 found that bilayer Cr2Ge2Te6 is a Heisenberg-type ferromagnet and the Curie temperature is about 40 K. The magnetic field control of the transition temperature of bilayer Cr2Ge2Te6 is displayed in Fig. 20(a). Under a very small external magnetic field, magnetic anisotropy would be induced, and the corresponding TC will increase rapidly. The picture of spin-wave excitation can explain the weak magnetic fields effect. For six-layer Cr2Ge2Te6 under a magnetic field of 0.3 T, the calculated Curie temperature approaches the bulk value of 66 K. When ignoring the single ion anisotropy, the magnetic field helps increase the magnetic stiffness logarithmically in 2D materials, which is different from the exchange interactions in 3D materials. In bulk Cr2Ge2Te6, the TC enhancement originates from the effect of interlayer coupling.

FIG. 20. (a) The magnetic field controlled TC of bilayer Cr2Ge2Te6. (b) The 3D plot of angle dependent magnetization under selected magnetic field. (c) The band structures with magnetic moment along in-plane a axis and out-of-plane c axis. Panel (a) reproduced with permission from Gong et al., Nature 546, 265 (2017). Copyright 2017 Springer Nature.3737. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature 546(7657), 265 (2017). https://doi.org/10.1038/nature22060 Panel (b) reproduced with permission from Liu et al., Phys. Rev. B 100, 104403 (2019). Copyright 2019 American Physical Society.433433. W. Liu, Y. Wang, J. Fan, L. Pi, M. Ge, L. Zhang, and Y. Zhang, Phys. Rev. B 100(10), 104403 (2019). https://doi.org/10.1103/PhysRevB.100.104403 Panel (c) reproduced with permission from Klein et al., Science 360, 1218 (2018). Copyright 2018 American Association for the Advancement of Science.435435. D. R. Klein, D. MacNeill, J. L. Lado, D. Soriano, E. Navarro-Moratalla, K. Watanabe, T. Taniguchi, S. Manni, P. Canfield, J. Fernández-Rossier, and P. Jarillo-Herrero, Science 360(6394), 1218 (2018). https://doi.org/10.1126/science.aar3617

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Large external magnetic field can directly tune the magnetic coupling of 2D magnets. Liu et al.433433. W. Liu, Y. Wang, J. Fan, L. Pi, M. Ge, L. Zhang, and Y. Zhang, Phys. Rev. B 100(10), 104403 (2019). https://doi.org/10.1103/PhysRevB.100.104403 systematically investigated the anisotropic behavior of Fe3-xGeTe2 in terms of anisotropic magnetization, magnetic entropy change, and critical behavior. Figure 20(b) presents the magnetization evolution between different magnetic field directions. The magnetization exhibits the minimum when H‖ab, and it reaches the maximum when H‖c, confirming that the easy axis of magnetization is along the c axis. The anisotropic magnetic entropy changes further give two types of magnetic couplings in Fe3-xGeTe2 for different magnetic field directions. Therefore, it was inferred that the magnetic correlation around TC can be easily affected by magnetic field. Jiang et al.434434. P. Jiang, L. Li, Z. Liao, Y. X. Zhao, and Z. Zhong, Nano Lett. 18(6), 3844 (2018). https://doi.org/10.1021/acs.nanolett.8b01125 suggested the spin direction of 2D CrI3 can be switched from out-of-plane to in-plane by applying an in-plane external magnetic field to overcome the MAE barrier. The change of spin direction can significantly modify the electronic band structure, including Fermi surface, topological states, and bandgap [Fig. 20(c)]. Moreover, the impact of magnetic field is manifested by tunneling through the 2D magnets-based junctions. For example, Klein et al.435435. D. R. Klein, D. MacNeill, J. L. Lado, D. Soriano, E. Navarro-Moratalla, K. Watanabe, T. Taniguchi, S. Manni, P. Canfield, J. Fernández-Rossier, and P. Jarillo-Herrero, Science 360(6394), 1218 (2018). https://doi.org/10.1126/science.aar3617 reported that metamagnetic transition results in magnetoresistance values of 95%, 300%, and 550% for bilayer, trilayer, and tetralayer CrI3 barriers, respectively.

E. Interfacial engineering

The emerging 2D intrinsic vdW magnets offer an immediate playground to engineer them into various composites, which provide fruitful combinations for tailoring the physical properties and exploring the related applications on spintronics and quantum computing.436436. M. Gibertini, M. Koperski, A. F. Morpurgo, and K. S. Novoselov, Nat. Nanotechnol. 14(5), 408 (2019). https://doi.org/10.1038/s41565-019-0438-6 Choosing a 2D intrinsic magnet as one part of heterostructure, many different types of 2D materials can be stacked in the vertical direction as the other part. For example, one can integrate different 2D magnets together, stack the same kind of 2D magnets together, or combine 2D magnets with some other non-magnetic 2D materials. No doubt, the interlayer magnetic coupling in the resulting heterostructure is important, which is susceptible to the contacting materials in terms of vdW force/chemical bond, magnetic ordering, stacking modes, and the number of layers. Based on different combinations, many important mechanisms to modulate the magnetic properties have been proposed, including symmetry breaking, interlayer charge transfer, build-in electric field, overlap of electron wave functions, band alignment, orbital hybridization, dielectric screening, electron hopping paths, and SOC proximity.9090. W. Zhang, P. K. J. Wong, R. Zhu, and A. T. S. Wee, InfoMat 1(4), 479 (2019). https://doi.org/10.1002/inf2.12048 These strategies for enhancing the TC by tuning their interfacial interaction are broadly highlighted as interfacial engineering.

As we stated above, the magneto-optical Kerr effect firstly confirmed the existence of magnetism in atomically thin CrI3 sheets.2828. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546(7657), 270 (2017). https://doi.org/10.1038/nature22391 Remarkably, 2D CrI3 systems also exhibit magnetic response dependent on the number of layers. The magnetic ground states of monolayer, bilayer, and trilayer CrI3 are FM, AFM, FM, respectively, while the magnetic ground state of 3D bulk CrI3 crystal is FM. The AFM interlayer coupling in bilayer CrI3 is mainly due to structural transition437437. L. Thiel, Z. Wang, M. A. Tschudin, D. Rohner, I. Gutiérrez-Lezama, N. Ubrig, M. Gibertini, E. Giannini, A. F. Morpurgo, and P. Maletinsky, Science 364(6444), 973 (2019). https://doi.org/10.1126/science.aav6926 and super-superexchange interaction.2323. N. Sivadas, S. Okamoto, X. Xu, C. J. Fennie, and D. Xiao, Nano Lett. 18(12), 7658 (2018). https://doi.org/10.1021/acs.nanolett.8b03321 The TC of monolayer and trilayer CrI3 is 45 and 61 K, respectively, meaning that the magnetic coupling is strengthened as the thickness of CrI3 sheet increases. The dependences of TC/TN on the number of layers have also been found in the other experimentally fabricated 2D magnets, including Fe3GeTe2,41,5041. Z. Fei, B. Huang, P. Malinowski, W. Wang, T. Song, J. Sanchez, W. Yao, D. Xiao, X. Zhu, A. F. May, W. Wu, D. H. Cobden, J. H. Chu, and X. Xu, Nat. Mater. 17(9), 778 (2018). https://doi.org/10.1038/s41563-018-0149-750. Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen, and Y. Zhang, Nature 563(7729), 94 (2018). https://doi.org/10.1038/s41586-018-0626-9 CrGeTe3,3737. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature 546(7657), 265 (2017). https://doi.org/10.1038/nature22060 FePS3,4848. J.-U. Lee, S. Lee, J. H. Ryoo, S. Kang, T. Y. Kim, P. Kim, C.-H. Park, J.-G. Park, and H. Cheong, Nano Lett. 16(12), 7433 (2016). https://doi.org/10.1021/acs.nanolett.6b03052 and MnBi2Te4.319319. M. M. Otrokov, I. P. Rusinov, M. Blanco-Rey, M. Hoffmann, A. Y. Vyazovskaya, S. V. Eremeev, A. Ernst, P. M. Echenique, A. Arnau, and E. V. Chulkov, Phys. Rev. Lett. 122(10), 107202 (2019). https://doi.org/10.1103/PhysRevLett.122.107202 Unlike CrI3, there is no thickness-induced flipping of magnetic ground state in multilayer Fe3GeTe2, CrGeTe3, and FePS3 systems. However, their increasing trend with the number of layers behaves differently, which are more pronounced in Fe3GeTe2 and CrGeTe3. The TC of four- or five-layer Fe3GeTe2 is 220 K, dropping to 180 K for bilayer, and finally to 130 K for monolayer.4141. Z. Fei, B. Huang, P. Malinowski, W. Wang, T. Song, J. Sanchez, W. Yao, D. Xiao, X. Zhu, A. F. May, W. Wu, D. H. Cobden, J. H. Chu, and X. Xu, Nat. Mater. 17(9), 778 (2018). https://doi.org/10.1038/s41563-018-0149-7 For CrGeTe3, the TC of bilayer and bulk phase is 41 and 66 K, respectively. In contrast, the value of TN in AFM FePS3 is not sensitive to the number of layers, with a fixed value of 118 K.4848. J.-U. Lee, S. Lee, J. H. Ryoo, S. Kang, T. Y. Kim, P. Kim, C.-H. Park, J.-G. Park, and H. Cheong, Nano Lett. 16(12), 7433 (2016). https://doi.org/10.1021/acs.nanolett.6b03052 In addition, the unique layer-dependent magnetism has also been found in MnBi2Te4.319319. M. M. Otrokov, I. P. Rusinov, M. Blanco-Rey, M. Hoffmann, A. Y. Vyazovskaya, S. V. Eremeev, A. Ernst, P. M. Echenique, A. Arnau, and E. V. Chulkov, Phys. Rev. Lett. 122(10), 107202 (2019). https://doi.org/10.1103/PhysRevLett.122.107202 The monolayer MnBi2Te4 is a topologically trivial ferromagnet, whereas the multilayer systems made up of odd and even numbers of layers are interlayer ferromagnets and antiferromagnets, respectively.

To further improve the Curie temperature, 2D heterostructures consisting of different magnetic materials are highly anticipated. At the interface of vdW heterostructures, more significant charge transfer and increasing external extra spin-exchange paths can be introduced to enhance the interlayer coupling strength.438–440438. K. Zollner, P. E. Faria, and J. Fabian, Phys. Rev. B 101(8), 085112 (2020). https://doi.org/10.1103/PhysRevB.101.085112439. H. X. Fu, C. X. Liu, and B. H. Yan, Sci. Adv. 6(10), eaaz0948 (2020). https://doi.org/10.1126/sciadv.aaz0948440. S. B. Chen, C. X. Huang, H. S. Sun, J. F. Ding, P. Jena, and E. J. Kan, J. Phys. Chem. C 123(29), 17987 (2019). https://doi.org/10.1021/acs.jpcc.9b04631 For example, Fu et al.439439. H. X. Fu, C. X. Liu, and B. H. Yan, Sci. Adv. 6(10), eaaz0948 (2020). https://doi.org/10.1126/sciadv.aaz0948 proposed to induce out-of-plane surface magnetism in the AFM MnBi2Te4 films via magnetism proximity with magnetic CrI3 substrate. A strong exchange bias of ∼40 meV originates from the long Cr-eg orbital tails that hybridize strongly with Te-p orbitals. Taking monolayer CrI3 on MoTe2 as a prototype system, Chen et al.440440. S. B. Chen, C. X. Huang, H. S. Sun, J. F. Ding, P. Jena, and E. J. Kan, J. Phys. Chem. C 123(29), 17987 (2019). https://doi.org/10.1021/acs.jpcc.9b04631 revealed that CrI3/MoTe2 heterostructure is an intrinsic FM semiconductor with TC of ∼60 K, which is 15 K higher than that of pure CrI3. The value of TC can be further enhanced to ∼85 K by applying an out-of-plane pressure of 4.2 GPa, which corresponds to the reduced interlayer distance of 1.2 Å. Such a doubling of TC comes from the introduction of extra spin Cr–Te–Cr superexchange paths [Fig. 21(a)].

FIG. 21. (a) The Curie temperature and the additional superexchange interactions in compressed and uncompressed CrI3/MoTe2 heterostructure. (b)–(d) The exchange pathways for type I-I, type II-II, and type I-II bilayers, respectively. Δ and U represent the t2g-eg crystal field splitting and on-site Hubbard energy, respectively. π and σ represent the d-p atomic bonding type. Panel (a) reproduced with permission from Chen et al., J. Phys. Chem. C 123, 17987 (2019). Copyright 2019 American Chemical Society.440440. S. B. Chen, C. X. Huang, H. S. Sun, J. F. Ding, P. Jena, and E. J. Kan, J. Phys. Chem. C 123(29), 17987 (2019). https://doi.org/10.1021/acs.jpcc.9b04631 Panels (b)–(d) reproduced with permission from Xiao et al., 2D Mater. 7, 045010 (2020). Copyright 2020 IOP.2424. J. Xiao and B. Yan, 2D Mater. 7(4), 045010 (2020). https://doi.org/10.1088/2053-1583/ab9ea4

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Motivated by these discussions, Liu et al.441441. N. Liu, S. Zhou, and J. Zhao, Phys. Rev. Mater. 4(9), 094003 (2020). https://doi.org/10.1103/PhysRevMaterials.4.094003 recently investigated the magnetic coupling between selected bulk semiconducting substrates and bilayer CrI3, such as CdSe (0001), ZnS (0001), ZnO (0001), Si (111), SnS, MoS2, WSe2, GaSe, h-BN, black phosphorus, and InSe. They found that the relatively strong covalent interaction, i.e., CdSe (0001), ZnS (0001), and ZnO (0001), would significantly enhance the interlayer exchange. Meanwhile, the stability of intralayer FM state has also been improved. Hence, AFM to FM transition was observed on bilayer CrI3. DFT calculations further confirmed that such strong proximity effect originates from the prominent charge transfer from substrates. The interlayer coupling between semiconducting substrates and bilayer CrI3 leads to charge doping from the semiconducting substrates to the band structures of CrI3, which in turn enhances the occupation of eg orbitals of Cr atom and significantly increases the t2g-eg hybridization. Consequently, the FM exchange coupling is strengthened.441441. N. Liu, S. Zhou, and J. Zhao, Phys. Rev. Mater. 4(9), 094003 (2020). https://doi.org/10.1103/PhysRevMaterials.4.094003 On the experimental side, Xiu et al. also observed interfacial proximity effect at Fe3GeTe2/CrSb interface by performing elemental-specific XMCD measurements, which would enhance TC of four-layer Fe3GeTe2 from 140 to 230 K. The inverse proximity effect drives the interfacial antiferromagnetic CrSb into ferromagnetic state, and the Fe-Te/Cr-Sb interface is strongly ferromagnetic coupled. Meanwhile, doping of spin-polarized electrons by the interfacial Cr layer gives rise to enhancement of TC of the Fe3GeTe2 films.442442. F. Xiu, H. Wu, Y. Xu, J. Zou, X. Kou, S. A. Morton, A. T. N'Diaye, A. T. S. Wee, P. K. J. Wong, L. Ai, C. Huang, H. Gao, Y. Yang, J. Sun, W. Zhang, Z. Liao, X. Zhang, Z. Li, E. Zhang, W. Liu, K. Yang, and S. Liu, Natl. Sci. Rev. 7(4), 745 (2020). https://doi.org/10.1093/nsr/nwz205

Within the framework of octahedral crystal field, a more direct electron-counting rule has been proposed to describe the interlayer magnetic coupling of magnetic bilayers.443443. J. Xiao and B. Yan, arXiv:2003.09942 (2020). The components include MX2 (M=V, Cr, Mn; X = S, Se), MX2 (M = Mn, Fe, Co, Ni; X = Cl, Br), MI3 (M =V, Cr), and CrGeTe3 monolayers. The exchange interaction in all these 2D magnetic monolayers has been well demonstrated by the superexchange mechanism. Based on the occupation number of d electrons, their electronic configurations can be denoted as type-I t2gxegy (x + y < 5) and type-II t2gxegy (x + y ≥ 5). In other words, there is no empty low-energy d orbital in the type-II layer. Therefore, three types of bilayer heterostructures can be built by these two kinds of monolayer components, i.e., type I-I, II-II, and I-II. By considering the hopping pathways, one can figure out that the exchange interaction between the occupied and occupied orbitals (type II) belongs to AFM ordering. However, the hopping pathways through the occupied-to-occupied orbitals and the occupied-to-empty orbitals coexist; thus type I-I and I-II bilayer structures exhibit competing FM and AFM orderings. Moreover, FM coupling is usually more favorable for I-II bilayer because of the orbital orientation and large on-site U value. All these discussions are illustrated in Figs. 21(b)–21(d). This exchange mechanism can be also applied to explain most of the magnetic metallic bilayers well (VSe2, CrS2, MnSe2, FeCl2, and FeBr2). Beyond this mechanism, the intralayer itinerant carriers should be introduced, which would bring about additional FM exchange effect.443443. J. Xiao and B. Yan, arXiv:2003.09942 (2020).

For the heterojunctions consisting of magnetic and non-magnetic monolayers, the non-magnetic part can experience strong magnetic exchange field (MEF), which is termed as magnetic proximity effect. This effect can break the time reversal symmetry either to introduce FM ordering into a topological insulator (TI)444–448444. F. Katmis, V. Lauter, F. S. Nogueira, B. A. Assaf, M. E. Jamer, P. Wei, B. Satpati, J. W. Freeland, I. Eremin, D. Heiman, P. Jarillo-Herrero, and J. S. Moodera, Nature 533(7604), 513 (2016). https://doi.org/10.1038/nature17635445. C. Y. Yang, Y. H. Lee, K. H. O. Yang, K. C. Chiu, C. Tang, Y. W. Liu, Y. F. Zhao, C. Z. Chang, F. H. Chang, H. J. Lin, J. Shi, and M. T. Lin, Appl. Phys. Lett. 114(8), 082403 (2019). https://doi.org/10.1063/1.5083931446. C. Lee, F. Katmis, P. Jarillo-Herrero, J. S. Moodera, and N. Gedik, Nat. Commun. 7(1), 12014 (2016). https://doi.org/10.1038/ncomms12014447. Y. S. Hou, J. Kim, and R. Q. Wu, Sci. Adv. 5(5), eaaw1874 (2019). https://doi.org/10.1126/sciadv.aaw1874448. Q. L. He, X. F. Kou, A. J. Grutter, G. Yin, L. Pan, X. Y. Che, Y. X. Liu, T. X. Nie, B. Zhang, S. M. Disseler, B. J. Kirby, W. Ratcliff, Q. M. Shao, K. Murata, X. D. Zhu, G. Q. Yu, Y. B. Fan, M. Montazeri, X. D. Han, J. A. Borchers, and K. L. Wang, Nat. Mater. 16(1), 94 (2017). https://doi.org/10.1038/nmat4783 or to lift the valley degeneracy of graphene and TMD.449–456449. Y. F. Wu, H. D. Song, L. Zhang, X. Yang, Z. H. Ren, D. M. Liu, H. C. Wu, J. S. Wu, J. G. Li, Z. Z. Jia, B. M. Yan, X. S. Wu, C. G. Duan, G. R. Han, Z. M. Liao, and D. P. Yu, Phys. Rev. B 95(19), 195426 (2017). https://doi.org/10.1103/PhysRevB.95.195426450. C. Zhao, T. Norden, P. Y. Zhang, P. Q. Zhao, Y. C. Cheng, F. Sun, J. P. Parry, P. Taheri, J. Q. Wang, Y. H. Yang, T. Scrace, K. F. Kang, S. Yang, G. X. Miao, R. Sabirianov, G. Kioseoglou, W. Huang, A. Petrou, and H. Zeng, Nat. Nanotechnol. 12(8), 757 (2017). https://doi.org/10.1038/nnano.2017.68451. D. Zhong, K. L. Seyler, X. Y. Linpeng, R. Cheng, N. Sivadas, B. Huang, E. Schmidgall, T. Taniguchi, K. Watanabe, M. A. McGuire, W. Yao, D. Xiao, K. M. C. Fu, and X. D. Xu, Sci. Adv. 3(5), e1603113 (2017). https://doi.org/10.1126/sciadv.1603113452. J. F. Xie, L. Jia, H. G. Shi, D. Z. Yang, and M. S. Si, Jpn. J. Appl. Phys. 58(1), 010906 (2019). https://doi.org/10.7567/1347-4065/aaf222453. Z. Y. Zhang, X. J. Ni, H. Q. Huang, L. Hu, and F. Liu, Phys. Rev. B 99(11), 115441 (2019). https://doi.org/10.1103/PhysRevB.99.115441454. K. Zollner, P. E. Faria, and J. Fabian, Phys. Rev. B 100(8), 085128 (2019). https://doi.org/10.1103/PhysRevB.100.085128455. K. L. Seyler, D. Zhong, B. Huang, X. Linpeng, N. P. Wilson, T. Taniguchi, K. Watanabe, W. Yao, D. Xiao, M. A. McGuire, K.-M. C. Fu, and X. Xu, Nano Lett. 18(6), 3823 (2018). https://doi.org/10.1021/acs.nanolett.8b01105456. W. Zhang, L. Zhang, P. K. J. Wong, J. Yuan, G. Vinai, P. Torelli, G. van der Laan, Y. P. Feng, and A. T. S. Wee, ACS Nano 13(8), 8997 (2019). https://doi.org/10.1021/acsnano.9b02996 When a TI is in contact with a ferromagnet, both time-reversal and inversion symmetries are broken at the interface. An energy gap is thus formed at the TI surface, and its electrons gain a net magnetic moment through short-range exchange interactions. For example, the integration of monolayer nonmagnetic WSe2 and ultrathin FM semiconductor CrI3 provides unprecedented control of spin and valley pseudospin in WSe2, where a large MEF of nearly 13 T and rapid switching of the WSe2 valley splitting and polarization via flipping of the CrI3 magnetism are detected.451451. D. Zhong, K. L. Seyler, X. Y. Linpeng, R. Cheng, N. Sivadas, B. Huang, E. Schmidgall, T. Taniguchi, K. Watanabe, M. A. McGuire, W. Yao, D. Xiao, K. M. C. Fu, and X. D. Xu, Sci. Adv. 3(5), e1603113 (2017). https://doi.org/10.1126/sciadv.1603113 Moreover, the WSe2 photoluminescence intensity strongly depends on the relative alignment between photoexcited spins in WSe2 and CrI3 magnetization, because of ultrafast spin-dependent charge hopping across the heterostructure interface. Zhang et al.456456. W. Zhang, L. Zhang, P. K. J. Wong, J. Yuan, G. Vinai, P. Torelli, G. van der Laan, Y. P. Feng, and A. T. S. Wee, ACS Nano 13(8), 8997 (2019). https://doi.org/10.1021/acsnano.9b02996 believe that the monolayer VSe2 is on the verge of magnetic transition. Though interfacial hybridization with Co atomic overlayer, a magnetic moment of ∼0.4 μB per V atom has been detected experimentally. Such magnetic interface is free from extrinsic contamination and could be useful for many spin-based effects.

For the heterojunctions consisting of magnetic and non-magnetic monolayers, the magnetic part can also experience a magnetic phase transition. For example, heterostructures of α-RuCl3 on graphene, WSe2, and EuS have been recently synthesized.457457. Y. Wang, J. Balgley, E. Gerber, M. Gray, N. Kumar, X. Lu, J.-Q. Yan, A. Fereidouni, R. Basnet, S. J. Yun, D. Suri, H. Kitadai, T. Taniguchi, K. Watanabe, X. Ling, J. Moodera, Y. H. Lee, H. O. H. Churchill, J. Hu, L. Yang, E.-A. Kim, D. G. Mandrus, E. A. Henriksen, and K. S. Burch, Nano Lett. 20(12), 8446 (2020). https://doi.org/10.1021/acs.nanolett.0c03493 Among them, the insulating α-RuCl3 layer is thought to be in proximity to a quantum spin liquid. The heterostructure undergoes hole doping of the graphene, WSe2, and EuS layers with low work function and electron doping of α-RuCl3 layer,457457. Y. Wang, J. Balgley, E. Gerber, M. Gray, N. Kumar, X. Lu, J.-Q. Yan, A. Fereidouni, R. Basnet, S. J. Yun, D. Suri, H. Kitadai, T. Taniguchi, K. Watanabe, X. Ling, J. Moodera, Y. H. Lee, H. O. H. Churchill, J. Hu, L. Yang, E.-A. Kim, D. G. Mandrus, E. A. Henriksen, and K. S. Burch, Nano Lett. 20(12), 8446 (2020). https://doi.org/10.1021/acs.nanolett.0c03493 respectively. This phenomenon mainly originates from charge transfer between the correlated insulating layer and itinerant layer.458458. S. Biswas, Y. Li, S. M. Winter, J. Knolle, and R. Valentí, Phys. Rev. Lett. 123(23), 237201 (2019). https://doi.org/10.1103/PhysRevLett.123.237201 In addition, magnetic tunnel junction is also very important to develop the spintronic device. The large magnetoresistance amounting was found in graphite-CrI3-graphite and Fe3GeTe2-BN-Fe3GeTe2 multilayer structures.154,435,459,460154. T. Song, X. Cai, M. W.-Y. Tu, X. Zhang, B. Huang, N. P. Wilson, K. L. Seyler, L. Zhu, T. Taniguchi, K. Watanabe, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao, and X. Xu, Science 360(6394), 1214 (2018). https://doi.org/10.1126/science.aar4851435. D. R. Klein, D. MacNeill, J. L. Lado, D. Soriano, E. Navarro-Moratalla, K. Watanabe, T. Taniguchi, S. Manni, P. Canfield, J. Fernández-Rossier, and P. Jarillo-Herrero, Science 360(6394), 1218 (2018). https://doi.org/10.1126/science.aar3617459. H. H. Kim, B. Yang, T. Patel, F. Sfigakis, C. Li, S. Tian, H. Lei, and A. W. Tsen, Nano Lett. 18(8), 4885 (2018). https://doi.org/10.1021/acs.nanolett.8b01552460. Z. Wang, D. Sapkota, T. Taniguchi, K. Watanabe, D. Mandrus, and A. F. Morpurgo, Nano Lett. 18(7), 4303 (2018). https://doi.org/10.1021/acs.nanolett.8b01278

F. Defect engineering

Defects, such as vacancies, adatoms, and substitutional impurities, inevitably exist in 2D materials. The presence of these defects leads to significant impacts on the magnetic properties. For example, many experimental studies have revealed that room-temperature ferromagnetism can be introduced into nonmagnetic TMDs like MoS2, PtSe2, SnS2, WS2, MoTe2, and WSe2 via doping of 3d/4d transition metal atoms (i.e., Ti, V, Cr, Mn, Fe, Co, Ta, and Ni).461–464461. A. Avsar, A. Ciarrocchi, M. Pizzochero, D. Unuchek, O. V. Yazyev, and A. Kis, Nat. Nanotechnol. 14(7), 674 (2019). https://doi.org/10.1038/s41565-019-0467-1462. B. Li, T. Xing, M. Zhong, L. Huang, N. Lei, J. Zhang, J. Li, and Z. Wei, Nat. Commun. 8(1), 1958 (2017). https://doi.org/10.1038/s41467-017-02077-z463. P. M. Coelho, H.-P. Komsa, K. Lasek, V. Kalappattil, J. Karthikeyan, M.-H. Phan, A. V. Krasheninnikov, and M. Batzill, Adv. Electron. Mater. 5(5), 1900044 (2019). https://doi.org/10.1002/aelm.201900044464. L. Yang, H. Wu, W. Zhang, X. Lou, Z. Xie, X. Yu, Y. Liu, and H. Chang, Adv. Electron. Mater. 5(10), 1900552 (2019). https://doi.org/10.1002/aelm.201900552 Therefore, various strategies of defect engineering can be developed for realization of the 2D intrinsic magnets with high Curie temperature. Rational design of defects is able to optimize their types, concentration, and spatial distribution. Hence, understanding the role of defects on magnetic exchange interaction as well as developing effective defect engineering schemes are of great significance for the future development of 2D spintronics.

Based on DFT calculations, Zhao et al.465465. Y. Zhao, L. Lin, Q. Zhou, Y. Li, S. Yuan, Q. Chen, S. Dong, and J. Wang, Nano Lett. 18(5), 2943 (2018). https://doi.org/10.1021/acs.nanolett.8b00314 investigated the electronic and magnetic properties of CrI3 monolayer with surface I vacancies (denoted as IV-CrI3). First, the incorporation of I vacancies would break the symmetry. The two Cr atoms located close to I vacancy (denoted as I-Cr atoms) are different from the other Cr atoms. The magnetic moment of the I-Cr atom increases from 3 to 3.5 μB due to about ∼0.5 electrons gained from each I vacancy. Second, the introduction of I vacancies will reduce the bandgap. With vacancy concentration of 1.96 × 10−6 mol/m2, the bandgap will decrease from 1.13 eV for pristine CrI3 to 0.16 eV for IV-CrI3. More importantly, incorporation of I vacancies is able to improve TC. The TC of defective IV-CrI3 monolayers with vacancy concentrations of 0.65, 0.98, and 1.96 × 10−6 mol/m2 are 38, 38, and 44 K, respectively, in comparison with TC = 35 K for pristine CrI3. To reveal the origin of such increments of Curie temperature, the exchange mechanisms of CrI3 and IV-CrI3 are schematically displayed in Figs. 22(a) and 22(b), respectively. The virtual hopping of two pathways, i.e., t2g and eg levels, and eg and eg levels, are affected by I vacancies. With I vacancy, the former hopping pathway enhances the FM superexchange interaction by shortening the separation of t2g and eg levels. The latter one also strengthens FM coupling around the I vacancy, which is dominated by double exchange interaction. As a result, the effective ferromagnetic exchange is enhanced.465465. Y. Zhao, L. Lin, Q. Zhou, Y. Li, S. Yuan, Q. Chen, S. Dong, and J. Wang, Nano Lett. 18(5), 2943 (2018). https://doi.org/10.1021/acs.nanolett.8b00314

FIG. 22. (a) The magnetic exchange mechanism of pristine CrI3. (b) The magnetic exchange mechanism of CrI3 with I vacancy. (c) The energy difference of FM and AFM states (ΔE) from DFT calculations (blue stars) and Heisenberg model calculations (red circles). (d) Relationship between ΔE and the Cr–Cr bond length near the point defect. Panels (a) and (b) reproduced with permission from Zhao et al., Nano Lett. 18, 2943 (2018). Copyright 2018 American Chemical Society.465465. Y. Zhao, L. Lin, Q. Zhou, Y. Li, S. Yuan, Q. Chen, S. Dong, and J. Wang, Nano Lett. 18(5), 2943 (2018). https://doi.org/10.1021/acs.nanolett.8b00314 Panels (c) and (d) reproduced with permission from Wang et al., Chem. Mater. 32, 1545 (2020). Copyright 2020, American Chemical Society.466466. R. Wang, Y. Su, G. Yang, J. Zhang, and S. Zhang, Chem. Mater. 32(4), 1545 (2020). https://doi.org/10.1021/acs.chemmater.9b04645

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The effects of different defect types on the magnetic performance of CrI3 monolayer have been discussed by Wang et al. based on defect theory and first-principles calculations.466466. R. Wang, Y. Su, G. Yang, J. Zhang, and S. Zhang, Chem. Mater. 32(4), 1545 (2020). https://doi.org/10.1021/acs.chemmater.9b04645 In total, 20 types of defects have been constructed, including vacancy, interstitial, substitution, and bond-rotation defects. The calculated energy differences between FM and AFM states (ΔE) are summarized in Fig. 22(c). It was found that most point defects, such as VCr, VI, VCr2-2, VCr2-4, and CrI, can increase the energy difference ΔE. Hence, the resulted TC will be also enhanced, and the highest TC reaches 210 K in CrI3 system with CrI defect. In addition, the relationship between Cr–Cr distance and ΔE are discussed and shown in Fig. 22(d). One can see that AFM (FM) appears when Cr−Cr distance is less (larger) than 3.70 Å (4.04 Å). This means that point defects in 2D CrI3 can trigger the FM-AFM transition by distorting their local configuration. Recently, similar results have also been discussed by Pizzochero et al.467467. M. Pizzochero, J. Phys. D: Appl. Phys. 53(24), 244003 (2020). https://doi.org/10.1088/1361-6463/ab7ca3 The magnetic properties of CrI3 monolayer embedded with transition metal atoms of most 3d and 4d elements have been evaluated using DFT calculations.468468. A.-M. Hu, X.-H. Zhang, H.-J. Luo, and W.-Z. Xiao, Mater. Today Commun. 25, 101438 (2020). https://doi.org/10.1016/j.mtcomm.2020.101438 Among them, Ti implantation elevates the magnetic moment from 6.0 to 10 μB per unit cell and renders the CrI3 monolayer transition from semiconducting to half-metallic. The estimated TC of Ti-embedded CrI3 monolayer reaches up to 282 K.

Since 2D materials have large surface-to-volume ratio, they are favorable for adsorption of other atoms or gas molecules. As a representative model, Guo et al.469469. Y. Guo, S. Yuan, B. Wang, L. Shi, and J. Wang, J. Mater. Chem. C 6(21), 5716 (2018). https://doi.org/10.1039/C8TC01302K found that ultrathin CrI3 nanosheets can be tailored from FM insulator to FM half-metal by adsorption of Li atoms. The total magnetic moment and energy difference between FM and AFM phase (EAFM–FM) of Li adsorbed CrI3 sheets increase linearly with the increase of Li concentration. For 100% Li coverage, the EAFM–FM can reach up to 125 meV, which is 50% higher than that of pure CrI3 monolayer and suggests a much higher TC. Bader charge analysis showed that each adsorbed Li atom donates about 0.83 electrons to the six surrounding I atoms. In Sec. IV C, we have already discussed that charge doping can significantly improve the magnetic stability.

Considering the exposed atmosphere, the magnetic properties of Cr2Ge2Te6 monolayer adsorbed with various gas molecules (i.e., CO, CO2, H2O, N2, NH3, NO, NO2, O2, and SO2) have been systematically investigated.470470. J. He, G. Ding, C. Zhong, S. Li, D. Li, and G. Zhang, J. Mater. Chem. C 7(17), 5084 (2019). https://doi.org/10.1039/C8TC05530K The former five molecules behave as donors, whereas the latter four molecules act as acceptors. All these gas molecules can effectively enhance the ferromagnetism and Curie temperature of Cr2Ge2Te6 monolayer, which are ascribed to the considerable charge transfer as well as the alignment of the frontier molecular orbital. Among them, the TC of NO and NO2 adsorbed Cr2Ge2Te6 systems are 213 and 205 K, respectively, which are substantially higher than 156 K of pristine Cr2Ge2Te6.

Besides FM semiconductor, one should also note that the defects in itinerant FM metal may either suppress or retain the FM coupling. In 2D metal VSe2, theoretical studies suggested that the weak localization effect introduced by some specific defects would lead to a FM-PM transformation.471471. Q. Cao, F. F. Yun, L. Sang, F. Xiang, G. Liu, and X. Wang, Nanotechnology 28(47), 475703 (2017). https://doi.org/10.1088/1361-6528/aa8f6c Based on the magnetic data, the paramagnetism of 2D VSe2 is possibly attributed to edge related defects, interstitial atoms or dislocations. Recent STM/XMCD/MFM experiments by Chua's group have also demonstrated this phenomenon.192192. R. Chua, J. Yang, X. He, X. Yu, W. Yu, F. Bussolotti, P. K. J. Wong, K. P. Loh, M. B. H. Breese, K. E. J. Goh, Y. L. Huang, and A. T. S. Wee, Adv. Mater. 32(24), 2000693 (2020). https://doi.org/10.1002/adma.202000693 They observed the formation of Se‐deficient line epitaxially grown on MoS2 via thermal annealing and these reconstructed VSe2 monolayers displayed room temperature ferromagnetism. The corresponding DFT calculations have also indicated the enhancement of magnetization after reconstruction.

To confirm the intrinsic ferromagnetism, Chua et al. inferred that defect-free sample is the key in 2D VSe2.192192. R. Chua, J. Yang, X. He, X. Yu, W. Yu, F. Bussolotti, P. K. J. Wong, K. P. Loh, M. B. H. Breese, K. E. J. Goh, Y. L. Huang, and A. T. S. Wee, Adv. Mater. 32(24), 2000693 (2020). https://doi.org/10.1002/adma.202000693 For 2D MnSe2, the presence of high-density Se vacancies in single layer MnSe2 can stay as a dynamically stable ferromagnetic 2D crystal.144144. I. Eren, F. Iyikanat, and H. Sahin, Phys. Chem. Chem. Phys. 21(30), 16718 (2019). https://doi.org/10.1039/C9CP03112J Considering the total energies for two defective magnetic phases, the FM state still yields 15 meV more per formula than the AFM state.

G. Janus engineering

In the above contents, we have already discussed many feasible strategies to modify the magnetic properties of 2D materials, including intercalations, stacking the 2D van der Waals heterojunction, and applying an external electric field and strain. In fact, they all indicated the decisive role of symmetry breaking of atomic structures. Two-dimensional Janus materials, naturally possessing the out-of-plane mirror asymmetry, are expected to modify the magnetic exchange interaction. In experiments, such 2D Janus materials have been successfully fabricated. For example, Janus MoSSe monolayer materials have been prepared by selenizing MoS2 monolayer or substituted sulfurization reaction for MoSe2 monolayer.472,473472. A.-Y. Lu, H. Zhu, J. Xiao, C.-P. Chuu, Y. Han, M.-H. Chiu, C.-C. Cheng, C.-W. Yang, K.-H. Wei, Y. Yang, Y. Wang, D. Sokaras, D. Nordlund, P. Yang, D. A. Muller, M.-Y. Chou, X. Zhang, and L.-J. Li, Nat. Nanotechnol. 12(8), 744 (2017). https://doi.org/10.1038/nnano.2017.100473. J. Zhang, S. Jia, I. Kholmanov, L. Dong, D. Er, W. Chen, H. Guo, Z. Jin, V. B. Shenoy, L. Shi, and J. Lou, ACS Nano 11(8), 8192 (2017). https://doi.org/10.1021/acsnano.7b03186

According to previous experiments, the transition metal trihalides CrI3, VI3, and TMD VSe2 were reported to be FM materials. Starting from the structures of transition metal trihalides (MX3) and TMD (MX2), the corresponding Janus structures of MX3 and MX2 can be constructed by replacing all X atoms in one plane by another halide/chalcogenide Y atoms, labeled as M2X3Y3 and MXY, respectively. The point group symmetry of both MX3 and MX2 monolayers is D3v. Accordingly, the 3d orbitals of transition metal atom M would split into two-fold degenerate dz2 and dx2-y2 orbitals and three-fold degenerate dxz, dyz, and dxy orbitals. Due to the breaking of mirror symmetry, the point group symmetry of Janus M2X3Y3 and MXY reduces to C3v. The different halide/chalcogenide atoms in the top and bottom layers would induce non-degenerated 3d states; that is to say, the five dxz, dyz, dxy, dz2, and dx2-y2 orbitals have distinct features. Based on different electronegativities of the halide/chalcogenide atoms in the top and bottom layers, the strength of FM coupling in M2X3Y3 and MXY monolayers is mediated by X/Y atoms through a superexchange mechanism or a double exchange mechanism.25,47425. F. Zhang, Y.-C. Kong, R. Pang, L. Hu, P.-L. Gong, X.-Q. Shi, and Z.-K. Tang, New J. Phys. 21(5), 053033 (2019). https://doi.org/10.1088/1367-2630/ab1ee4474. F. Zhang, W. Mi, and X. Wang, Adv. Electron. Mater. 6(1), 1900778 (2020). https://doi.org/10.1002/aelm.201900778 Therefore, high TC could be obtained by Janus MX3 and MX2 monolayers.474–477474. F. Zhang, W. Mi, and X. Wang, Adv. Electron. Mater. 6(1), 1900778 (2020). https://doi.org/10.1002/aelm.201900778475. J. He and S. Li, Comput. Mater. Sci. 152, 151 (2018). https://doi.org/10.1016/j.commatsci.2018.05.049476. C. Zhang, Y. Nie, S. Sanvito, and A. Du, Nano Lett. 19(2), 1366 (2019). https://doi.org/10.1021/acs.nanolett.8b05050477. Y. Ren, Q. Li, W. Wan, Y. Liu, and Y. Ge, Phys. Rev. B 101(13), 134421 (2020). https://doi.org/10.1103/PhysRevB.101.134421

As a specific example, DFT calculations by He et al.475475. J. He and S. Li, Comput. Mater. Sci. 152, 151 (2018). https://doi.org/10.1016/j.commatsci.2018.05.049 predicted that the Janus TMD monolayers have large spin polarization and high Curie temperature. The room-temperature Curie temperatures were found for 2D VSSe and VSeTe among Janus systems of MXY (M = V, Cr, Mn; X, Y = S, Se, Te; X ≠ Y). The V atoms and nearest-neighboring S/Se/Te atoms keep an AFM spin arrangement. Hence, double exchange interaction induced FM ordering is most favorable. Zhang et al.476476. C. Zhang, Y. Nie, S. Sanvito, and A. Du, Nano Lett. 19(2), 1366 (2019). https://doi.org/10.1021/acs.nanolett.8b05050 have also found that VSSe monolayer is a highly stable room-temperature ferromagnet (TC = 346∼1079 K) by particle-swarm search and DFT calculations.

Stimulated by the low TC of CrI3, the magnetic properties of 2D Janus Cr2I3X3 (X = Br, Cl) monolayers have been studied by DFT calculations.474474. F. Zhang, W. Mi, and X. Wang, Adv. Electron. Mater. 6(1), 1900778 (2020). https://doi.org/10.1002/aelm.201900778 The exchange energies in CrI3, Cr2I3Br3, and Cr2I3Cl3 were 42.7 meV, 25.7 meV, and 20.5 meV, respectively, indicating their FM ground states. Based on MFT theory and Heisenberg model, the TC of CrI3, Cr2I3Br3, and Cr2I3Cl3 were predicted to be 55, 33, and 26 K, respectively. Moaied et al. systemically explored the electronic and magnetic properties of CrX3 (X = Cl, Br, I) and their Janus monolayers X3-Cr2-Y3 (X, Y = Cl, Br, I, X; X ≠ Y). They found both electronic gap and Curie temperature are sensitive to the halide atoms. Unfortunately, the TC of Janus systems is lower than that of CrI3. Unlike in CrI3, the Janus strategy shows a positive effect on TC in VI3.477477. Y. Ren, Q. Li, W. Wan, Y. Liu, and Y. Ge, Phys. Rev. B 101(13), 134421 (2020). https://doi.org/10.1103/PhysRevB.101.134421 From first-principles calculations, the Curie temperatures of VI3-derived Janus monolayers, i.e., V2Cl3I3, V2Br3I3, and V2Cl3Br3, were determined to be 240, 224, and 232 K, respectively, which is at least 170 K higher than the value of VI3 (50 K). Such dramatic increment on the TC of Janus VI3 monolayers was ascribed to the reduced virtual exchange gap Gex from one occupied t2g state to empty eg states, which mainly determines the strength of FM coupling. The corresponding Gex values were 1.73, 2.156, 0.395, 0.397, and 0.445 for VI3, CrI3, V2Cl3I3, V2Br3I3, and V2Cl3Br3, respectively. Thus, the superexchange interactions in V2Cl3I3, V2Br3I3, and V2Cl3Br3 are enhanced relative to VI3 and CrI3, owing to the reduced virtual exchange gap, Gex.

H. Optical controlling

Beyond the above modification strategies, optical controlling magnetic properties are also highly anticipated, since no contact is involved. To revolutionize the future technology of magnetic storage and spintronics, optical induced manipulation of spin has advantages of fast speed and low power dissipative.478478. J. K. Dewhurst, P. Elliott, S. Shallcross, E. K. U. Gross, and S. Sharma, Nano Lett. 18(3), 1842 (2018). https://doi.org/10.1021/acs.nanolett.7b05118 Recent breakthrough in 2D magnets highlights the research of optically tuning of magnetism. Several pioneer works have already been carried out to investigate the interaction of light and magnetism.

Based on first-principles calculations, Tian et al.479479. Y. Tian, W. Gao, E. A. Henriksen, J. R. Chelikowsky, and L. Yang, Nano Lett. 19(11), 7673 (2019). https://doi.org/10.1021/acs.nanolett.9b02523 studied the ground state of monolayer RuCl3 under optical doping. They found that optical doping can cause a phase transition from spin-liquid phase to FM ordering with a moderate electron-hole (e-h) density. The optically tunable 2D magnetism in RuCl3 and the calculated exchange coupling constants under different doping densities are schematically plotted in Figs. 23(a)–23(c). We can see both ferromagnetism and Curie temperature are significantly increased with increasing optical doping e-h pair density. As e-h pair reaches up to 3× 1013 cm−2, TC is close to room temperature. Such enhancement originates from the itinerant electron mechanism, which is demonstrated by PDOS analysis. The Van Hove singularities in the PDOS appear right above and below the Fermi energy, which have the characteristics of localized Ru t2g orbital.479479. Y. Tian, W. Gao, E. A. Henriksen, J. R. Chelikowsky, and L. Yang, Nano Lett. 19(11), 7673 (2019). https://doi.org/10.1021/acs.nanolett.9b02523

FIG. 23. (a) Schematic plot of the optically tunable magnetism in 2D RuCl3. (b) The exchange coupling constants according to optical doping in RuCl3. (c) Variation of TC for RuCl3 under optical e-h doping. (d) The time evolution of local magnetic moment in Cr2VC2F2. (e) The relative magnetization dynamics for Cr1, Cr2, and V atom in Cr2VC2F2. (f)–(h) The snapshots of magnetization density at different time. Panels (a)–(c) reproduced with permission from Tian et al., Nano Lett. 19, 7673 (2019). Copyright 2019 American Chemical Society.479479. Y. Tian, W. Gao, E. A. Henriksen, J. R. Chelikowsky, and L. Yang, Nano Lett. 19(11), 7673 (2019). https://doi.org/10.1021/acs.nanolett.9b02523 Panels (d)–(h) reproduced with permission from He et al., J. Phys. Chem. Lett. 11, 6219 (2020). Copyright 2020 American Chemical Society.480480. J. He and T. Frauenheim, J. Phys. Chem. Lett. 11(15), 6219 (2020). https://doi.org/10.1021/acs.jpclett.0c02007

• PPT
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• High resolution

The optically manipulating magnetic order transition was also predicted in MXenes.480480. J. He and T. Frauenheim, J. Phys. Chem. Lett. 11(15), 6219 (2020). https://doi.org/10.1021/acs.jpclett.0c02007 DFT calculations revealed that the initial ground states of Cr2VC2F2, Mo2VC2F2, Mo2VN2F2, Mo3C2F2, and Mo3N2F2 are ferrimagnetic. The real time time-dependent DFT simulations on these MXenes showed that the FiM state will transform to FM state at the early stage of simulation. Figures 23(d)–23(h) display the spin dynamics of Cr2VC2F2 MXene under a laser pulse. The local magnetic moments on both Cr and V atoms change dramatically. However, the total magnetic moment in the MXene is retained. At 5.8 fs, the spin direction of V atom is reversed from –0.4 to 0.9 μB, which results in a magnetic ordering transition from FiM to FM. The microscopic mechanism underpinning this ultrafast switching of magnetic ordering is governed by optically induced inter-site spin transfer effect. In addition, other critical magnetic parameters, such as MAE and magnetic exchange field, can be optically controlled in WSe2/CrI3 heterostructures and CrI3 monolayer.455,481455. K. L. Seyler, D. Zhong, B. Huang, X. Linpeng, N. P. Wilson, T. Taniguchi, K. Watanabe, W. Yao, D. Xiao, M. A. McGuire, K.-M. C. Fu, and X. Xu, Nano Lett. 18(6), 3823 (2018). https://doi.org/10.1021/acs.nanolett.8b01105481. J. Kim, K.-W. Kim, B. Kim, C.-J. Kang, D. Shin, S.-H. Lee, B.-C. Min, and N. Park, Nano Lett. 20(2), 929 (2020). https://doi.org/10.1021/acs.nanolett.9b03815

V. CONCLUSION AND OUTLOOK

Section:

In this paper, we have comprehensively reviewed recent experimental and theoretical progress on the 2D intrinsic magnets. Their fundamental physical parameters, magnetic origin, and underlying mechanism of exchange interaction have been discussed. Despite the great achievements during the past decade, the research of 2D intrinsic magnets is still in its early stage and calls for continuous efforts. Going forward, there are four rapidly expanding fields in the foreseeable future. The first one is the discovery of “unknown” room-temperature 2D magnets. The second one is to deeply understand the spin coupling mechanism and provide some feasible ways to manipulate the spin. The third one is to further explore the complex spin-based effects, especially on systems with both magnetism and superconductivity, FM and ferroelectrics (FE), FM and ferroelastics (FA), magnetism and TI, and magnetism and thermoelectricity. Based on the newly found 2D intrinsic magnets, the fourth one is to integrate them into practical devices. We will further elaborate on these issues in this section.

From the theoretical point of view, many hypothetical 2D magnetic materials have been proposed. However, their structural stability, environmental stability at ambient air, and experimental feasibility for synthesis still need to be further confirmed.31,9231. Z. Zhang, J. Shang, C. Jiang, A. Rasmita, W. Gao, and T. Yu, Nano Lett. 19(5), 3138 (2019). https://doi.org/10.1021/acs.nanolett.9b0055392. X. Zhang and C. Gong, Science 363(6428), 4450 (2019). https://doi.org/10.1126/science.aav4450 Moreover, their magnetic ground states and Curie temperatures sometimes depend on the theoretical methodology, e.g., exchange-correlation functionals, the choice of U term and the details of Heisenberg model. Some are poor functionals and/or don't properly include correlation effect, which may give inaccurate results. In this regard, the electronic and magnetic properties of these 2D materials should be calculated with high-level accuracy. Meanwhile, these reliable results will provide a starting point for further data analysis and screening.68,48268. Y. Zhu, X. Kong, T. D. Rhone, and H. Guo, Phys. Rev. Mater. 2(8), 081001 (2018). https://doi.org/10.1103/PhysRevMaterials.2.081001482. J. Zhou, L. Shen, M. D. Costa, K. A. Persson, S. P. Ong, P. Huck, Y. Lu, X. Ma, Y. Chen, H. Tang, and Y. P. Feng, Sci. Data 6(1), 86 (2019). https://doi.org/10.1038/s41597-019-0097-3 Then high-throughput computation and machine learning can greatly accelerate the discovery of 2D magnetic materials and help understand the magnetic exchange interaction as well as the origin of magnetic ordering thoroughly.483483. J. Nelson and S. Sanvito, Phys. Rev. Mater. 3(10), 104405 (2019). https://doi.org/10.1103/PhysRevMaterials.3.104405

On the experimental side, besides exfoliation of 2D magnets from the corresponding 3D layered materials, other approaches for directly growing high-quality 2D magnets should be developed. For example, MBE allows us to create novel 2D ultrathin films from those that are not inherently layered materials. This method has demonstrated its success in preparing 2D magnetic, CrI3,484484. P. Li, C. Wang, J. Zhang, S. Chen, D. Guo, W. Ji, and D. Zhong, Sci. Bull. 65(13), 1064 (2020). https://doi.org/10.1016/j.scib.2020.03.031 TMDs (VSe2, MnSe2, VTe2, CrTe2), and MnSn at high temperature.34,35,192,48534. M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan, and M. Batzill, Nature Nanotechnol. 13(4), 289 (2018). https://doi.org/10.1038/s41565-018-0063-935. J. Li, B. Zhao, P. Chen, R. Wu, B. Li, Q. Xia, G. Guo, J. Luo, K. Zang, Z. Zhang, H. Ma, G. Sun, X. Duan, and X. Duan, Adv. Mater. 30(36), 1801043 (2018). https://doi.org/10.1002/adma.201801043192. R. Chua, J. Yang, X. He, X. Yu, W. Yu, F. Bussolotti, P. K. J. Wong, K. P. Loh, M. B. H. Breese, K. E. J. Goh, Y. L. Huang, and A. T. S. Wee, Adv. Mater. 32(24), 2000693 (2020). https://doi.org/10.1002/adma.202000693485. K. Lasek, P. M. Coelho, K. Zberecki, Y. Xin, S. K. Kolekar, J. Li, and M. Batzill, ACS Nano 14(7), 8473 (2020). https://doi.org/10.1021/acsnano.0c02712 By carefully controlling the temperature of CVD method, Kang et al.209209. L. Kang, C. Ye, X. Zhao, X. Zhou, J. Hu, Q. Li, D. Liu, C. M. Das, J. Yang, D. Hu, J. Chen, X. Cao, Y. Zhang, M. Xu, J. Di, D. Tian, P. Song, G. Kutty, Q. Zeng, Q. Fu, Y. Deng, J. Zhou, A. Ariando, F. Miao, G. Hong, Y. Huang, S. J. Pennycook, K.-T. Yong, W. Ji, X. R. Wang, and Z. Liu, Nat. Commun. 11(1), 3729 (2020). https://doi.org/10.1038/s41467-020-17253-x have synthesized antiferromagnetic ultrathin 2D layered tetragonal FeTe nanoplates and ferromagnetic non-layered hexagonal FeTe nanoplates with thickness down to 2.8 and 3.6 nm on SiO2/Si substrates, respectively. The observed TN of the former phase is 71.8 K, while the TC of the latter phase is 220 K. In addition, chemical vapor transport is also an efficient strategy for producing highly crystalline 2D magnets in industry, such as CrI3 nanolayer.486486. M. Grönke, B. Buschbeck, P. Schmidt, M. Valldor, S. Oswald, Q. Hao, A. Lubk, D. Wolf, U. Steiner, B. Büchner, and S. Hampel, Adv. Mater. Inter. 6(24), 1901410 (2019). https://doi.org/10.1002/admi.201901410 Han et al.487487. N. Han, D. Yang, C. Zhang, X. Zhang, J. Shao, Y. Cheng, and W. Huang, J. Phys. Chem. Lett. 11(21), 9453 (2020). https://doi.org/10.1021/acs.jpclett.0c02717 further demonstrated the important role of iodine buffer layer and the role of CrI2 clusters as building units, which pointed out the reason of achieving 2D CrI3 sheets with nanolayer. In addition, syntheses of 2D magnetic films using techniques like electrochemical deposition, metal-organic chemical vapor deposition, pulsed laser deposition, sputtering, and thermal evaporation are in their infancy and need further investigation. All these methods provide valuable insights for the preparation of 2D magnets, which could certainly extend the experimental database of emerging 2D magnetic materials. Moreover, direct growth of 2D magnets on Si substrates is beneficial for compatibility with the mature Si technology.

With respect to the specific category of 2D intrinsic magnets, 2D binary transition halides have received the most attention so far. However, the dominated d-p-d superexchange interaction usually leads to very low TC. Hence, the effective methods (such as electron doping and phase controlling) to improve the TC of these semiconductor need to be further explored. To date, few 2D TMD materials have been demonstrated as high-temperature FM metals. However, there are still some disagreements on their magnetic behavior. The effects of CDW and defects on the magnetic ground states need to be carefully examined. Both effects contribute to the ongoing controversial debates regarding the magnetic properties of 2D VSe2.192192. R. Chua, J. Yang, X. He, X. Yu, W. Yu, F. Bussolotti, P. K. J. Wong, K. P. Loh, M. B. H. Breese, K. E. J. Goh, Y. L. Huang, and A. T. S. Wee, Adv. Mater. 32(24), 2000693 (2020). https://doi.org/10.1002/adma.202000693 Moreover, new FM semiconductor phases are still highly expected in the 2D TMD families. We surprisingly noticed that plenty of MXene phases are predicted to possess high TC. However, their magnetic properties are sensitive to the functional groups terminated on the outer surface. Owing to the difficulty of attaining MXene sheets with ordered functional groups, it becomes a rather challenging task to prepare the robust magnetic MXenes in laboratory. Among ternary transition metal compounds M-X-Y, the relationship between magnetism and composition is an important topic. Among this big family of 2D materials, many promising systems stand out, such as CrXTe3 (X = Si, Ge, Sn), MPX3 (X = S, Se, Te), Fe-Ge-Te, MnBi2Te4, and MXY (X = O, S, Se, Te, N; Y = Cl, Br, I) compounds. Some of them have been successfully synthesized in laboratory and found to exhibit high TC, novel layer-dependent AFM behavior, interesting topological quantum states, and high carrier mobility. Therefore, we expect to find more 2D analogues in this family. Moreover, the random combinations of M, X, and Y atoms in ternary transition metal compounds may further cause more complicated magnetic exchange interactions, which in turn would be beneficial to achieve high magnetic transition temperature.

The long-range p-electron and f-electron based 2D magnets were reported in a series nonstoichiometric compounds and Gd-based compounds, respectively. The competition between the localized and delocalized behavior of electrons may bring into new magnetic exchange interaction mechanism. Hence, relevant efforts toward high-temperature magnetism are promising. Moreover, a series of ultrathin films and non-vdW materials, which exhibit room temperature FM ordering, were also reported.34,35,172,209,485,48834. M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan, and M. Batzill, Nature Nanotechnol. 13(4), 289 (2018). https://doi.org/10.1038/s41565-018-0063-935. J. Li, B. Zhao, P. Chen, R. Wu, B. Li, Q. Xia, G. Guo, J. Luo, K. Zang, Z. Zhang, H. Ma, G. Sun, X. Duan, and X. Duan, Adv. Mater. 30(36), 1801043 (2018). https://doi.org/10.1002/adma.201801043172. J.-Y. You, C. Chen, Z. Zhang, X.-L. Sheng, S. A. Yang, and G. Su, Phys. Rev. B 100(6), 064408 (2019). https://doi.org/10.1103/PhysRevB.100.064408209. L. Kang, C. Ye, X. Zhao, X. Zhou, J. Hu, Q. Li, D. Liu, C. M. Das, J. Yang, D. Hu, J. Chen, X. Cao, Y. Zhang, M. Xu, J. Di, D. Tian, P. Song, G. Kutty, Q. Zeng, Q. Fu, Y. Deng, J. Zhou, A. Ariando, F. Miao, G. Hong, Y. Huang, S. J. Pennycook, K.-T. Yong, W. Ji, X. R. Wang, and Z. Liu, Nat. Commun. 11(1), 3729 (2020). https://doi.org/10.1038/s41467-020-17253-x485. K. Lasek, P. M. Coelho, K. Zberecki, Y. Xin, S. K. Kolekar, J. Li, and M. Batzill, ACS Nano 14(7), 8473 (2020). https://doi.org/10.1021/acsnano.0c02712488. A. P. Balan, S. Radhakrishnan, C. F. Woellner, S. K. Sinha, L. Deng, C. L. Reyes, B. M. Rao, M. Paulose, R. Neupane, A. Apte, V. Kochat, R. Vajtai, A. R. Harutyunyan, C. W. Chu, G. Costin, D. S. Galvao, A. A. Martí, P. A. van Aken, O. K. Varghese, C. S. Tiwary, A. Malie Madom Ramaswamy Iyer, and P. M. Ajayan, Nat. Nanotechnol. 13(7), 602 (2018). https://doi.org/10.1038/s41565-018-0134-y It is therefore anticipated that large amounts of 2D magnetic materials beyond vdW family will be unveiled soon. There is also plenty of room in the 2D organic magnets, as the combination of coordination chemistry and crystal engineering enables intentional design of organic molecule based 2D frameworks with good magnetic stability and highly tunable magnetic properties. So far, the general performance of 2D organic magnets is still modest compared to that of 2D inorganic magnets. Room-temperature FM semiconductors are expected by rational design of molecular assemblies and organic ligands.

Generally speaking, AFM ordering in 3D materials is more common than FM ordering. However, 2D antiferromagnetic materials are rarely reported in comparison with the widely investigated 2D ferromagnets. In fact, many unique properties make 2D AFM materials even superior to 2D ferromagnets for practical device implementations. 2D antiferromagnets may allow the continuous miniaturization of spintronic devices. They have the advantage of being insensitive to the parasitic external magnetic fields and high read/write memory, and are thus poise to become an integral part of the next-generation logical devices and memory.489489. C. Ó. Coileáin and H. C. Wu, Spin 7(3), 1740014 (2017). https://doi.org/10.1142/S2010324717400148

Recently, 2D magnets with complex spin configurations are also of great interest, which are most relevant to quantum Hall effect,490,491490. M. Lee, W. Kang, Y. Onose, Y. Tokura, and N. P. Ong, Phys. Rev. Lett. 102(18), 186601 (2009). https://doi.org/10.1103/PhysRevLett.102.186601491. A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P. G. Niklowitz, and P. Böni, Phys. Rev. Lett. 102(18), 186602 (2009). https://doi.org/10.1103/PhysRevLett.102.186602 high-temperature superconductivity,492492. P. Liu, X. Luo, Y. Cheng, X.-W. Wang, W. Wang, H. Liu, K. Cho, W.-H. Wang, and F. Lu, J. Phys.: Condens. Matter 30(32), 325801 (2018). https://doi.org/10.1088/1361-648X/aad0d1 and data storage.493493. D. Foster, C. Kind, P. J. Ackerman, J.-S. B. Tai, M. R. Dennis, and I. I. Smalyukh, Nat. Phys. 15(7), 655 (2019). https://doi.org/10.1038/s41567-019-0476-x Therefore, their identification and interpretation are the important issues. For example, the concept of quantum spin liquid has been first proposed in 1973 as the ground state for a system of spin on a triangular lattice.494494. P. W. Anderson, Mater. Res. Bull. 8(2), 153 (1973). https://doi.org/10.1016/0025-5408(73)90167-0 One intuitive description of the quantum spin liquid state is as a liquid of disordered spins. This state is not like the other disordered states, which will preserve its disorder to very low temperatures. Until now, no real 2D magnetic material with quantum spin liquid state has been identified. Based on previous investigations,495495. L. Savary and L. Balents, Rep. Prog. Phys. 80(1), 016502 (2017). https://doi.org/10.1088/0034-4885/80/1/016502 there have been many justifications to look for 2D quantum spin liquid: (1) frustration; (2) low spin; (3) the proximity to the Mott transition; (4) all the proposed spin liquid candidates follow the triangular, honeycomb, Kagome, hyperkagome, and square lattices.496496. L. Balents, Nature 464(7286), 199 (2010). https://doi.org/10.1038/nature08917 Moreover, several theoretical spin models have been proposed to describe quantum spin liquid state, including Kitaev model, spin 1/2 antiferromagnetic Heisenberg model, triangle J1-J2 model, and so on. In addition, several semiempirical methods are also reported to screen out the 2D quantum spin liquid rapidly. For example, Liu et al. predicted the quantum phase transition occurs when the ratio between the second neighboring exchange interaction and the first neighboring interaction falls into the spin liquid range (0.21 ∼ 0.28).492492. P. Liu, X. Luo, Y. Cheng, X.-W. Wang, W. Wang, H. Liu, K. Cho, W.-H. Wang, and F. Lu, J. Phys.: Condens. Matter 30(32), 325801 (2018). https://doi.org/10.1088/1361-648X/aad0d1

Nowadays, many strategies have been proposed to modify the magnetic properties of 2D materials, including strain engineering, intercalation, electric controlling, magnetic field, interfacial engineering, defect engineering, Janus engineering, and optical tuning. However, these strategies have only been assessed for a few experimentally reported 2D magnets. For plenty of the newly discovered 2D magnets, their magnetic responses to strain, electronic doping, magnetic field, and other modification strategies have not been unveiled. In addition, these strategies mainly focus on optimization of the exchange interaction, while magnetic anisotropy is also crucial for suppressing fluctuations and destroying the long-range ordering, which should be taken into account simultaneously. For practical device applications, many approaches might be properly combined for the best performance of 2D magnets.

The coexistence of FM and ferroelectrics, FM and ferroelastics, namely, multiple ferroic phase, could lead to novel physics and new applications. For example, the FM-FE coupling, known as the magnetoelectric effect, is able to generate unique ability of tuning magnetism by applying electric field and vice versa, which are very promising for logic devices.497,498497. Y. Lu, R. Fei, X. Lu, L. Zhu, L. Wang, and L. Yang, ACS Appl. Mater. Interfaces 12(5), 6243 (2020). https://doi.org/10.1021/acsami.9b19320498. C. Huang, Y. Du, H. Wu, H. Xiang, K. Deng, and E. Kan, Phys. Rev. Lett. 120(14), 147601 (2018). https://doi.org/10.1103/PhysRevLett.120.147601 The strong FE and FA coupling will provide an extraordinary platform for the design of strain controllable spintronic devices. Among them, 2D FM has been well investigated, while 2D FE and FA are rarely found. So far, only a few candidates of 2D multiferroic materials have been proposed, including VOCl2, VOBr2, VOI2, CrSX (X = Cl, Br, I), and Hf2VC2F2.19,499,50019. J.-J. Zhang, L. Lin, Y. Zhang, M. Wu, B. I. Yakobson, and S. Dong, J. Am. Chem. Soc. 140(30), 9768 (2018). https://doi.org/10.1021/jacs.8b06475499. H. Tan, M. Li, H. Liu, Z. Liu, Y. Li, and W. Duan, Phys. Rev. B 99(19), 195434 (2019). https://doi.org/10.1103/PhysRevB.99.195434500. B. Xu, S. Li, K. Jiang, J. Yin, Z. Liu, Y. Cheng, and W. Zhong, Appl. Phys. Lett. 116(5), 052403 (2020). https://doi.org/10.1063/1.5140644 Based on the finding of 2D FM materials, searching and designing 2D multiple ferroic materials are still underway. In this regard, 2D multiple ferroic materials hold promising opportunities in practical applications for subsequent investigations.501501. X. Tang and L. Kou, J. Phys. Chem. Lett. 10(21), 6634 (2019). https://doi.org/10.1021/acs.jpclett.9b01969

It would be also important to know the interplay between magnetism and superconductivity, which is the main topic in the fields of high-temperature superconductivity and superconductor spintronics. Normally, these two states are mutually exclusive. However, their coexistence was observed in some specific layered cases, such as LaAlO2/SrTiO3 interfaces,502,503502. J. A. Bert, B. Kalisky, C. Bell, M. Kim, Y. Hikita, H. Y. Hwang, and K. A. Moler, Nat. Phys. 7(10), 767 (2011). https://doi.org/10.1038/nphys2079503. L. Li, C. Richter, J. Mannhart, and R. C. Ashoori, Nat. Phys. 7(10), 762 (2011). https://doi.org/10.1038/nphys2080 molecule-adsorbed NbSe2,504504. X. Zhu, Y. Guo, H. Cheng, J. Dai, X. An, J. Zhao, K. Tian, S. Wei, X. C. Zeng, C. Wu, and Y. Xie, Nat. Commun. 7(1), 11210 (2016). https://doi.org/10.1038/ncomms11210 cuprates, and Fe-based superconductors.505–507505. M. D. Lumsden and A. D. Christianson, J. Phys.: Condens. Matter 22(20), 203203 (2010). https://doi.org/10.1088/0953-8984/22/20/203203506. A. A. Kordyuk, Low Temp. Phys. 38(9), 888 (2012). https://doi.org/10.1063/1.4752092507. C. V. Topping, F. K. K. Kirschner, S. J. Blundell, P. J. Baker, D. N. Woodruff, F. Schild, H. Sun, and S. J. Clarke, Phys. Rev. B 95(13), 134419 (2017). https://doi.org/10.1103/PhysRevB.95.134419 Several explanations of the appearance of magnetism in superconductivity have been proposed, including Fermi surface nesting, local moments interacting via frustrated superexchange interactions, local moments interacting via longer range interactions primarily of itinerant nature, and orbital ordering. However, many of the details remain unknown, especially the investigation of long-range magnetic ordering present in 2D superconductors.505505. M. D. Lumsden and A. D. Christianson, J. Phys.: Condens. Matter 22(20), 203203 (2010). https://doi.org/10.1088/0953-8984/22/20/203203

Moreover, the combination between FM and TI will lead to QAH effect. So far, QAH effect has been experimentally confirmed in Cr-doped (Bi,Sb)2Te3,508508. C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang, Z.-Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C. Zhang, K. He, Y. Wang, L. Lu, X.-C. Ma, and Q.-K. Xue, Science 340(6129), 167 (2013). https://doi.org/10.1126/science.1234414 layered materials of MnBi2Te4,4343. Y. Deng, Y. Yu, M. Z. Shi, Z. Guo, Z. Xu, J. Wang, X. H. Chen, and Y. Zhang, Science 367(6480), 895 (2020). https://doi.org/10.1126/science.aax8156 and twisted bilayer graphene.509509. M. Serlin, C. L. Tschirhart, H. Polshyn, Y. Zhang, J. Zhu, K. Watanabe, T. Taniguchi, L. Balents, and A. F. Young, Science 367(6480), 900 (2020). https://doi.org/10.1126/science.aay5533 However, the operational temperatures of them are low, which prohibit practical applications of the fascinating quantum transport phenomenon in QAH insulators. Therefore, one still needs to establish different physical scenarios to realize QAH insulators with high working temperature. Based on the known 2D magnet database, the reported high-temperature Dirac half metals without considering SOC should be carefully re-examined,93,110,161,162,172,377,382,383,510–51293. T. Cai, X. Li, F. Wang, S. Ju, J. Feng, and C. D. Gong, Nano Lett. 15(10), 6434 (2015). https://doi.org/10.1021/acs.nanolett.5b01791110. J. He, X. Li, P. Lyu, and P. Nachtigall, Nanoscale 9(6), 2246 (2017). https://doi.org/10.1039/C6NR08522A161. J. He, S. Ma, P. Lyu, and P. Nachtigall, J. Mater. Chem. C 4(13), 2518 (2016). https://doi.org/10.1039/C6TC00409A162. J. Sun, X. Zhong, W. Cui, J. Shi, J. Hao, M. Xu, and Y. Li, Phys. Chem. Chem. Phys. 22(4), 2429 (2020). https://doi.org/10.1039/C9CP05084A172. J.-Y. You, C. Chen, Z. Zhang, X.-L. Sheng, S. A. Yang, and G. Su, Phys. Rev. B 100(6), 064408 (2019). https://doi.org/10.1103/PhysRevB.100.064408377. L. Dong, Y. Kim, D. Er, A. M. Rappe, and V. B. Shenoy, Phys. Rev. Lett. 116(9), 096601 (2016). https://doi.org/10.1103/PhysRevLett.116.096601382. Y. Ma, Y. Dai, X. Li, Q. Sun, and B. Huang, Carbon 73, 382 (2014). https://doi.org/10.1016/j.carbon.2014.02.080383. Z. Wang, Z. Liu, and F. Liu, Phys. Rev. Lett. 110(19), 196801 (2013). https://doi.org/10.1103/PhysRevLett.110.196801510. Y. Li, D. West, H. Huang, J. Li, S. B. Zhang, and W. Duan, Phys. Rev. B 92(20), 201403 (2015). https://doi.org/10.1103/PhysRevB.92.201403511. X. Zhang, A. Wang, and M. Zhao, Carbon 84, 1 (2015). https://doi.org/10.1016/j.carbon.2014.11.049512. X. Kong, L. Li, O. Leenaerts, W. Wang, X.-J. Liu, and F. M. Peeters, Nanoscale 10(17), 8153 (2018). https://doi.org/10.1039/C8NR00571K which are potential precursors of QAH insulator or Chern insulator. When SOC is considered, the ferromagnetic Dirac half metal513513. H. Ishizuka and Y. Motome, Phys. Rev. Lett. 109(23), 237207 (2012). https://doi.org/10.1103/PhysRevLett.109.237207 or Dirac spin gapless semimetal514514. Z. Yue, Z. Li, L. Sang, and X. Wang, Small 16(31), 1905155 (2020). https://doi.org/10.1002/smll.201905155 will open a global gap at the Dirac points, giving rise to topological edge states with a nonzero integer Chern number.383,510,511383. Z. Wang, Z. Liu, and F. Liu, Phys. Rev. Lett. 110(19), 196801 (2013). https://doi.org/10.1103/PhysRevLett.110.196801510. Y. Li, D. West, H. Huang, J. Li, S. B. Zhang, and W. Duan, Phys. Rev. B 92(20), 201403 (2015). https://doi.org/10.1103/PhysRevB.92.201403511. X. Zhang, A. Wang, and M. Zhao, Carbon 84, 1 (2015). https://doi.org/10.1016/j.carbon.2014.11.049 Alternatively, one can directly design the QAH compounds, which combine the insulating heave elements with light 3d transition metal elements together. The former elements will help generate a large topological gap, while the latter elements would contribute to strong ferromagnetism. Such expectation has been fulfilled in MnBi2Te4 films, which have already been discussed in Sec. III E 4. Recently, several exciting works have been published,14,43,515–51714. J. Li, Y. Li, S. Du, Z. Wang, B.-L. Gu, S.-C. Zhang, K. He, W. Duan, and Y. Xu, Sci. Adv. 5(6), eaaw5685 (2019). https://doi.org/10.1126/sciadv.aaw568543. Y. Deng, Y. Yu, M. Z. Shi, Z. Guo, Z. Xu, J. Wang, X. H. Chen, and Y. Zhang, Science 367(6480), 895 (2020). https://doi.org/10.1126/science.aax8156515. C. Liu, Y. Wang, H. Li, Y. Wu, Y. Li, J. Li, K. He, Y. Xu, J. Zhang, and Y. Wang, Nat. Mater. 19(5), 522 (2020). https://doi.org/10.1038/s41563-019-0573-3516. J. Ge, Y. Liu, J. Li, H. Li, T. Luo, Y. Wu, Y. Xu, and J. Wang, Natl. Sci. Rev. 7(8), 1280 (2020). https://doi.org/10.1093/nsr/nwaa089517. Z. Li, J. Li, K. He, X. Wan, W. Duan, and Y. Xu, Phys. Rev. B 102(8), 081107 (2020). https://doi.org/10.1103/PhysRevB.102.081107 which mainly focused on the thickness effect of MnBi2Te4 films on the interlayer magnetism and band topology.

Very recently, Duan, Xu, and co-workers517517. Z. Li, J. Li, K. He, X. Wan, W. Duan, and Y. Xu, Phys. Rev. B 102(8), 081107 (2020). https://doi.org/10.1103/PhysRevB.102.081107 provided a powerful strategy to design 2D QAH insulators with high working temperature, and demonstrate its feasibility in the family of layered iron-based superconductor materials FeSe with Li decoration, i.e., LiFeSe. The electron injection from Li atoms to Fe atoms makes LiFeSe monolayer stably exist, and all Fe atoms are in the high-spin state with a magnetic moment of ∼3 μB. Inherited from the robust magnetism of Fe monolayer, the estimated TC of LiFeSe monolayer was about 1500 K. Moreover, there are four titled, anisotropic, and spin-polarized Dirac cones in LiFeSe monolayer, where QAH gap of 35 meV will be opened by inclusion SOC, which is larger than the thermal energy at room temperature. Intuitively, the idea of alkali metal injection can be extended to the other Fe/Co/Ni based 2D compounds.

To utilize the magnetic properties of 2D magnets, the correlations between charge and spin, as well as between phonon and spin are also crucial, because they play an important role in magnetic fluctuation, magnonic dissipation, and magnetic coupling.49,518–52049. Y. Tian, M. J. Gray, H. Ji, R. J. Cava, and K. S. Burch, 2D Mater. 3(2), 025035 (2016). https://doi.org/10.1088/2053-1583/3/2/025035518. A. Milosavljević, A. Šolajić, J. Pešić, Y. Liu, C. Petrovic, N. Lazarević, and Z. V. Popović, Phys. Rev. B 98(10), 104306 (2018). https://doi.org/10.1103/PhysRevB.98.104306519. S. Y. Kim, T. Y. Kim, L. J. Sandilands, S. Sinn, M.-C. Lee, J. Son, S. Lee, K.-Y. Choi, W. Kim, B.-G. Park, C. Jeon, H.-D. Kim, C.-H. Park, J.-G. Park, S. J. Moon, and T. W. Noh, Phys. Rev. Lett. 120(13), 136402 (2018). https://doi.org/10.1103/PhysRevLett.120.136402520. S. Petit, F. Moussa, M. Hennion, S. Pailhès, L. Pinsard-Gaudart, and A. Ivanov, Phys. Rev. Lett. 99(26), 266604 (2007). https://doi.org/10.1103/PhysRevLett.99.266604 Strong charge and spin couplings were found in a AFM NiPS3 monolayer, i.e., a close relationship that exists between electronic structure and magnetic ordering.519519. S. Y. Kim, T. Y. Kim, L. J. Sandilands, S. Sinn, M.-C. Lee, J. Son, S. Lee, K.-Y. Choi, W. Kim, B.-G. Park, C. Jeon, H.-D. Kim, C.-H. Park, J.-G. Park, S. J. Moon, and T. W. Noh, Phys. Rev. Lett. 120(13), 136402 (2018). https://doi.org/10.1103/PhysRevLett.120.136402 The mechanism of spin and phonon coupling can be regarded as interplay between the exchange interaction and the lattice deformation.4949. Y. Tian, M. J. Gray, H. Ji, R. J. Cava, and K. S. Burch, 2D Mater. 3(2), 025035 (2016). https://doi.org/10.1088/2053-1583/3/2/025035 Some pioneer experimental and theoretical investigations on spin and phonon coupling have been reported for CrGe(Si)Te3.518–521518. A. Milosavljević, A. Šolajić, J. Pešić, Y. Liu, C. Petrovic, N. Lazarević, and Z. V. Popović, Phys. Rev. B 98(10), 104306 (2018). https://doi.org/10.1103/PhysRevB.98.104306519. S. Y. Kim, T. Y. Kim, L. J. Sandilands, S. Sinn, M.-C. Lee, J. Son, S. Lee, K.-Y. Choi, W. Kim, B.-G. Park, C. Jeon, H.-D. Kim, C.-H. Park, J.-G. Park, S. J. Moon, and T. W. Noh, Phys. Rev. Lett. 120(13), 136402 (2018). https://doi.org/10.1103/PhysRevLett.120.136402520. S. Petit, F. Moussa, M. Hennion, S. Pailhès, L. Pinsard-Gaudart, and A. Ivanov, Phys. Rev. Lett. 99(26), 266604 (2007). https://doi.org/10.1103/PhysRevLett.99.266604521. B. H. Zhang, Y. S. Hou, Z. Wang, and R. Q. Wu, arXiv:1909.12968 (2019). Deep insights into the spin-phonon coupling in the other 2D magnets would be very worthwhile and may have impact on many relevant areas, such as spin filtering, spin Seebeck, and spin wave control.518–521518. A. Milosavljević, A. Šolajić, J. Pešić, Y. Liu, C. Petrovic, N. Lazarević, and Z. V. Popović, Phys. Rev. B 98(10), 104306 (2018). https://doi.org/10.1103/PhysRevB.98.104306519. S. Y. Kim, T. Y. Kim, L. J. Sandilands, S. Sinn, M.-C. Lee, J. Son, S. Lee, K.-Y. Choi, W. Kim, B.-G. Park, C. Jeon, H.-D. Kim, C.-H. Park, J.-G. Park, S. J. Moon, and T. W. Noh, Phys. Rev. Lett. 120(13), 136402 (2018). https://doi.org/10.1103/PhysRevLett.120.136402520. S. Petit, F. Moussa, M. Hennion, S. Pailhès, L. Pinsard-Gaudart, and A. Ivanov, Phys. Rev. Lett. 99(26), 266604 (2007). https://doi.org/10.1103/PhysRevLett.99.266604521. B. H. Zhang, Y. S. Hou, Z. Wang, and R. Q. Wu, arXiv:1909.12968 (2019).

Based on manipulation of the spin states, many new concept devices based on 2D intrinsic magnets have been proposed, including ultralow power electronic devices, spin transistor, spin valve, spin filter, logic, and magnetic memory. For example, a tunnel field effect transistor with a large on-off ratio (400%) was realized in graphene/CrI3/graphene junction.427,522427. S. Jiang, L. Li, Z. Wang, K. F. Mak, and J. Shan, Nat. Nanotechnol. 13(7), 549 (2018). https://doi.org/10.1038/s41565-018-0135-x522. J. J. Heath, M. Costa, M. Buongiorno-Nardelli, and M. A. Kuroda, Phys. Rev. B 101(19), 195439 (2020). https://doi.org/10.1103/PhysRevB.101.195439 Gong et al.523523. S. J. Gong, C. Gong, Y. Y. Sun, W. Y. Tong, C. G. Duan, J. H. Chu, and X. Zhang, Proc. Natl. Acad. Sci. 115(34), 8511 (2018). https://doi.org/10.1073/pnas.1715465115 also demonstrated that vertical electrical field was an effective way to achieve half-metallicity in A-type antiferromagnetic bilayers on VSe2 and realized the spin field effect transistor. Multiple spin filter magnetic tunnel junctions with a record of enhanced magnetoresistance (19 000%) were realized in four-layer CrI3 junction structures.154154. T. Song, X. Cai, M. W.-Y. Tu, X. Zhang, B. Huang, N. P. Wilson, K. L. Seyler, L. Zhu, T. Taniguchi, K. Watanabe, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao, and X. Xu, Science 360(6394), 1214 (2018). https://doi.org/10.1126/science.aar4851 Double spin filter was proposed in graphene/CrI3/graphene junction. In this model, the CrI3 tunnel barrier and the decoupled magnetic layers were used as the magnetic memory bit. Such decoupling provides electrical readout of the CrI3 magnetization state without additional ferromagnetic sensor layers, enabling facile detection of spin-orbit torques on the layered magnetic insulators.154154. T. Song, X. Cai, M. W.-Y. Tu, X. Zhang, B. Huang, N. P. Wilson, K. L. Seyler, L. Zhu, T. Taniguchi, K. Watanabe, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao, and X. Xu, Science 360(6394), 1214 (2018). https://doi.org/10.1126/science.aar4851 Based on the magnetic proximity exchange interaction at the interface, spin dependent optoelectronics and photonics have been observed in CrI3/WSe2 heterojunction.451451. D. Zhong, K. L. Seyler, X. Y. Linpeng, R. Cheng, N. Sivadas, B. Huang, E. Schmidgall, T. Taniguchi, K. Watanabe, M. A. McGuire, W. Yao, D. Xiao, K. M. C. Fu, and X. D. Xu, Sci. Adv. 3(5), e1603113 (2017). https://doi.org/10.1126/sciadv.1603113 The magnetization switching in 2D magnets by electric voltage was observed in Fe3GeTe2, which opens up new opportunities for potential voltage-controlled magnetoelectronics.5050. Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen, and Y. Zhang, Nature 563(7729), 94 (2018). https://doi.org/10.1038/s41586-018-0626-9 In addition, a new type of spin valve was theoretically designed in a CrI3/bilayer graphene/CrI3 heterojunction. Cardoso et al.524524. C. Cardoso, D. Soriano, N. A. García-Martínez, and J. Fernández-Rossier, Phys. Rev. Lett. 121(6), 067701 (2018). https://doi.org/10.1103/PhysRevLett.121.067701 found that gap opening only exists at the Dirac point in the antiparallel configuration, whereas the graphene bilayer remains conducting in the parallel configuration. These exciting innovative devices are all related to magnetic heterostructures. Stacking more potential room-temperature 2D magnets as the building blocks and investigating their performances in spintronic and quantum devices are just beginning.

All these exciting progresses will shed light on the design and synthesis of room-temperature 2D magnets with intrinsic FM/AFM ordering. Compared to the bulk phases, the atomic thinness of the layers also leads to strong tunability via strain, intercalation, external fields (electronic, optical, and magnetic), interfacial interaction, defects, and functional groups, as discussed in Sec. IV. The successive research of 2D magnets with novel properties would not only provide more abundant platform to explore the fundamental physics but also move forward to develop efficient non-volatile memory, spin-based logic devices, spin-dependent optoelectronics, and so on. In this regard, we believe that the development of 2D magnets is still in its infancy but has already shown its huge potential.

AUTHORS' CONTRIBUTIONS

Section:

All authors have contributed equally to this manuscript. All authors have reviewed final version of this manuscript.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11874097, 91961204, 12004065, 11964023) and the Fundamental Research Funds for the Central Universities of China (Grant No. DUT19LK12). We acknowledge the Xinghai Scholar project of Dalian University of Technology and the project of Dalian Youth Science and Technology Star (Grant No. 2017RQ012).

DATA AVAILABLITY

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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Which one of the following sets of ions represents a collection of isoelectronic species 1 point K+ Ca2+ Cl Na+ Ca2+ F Na+ SC 3/f all of these?

Which set represent isoelectronic species?

Which of the following is a set of isoelectronic ions?

What are examples of isoelectronic ions?