Magnetic anisotropy, exchange coupling and Dzyaloshinskii–Moriya interaction of two-dimensional magnets
Qirui Cui, Liming Wang, Yingmei Zhu, Jinghua Liang, Hongxin Yang
Magnetic anisotropy, exchange coupling and Dzyaloshinskii–Moriya interaction of two-dimensional magnets
The two-dimensional (2D) magnets provide novel opportunities for understanding magnetism and investigating spin related phenomena in several atomic thickness. Multiple features of 2D magnets, such as critical temperatures, magnetoelectric/magneto-optic responses, and spin configurations, depend on the basic magnetic terms that describe various spins interactions and cooperatively determine the spin Hamiltonian of studied systems. In this review, we present a comprehensive survey of three types of basic terms, including magnetic anisotropy that is intimately related with long-range magnetic order, exchange coupling that normally dominates the spin interactions, and Dzyaloshinskii−Moriya interaction (DMI) that favors the noncollinear spin configurations, from the theoretical aspect. We introduce not only the physical features and origin of these crucial terms in 2D magnets but also many correlated phenomena, which may lead to the advance of 2D spintronics.
magnetic anisotropy / exchange coupling / Dzyaloshinskii–Moriya interaction / two-dimensional magnets
[1] |
N. D. Mermin, H. Wagner. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys. Rev. Lett., 1966, 17(22): 1133
CrossRef
ADS
Google scholar
|
[2] |
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, X. Zhang. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature, 2017, 546(7657): 265
CrossRef
ADS
Google scholar
|
[3] |
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, X. Xu. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature, 2017, 546(7657): 270
CrossRef
ADS
Google scholar
|
[4] |
M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M. H. Phan, M. Batzill. Strong room-temperature ferromagnetism in VSe2 monolayers on van der Waals substrates. Nat. Nanotechnol., 2018, 13(4): 289
CrossRef
ADS
Google scholar
|
[5] |
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, R. K. Kawakami. Room temperature intrinsic ferromagnetism in epitaxial manganese selenide films in the monolayer limit. Nano Lett., 2018, 18(5): 3125
CrossRef
ADS
Google scholar
|
[6] |
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, Y. Zhang. Gate-tunable room-temperature ferromagnetism in two-dimensional Fe3GeTe2. Nature, 2018, 563(7729): 94
CrossRef
ADS
Google scholar
|
[7] |
J. Lee, S. Lee, J. H. Ryoo, S. Kang, T. Y. Kim, P. Kim, C. H. Park, J. G. Park, H. Cheong. Ising-type magnetic ordering in atomically thin FePS3. Nano Lett., 2016, 16(12): 7433
CrossRef
ADS
Google scholar
|
[8] |
G. Long, H. Henck, M. Gibertini, D. Dumcenco, Z. Wang, T. Taniguchi, K. Watanabe, E. Giannini, A. F. Morpurgo. Persistence of magnetism in atomically thin MnPS3 crystals. Nano Lett., 2020, 20(4): 2452
CrossRef
ADS
Google scholar
|
[9] |
A. Bedoya-Pinto, J. R. Ji, A. K. Pandeya, P. Gargiani, M. Valvidares, P. Sessi, J. M. Taylor, F. Radu, K. Chang, S. S. P. Parkin. Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer. Science, 2021, 374(6567): 616
CrossRef
ADS
Google scholar
|
[10] |
T. Song, X. Cai, M. W. 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, X. Xu. Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures. Science, 2018, 360(6394): 1214
CrossRef
ADS
Google scholar
|
[11] |
X. Wang, J. Tang, X. Xia, C. He, J. Zhang, Y. Liu, C. Wan, C. Fang, C. Guo, W. Yang, Y. Guang, X. Zhang, H. Xu, J. Wei, M. Liao, X. Lu, J. Feng, X. Li, Y. Peng, H. Wei, R. Yang, D. Shi, X. Zhang, Z. Han, Z. Zhang, G. Zhang, G. Yu, X. Han. Current-driven magnetization switching in a van der Waals ferromagnet Fe3GeTe2. Sci. Adv., 2019, 5(8): eaaw8904
CrossRef
ADS
Google scholar
|
[12] |
H. Fu, C. Liu, B. Yan. Exchange bias and quantum anomalous Hall effect in the MnBi2Te4/CrI3 heterostructure. Sci. Adv., 2020, 6(10): eaaz0948
CrossRef
ADS
Google scholar
|
[13] |
Y. Li, J. Li, Y. Li, M. Ye, F. Zheng, Z. Zhang, J. Fu, W. Duan, Y. Xu. High-temperature quantum anomalous Hall insulators in lithium-decorated iron-based superconductor materials. Phys. Rev. Lett., 2020, 125(8): 086401
CrossRef
ADS
Google scholar
|
[14] |
D. Zhong, K. L. Seyler, X. Linpeng, R. Cheng, N. Sivadas, B. Huang, E. Schmidgall, T. Taniguchi, K. Watanabe, M. A. McGuire, W. Yao, D. Xiao, K. M. C. Fu, X. Xu. Van der Waals engineering of ferromagnetic semiconductor heterostructures for spin and valleytronics. Sci. Adv., 2017, 3(5): e1603113
CrossRef
ADS
Google scholar
|
[15] |
K. Zollner, P. E. Faria Junior, J. Fabian. Proximity exchange effects in MoSe2 and WSe2 heterostructures with CrI3: Twist angle, layer, and gate dependence. Phys. Rev. B, 2019, 100(8): 085128
CrossRef
ADS
Google scholar
|
[16] |
L. Ai, E. Zhang, J. Yang, X. Xie, Y. Yang, Z. Jia, Y. Zhang, S. Liu, Z. Li, P. Leng, X. Cao, X. Sun, T. Zhang, X. Kou, Z. Han, F. Xiu, S. Dong. Van der Waals ferromagnetic Josephson junctions. Nat. Commun., 2021, 12(1): 6580
CrossRef
ADS
Google scholar
|
[17] |
W. Zhao, Z. Fei, T. Song, H. K. Choi, T. Palomaki, B. Sun, P. Malinowski, M. A. McGuire, J. H. Chu, X. Xu, D. H. Cobden. Magnetic proximity and nonreciprocal current switching in a monolayer WTe2 helical edge. Nat. Mater., 2020, 19(5): 503
CrossRef
ADS
Google scholar
|
[18] |
Q. H. Wang, A. Bedoya-Pinto, M. Blei, A. H. Dismukes, A. Hamo, S. Jenkins, M. Koperski, Y. Liu, Q. C. Sun, E. J. Telford, H. H. Kim, M. Augustin, U. Vool, J. X. Yin, L. H. Li, A. Falin, C. R. Dean, F. Casanova, R. F. L. Evans, M. Chshiev, A. Mishchenko, C. Petrovic, R. He, L. Zhao, A. W. Tsen, B. D. Gerardot, M. Brotons-Gisbert, Z. Guguchia, X. Roy, S. Tongay, Z. Wang, M. Z. Hasan, J. Wrachtrup, A. Yacoby, A. Fert, S. Parkin, K. S. Novoselov, P. Dai, L. Balicas, E. J. G. Santos. The magnetic genome of two-dimensional van der Waals materials. ACS Nano, 2022, 16(5): 6960
CrossRef
ADS
Google scholar
|
[19] |
D. Soriano, M. I. Katsnelson, J. Fernández-Rossier. Magnetic two-dimensional chromium trihalides: A theoretical perspective. Nano Lett., 2020, 20(9): 6225
CrossRef
ADS
Google scholar
|
[20] |
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, Y. Iwasa. Intrinsic 2D ferromagnetism in V5Se8 epitaxial thin films. Nano Lett., 2019, 19(12): 8806
CrossRef
ADS
Google scholar
|
[21] |
C. Tang, L. Zhang, A. Du. Tunable magnetic anisotropy in 2D magnets via molecular adsorption. J. Mater. Chem. C, 2020, 8(42): 14948
CrossRef
ADS
Google scholar
|
[22] |
C. Tang, K. Ostrikov, S. Sanvito, A. Du. Prediction of room-temperature ferromagnetism and large perpendicular magnetic anisotropy in a planar hypercoordinate FeB3 monolayer. Nanoscale Horiz., 2021, 6(1): 43
CrossRef
ADS
Google scholar
|
[23] |
M. Alsubaie, C. Tang, D. Wijethunge, D. Qi, A. Du. First-principles study of the enhanced magnetic anisotropy and transition temperature in a CrSe2 monolayer via hydrogenation. ACS Appl. Electron. Mater., 2022, 4(7): 3240
CrossRef
ADS
Google scholar
|
[24] |
V. L. Berezinskii. Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group (I): Classical systems. Sov. Phys. JETP, 1971, 32: 493
|
[25] |
V. L. Berezinskii. Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group (II): Quantum systems. Sov. Phys. JETP, 1972, 34: 610
|
[26] |
J. M. Kosterlitz, D. J. Thouless. Long range order and metastability in two dimensional solids and superfluids (application of dislocation theory). J. Phys. C, 1972, 5(11): L124
CrossRef
ADS
Google scholar
|
[27] |
J. M. Kosterlitz, D. J. Thouless. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C, 1973, 6(7): 1181
CrossRef
ADS
Google scholar
|
[28] |
J. M. Kosterlitz. The critical properties of the two-dimensional xy model. J. Phys. C, 1974, 7(6): 1046
CrossRef
ADS
Google scholar
|
[29] |
H. L. Zhuang, P. R. C. Kent, R. G. Hennig. Strong anisotropy and magnetostriction in the two-dimensional Stoner ferromagnet Fe3GeTe2. Phys. Rev. B, 2016, 93(13): 134407
CrossRef
ADS
Google scholar
|
[30] |
J. L. Lado, J. F. Rossier. On the origin of magnetic anisotropy in two dimensional CrI3. 2D Mater., 2017,
CrossRef
ADS
Google scholar
|
[31] |
L. Webster, J. A. Yan, Strain-tunable magnetic anisotropy in monolayer CrCl3. CrBr3, and CrI3. Phys. Rev. B, 2018, 98(14): 144411
CrossRef
ADS
Google scholar
|
[32] |
B. Yang, X. Zhang, H. Yang, X. Han, Y. Yan. Nonmetallic atoms induced magnetic anisotropy in monolayer chromium trihalides. J. Phys. Chem. C, 2019, 123(1): 691
CrossRef
ADS
Google scholar
|
[33] |
B. Yang, X. Zhang, H. Yang, X. Han, Y. Yan. Strain controlling transport properties of heterostructure composed of monolayer CrI3. Appl. Phys. Lett., 2019, 114(19): 192405
CrossRef
ADS
Google scholar
|
[34] |
F. J. Dyson. General theory of spin-wave interactions. Phys. Rev., 1956, 102(5): 1217
CrossRef
ADS
Google scholar
|
[35] |
F. Xue, Y. Hou, Z. Wang, R. Wu. Two-dimensional ferromagnetic van der Waals CrCl3 monolayer with enhanced anisotropy and Curie temperature. Phys. Rev. B, 2019, 100(22): 224429
CrossRef
ADS
Google scholar
|
[36] |
Y. Li, Z. Jiang, J. Li, S. Xu, W. Duan. Magnetic anisotropy of the two-dimensional ferromagnetic insulator MnBi2Te4. Phys. Rev. B, 2019, 100(13): 134438
CrossRef
ADS
Google scholar
|
[37] |
C. Xu, J. Feng, H. Xiang, L. Bellaiche. Interplay between Kitaev interaction and single ion anisotropy in ferromagnetic CrI3 and CrGeTe3 monolayers. npj Comput. Mater., 2018, 4: 57
CrossRef
ADS
Google scholar
|
[38] |
Q. Cui, J. Liang, B. Yang, Z. Wang, P. Li, P. Cui, H. Yang. Giant enhancement of perpendicular magnetic anisotropy and induced quantum anomalous Hall effect in graphene/NiI2 heterostructures via tuning the van der Waals interlayer distance. Phys. Rev. B, 2020, 101(21): 214439
CrossRef
ADS
Google scholar
|
[39] |
C. Gong, X. Zhang. Two-dimensional magnetic crystals and emergent heterostructure devices. Science, 2019, 363(6428): eaav4450
CrossRef
ADS
Google scholar
|
[40] |
S. Y. Park, D. S. Kim, Y. Liu, J. Hwang, Y. Kim, W. Kim, J. Y. Kim, C. Petrovic, C. Hwang, S. K. Mo, H. Kim, B. C. Min, H. C. Koo, J. Chang, C. Jang, J. W. Choi, H. Ryu. Controlling the magnetic anisotropy of the van der Waals ferromagnet Fe3GeTe2 through hole doping. Nano Lett., 2020, 20(1): 95
CrossRef
ADS
Google scholar
|
[41] |
Y. P. Wang, X. Y. Chen, M. Q. Long. Modifications of magnetic anisotropy of Fe3GeTe2 by the electric field effect. Appl. Phys. Lett., 2020, 116(9): 092404
CrossRef
ADS
Google scholar
|
[42] |
X. G. Ye, P. F. Zhu, W. Z. Xu, N. Z. Shang, K. H. Liu, Z. M. Liao. Orbit-transfer torque driven field-free switching of perpendicular magnetization chin. Phys. Lett., 2022, 39: 037303
CrossRef
ADS
Google scholar
|
[43] |
J. Seo, E. S. An, T. Park, S. Y. Hwang, G. Y. Kim, K. Song, W. Noh, J. Y. Kim, G. S. Choi, M. Choi, E. Oh, K. Watanabe, T. Taniguchi, J. H. Park, Y. J. Jo, H. W. Yeom, S. Y. Choi, J. H. Shim, J. S. Kim. Tunable high-temperature itinerant antiferromagnetism in a van der Waals magnet. Nat. Commun., 2021, 12(1): 2844
CrossRef
ADS
Google scholar
|
[44] |
X. Zhang, Q. Lu, W. Liu, W. Niu, J. Sun, J. Cook, M. Vaninger, P. F. Miceli, D. J. Singh, S. W. Lian, T. R. Chang, X. He, J. Du, L. He, R. Zhang, G. Bian, Y. Xu. Room-temperature intrinsic ferromagnetism in epitaxial CrTe2 ultrathin films. Nat. Commun., 2021, 12(1): 2492
CrossRef
ADS
Google scholar
|
[45] |
Y. Wang, M. E. Ziebel, L. Sun, J. T. Gish, T. J. Pearson, X. Z. Lu, A. E. Thorarinsdottir, M. C. Hersam, J. R. Long, D. E. Freedman, J. M. Rondinelli, D. Puggioni, T. D. Harris. Strong magnetocrystalline anisotropy arising from metal–ligand covalency in a metal–organic candidate for 2D magnetic order. Chem. Mater., 2021, 33(22): 8712
CrossRef
ADS
Google scholar
|
[46] |
A. Kitaev. Fault-tolerant quantum computation by anyons. Ann. Phys., 2003, 303(1): 2
CrossRef
ADS
Google scholar
|
[47] |
A. Kitaev. Anyons in an exactly solved model and beyond. Ann. Phys., 2006, 321(1): 2
CrossRef
ADS
Google scholar
|
[48] |
C. Xu, J. Feng, M. Kawamura, Y. Yamaji, Y. Nahas, S. Prokhorenko, Y. Qi, H. Xiang, L. Bellaiche. Possible Kitaev quantum spin liquid state in 2D materials with S = 3/2. Phys. Rev. Lett., 2020, 124(8): 087205
CrossRef
ADS
Google scholar
|
[49] |
L. J. Sandilands, Y. Tian, K. W. Plumb, Y. J. Kim, K. S. Burch. Scattering continuum and possible fractionalized excitations in α-RuCl3. Phys. Rev. Lett., 2015, 114(14): 147201
CrossRef
ADS
Google scholar
|
[50] |
H.-S. Kim, V. Vijay Shankar, A. Catuneanu, H. Y. Kee. Kitaev magnetism in honeycomb RuCl3 with intermediate spin−orbit coupling. Phys. Rev. B, 2015, 91: 241110(R)
CrossRef
ADS
Google scholar
|
[51] |
A. Banerjee, C. A. Bridges, J. Q. Yan, A. A. Aczel, L. Li, M. B. Stone, G. E. Granroth, M. D. Lumsden, Y. Yiu, J. Knolle, S. Bhattacharjee, D. L. Kovrizhin, R. Moessner, D. A. Tennant, D. G. Mandrus, S. E. Nagler. Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet. Nat. Mater., 2016, 15(7): 733
CrossRef
ADS
Google scholar
|
[52] |
S. M. Winter, Y. Li, H. O. Jeschke, R. Valentí. Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales. Phys. Rev. B, 2016, 93(21): 214431
CrossRef
ADS
Google scholar
|
[53] |
H. S. Kim, H. Y. Kee. Crystal structure and magnetism in α-RuCl3: An ab initio study. Phys. Rev. B, 2016, 93(15): 155143
CrossRef
ADS
Google scholar
|
[54] |
M. Hermanns, I. Kimchi, J. Knolle. Physics of the Kitaev model: Fractionalization, dynamic correlations, and material connections. Annu. Rev. Condens. Matter Phys., 2018, 9(1): 17
CrossRef
ADS
Google scholar
|
[55] |
A. Banerjee, P. Lampen-Kelley, J. Knolle, C. Balz, A. A. Aczel, B. Winn, Y. Liu, D. Pajerowski, J. Yan, C. A. Bridges, A. T. Savici, B. C. Chakoumakos, M. D. Lumsden, D. A. Tennant, R. Moessner, D. G. Mandrus, S. E. Nagler. Excitations in the field-induced quantum spin liquid state of α-RuCl3. npj Quant. Mater., 2018, 3: 8
CrossRef
ADS
Google scholar
|
[56] |
Y. Kasahara, K. Sugii, T. Ohnishi, M. Shimozawa, M. Yamashita, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, T. Shibauchi, Y. Matsuda. Unusual thermal Hall effect in a Kitaev spin liquid candidate α-RuCl3. Phys. Rev. Lett., 2018, 120(21): 217205
CrossRef
ADS
Google scholar
|
[57] |
H. Takagi, T. Takayama, G. Jackeli, G. Khaliullin, S. E. Nagler. Concept and realization of Kitaev quantum spin liquids. Nat. Rev. Phys., 2019, 1(4): 264
CrossRef
ADS
Google scholar
|
[58] |
J. A. Sears, L. E. Chern, S. Kim, P. J. Bereciartua, S. Francoual, Y. B. Kim, Y. J. Kim. Ferromagnetic Kitaev interaction and the origin of large magnetic anisotropy in α-RuCl3. Nat. Phys., 2020, 16(8): 837
CrossRef
ADS
Google scholar
|
[59] |
Y. Zhou, K. Kanoda, T. K. Ng. Quantum spin liquid states. Rev. Mod. Phys., 2017, 89(2): 025003
CrossRef
ADS
Google scholar
|
[60] |
H. J. Xiang, E. J. Kan, S. H. Wei, M. H. Whangbo, X. G. Gong. Predicting the spin-lattice order of frustrated systems from first principles. Phys. Rev. B, 2011, 84(22): 224429
CrossRef
ADS
Google scholar
|
[61] |
B. Goodenough. Theory of the role of covalence in the perovskite-type manganites [La,M(II)] MnO3. Phys. Rev., 1955, 100(2): 564
CrossRef
ADS
Google scholar
|
[62] |
J. Kanamori. Superexchange interaction and symmetry properties of electron orbitals. J. Phys. Chem. Solids, 1959, 10(2−3): 87
CrossRef
ADS
Google scholar
|
[63] |
P. W. Anderson. New approach to the theory of superexchange interactions. Phys. Rev., 1959, 115(1): 2
CrossRef
ADS
Google scholar
|
[64] |
C. Huang, J. Feng, F. Wu, D. Ahmed, B. Huang, H. Xiang, K. Deng, E. Kan. Toward intrinsic room-temperature ferromagnetism in two-dimensional semiconductors. J. Am. Chem. Soc., 2018, 140(36): 11519
CrossRef
ADS
Google scholar
|
[65] |
N. Sivadas, M. W. Daniels, R. H. Swendsen, S. Okamoto, D. Xiao. Magnetic ground state of semiconducting transition-metal trichalcogenide monolayers. Phys. Rev. B, 2015, 91(23): 235425
CrossRef
ADS
Google scholar
|
[66] |
Q. Pei, W. Mi. Electrical control of magnetic behavior and valley polarization of monolayer antiferromagnetic MnPSe3 on an insulating ferroelectric substrate from first principle. Phys. Rev. Appl., 2019, 11(1): 014011
CrossRef
ADS
Google scholar
|
[67] |
T. Olsen, Magnetic anisotropy, exchange interactions of two-dimensional FePS3. NiPS3 and MnPS3 from first principles calculations. J. Phys. D, 2021, 54(31): 314001
CrossRef
ADS
Google scholar
|
[68] |
J. Li, J. Y. Ni, X. Y. Li, H. J. Koo, M. H. Whangbo, J. S. Feng, H. J. Xiang. Intralayer ferromagnetism between S = 5/2 ions in MnBi2Te4: Role of empty Bi p states. Phys. Rev. B, 2020, 101(20): 201408
CrossRef
ADS
Google scholar
|
[69] |
C. Huang, J. Feng, J. Zhou, H. Xiang, K. Deng, E. Kan. Ultra-high-temperature ferromagnetism in intrinsic tetrahedral semiconductors. J. Am. Chem. Soc., 2019, 141(31): 12413
CrossRef
ADS
Google scholar
|
[70] |
Q. Cui, Y. Zhu, Y. Ga, J. Liang, P. Li, D. Yu, P. Cui, H. Yang. Anisotropic Dzyaloshinskii–Moriya interaction and topological magnetism in two-dimensional magnets protected by P4¯m2 crystal symmetry. Nano Lett., 2022, 22(6): 2334
CrossRef
ADS
Google scholar
|
[71] |
J. J. Zhang, L. Lin, Y. Zhang, M. Wu, B. I. Yakobson, S. Dong. Type-II multiferroic Hf2VC2F2 MXene monolayer with high transition temperature. J. Am. Chem. Soc., 2018, 140(30): 9768
CrossRef
ADS
Google scholar
|
[72] |
D. Amoroso, P. Barone, S. Picozzi. Spontaneous skyrmionic lattice from anisotropic symmetric exchange in a Ni-halide monolayer. Nat. Commun., 2020, 11(1): 5784
CrossRef
ADS
Google scholar
|
[73] |
J. Y. Ni, X. Y. Li, D. Amoroso, X. He, J. S. Feng, E. J. Kan, S. Picozzi, H. J. Xiang. Giant biquadratic exchange in 2D magnets and its role in stabilizing ferromagnetism of NiCl2 monolayers. Phys. Rev. Lett., 2021, 127(24): 247204
CrossRef
ADS
Google scholar
|
[74] |
H. Katsura, N. Nagaosa, A. V. Balatsky. Spin current and magnetoelectric effect in noncollinear magnets. Phys. Rev. Lett., 2005, 95(5): 057205
CrossRef
ADS
Google scholar
|
[75] |
D. Khomskii. Classifying multiferroics: Mechanisms and effects. Physics (College Park Md.), 2009, 2: 20
CrossRef
ADS
Google scholar
|
[76] |
Y. Tokura, S. Seki, N. Nagaosa. Multiferroics of spin origin. Rep. Prog. Phys., 2014, 77(7): 076501
CrossRef
ADS
Google scholar
|
[77] |
Q. Song, C. A. Occhialini, E. Ergeçen, B. Ilyas, D. Amoroso, P. Barone, J. Kapeghian, K. Watanabe, T. Taniguchi, A. S. Botana, S. Picozzi, N. Gedik, R. Comin. Evidence for a single-layer van der Waals multiferroic. Nature, 2022, 602(7898): 601
CrossRef
ADS
Google scholar
|
[78] |
D. R. Klein, D. MacNeill, J. L. Lado, D. Soriano, E. Navarro-Moratalla, K. Watanabe, T. Taniguchi, S. Manni, P. Canfield, J. Fernández-Rossier, P. Jarillo-Herrero. Probing magnetism in 2D van der Waals crystalline insulators via electron tunneling. Science, 2018, 360(6394): 1218
CrossRef
ADS
Google scholar
|
[79] |
Z. Wang, I. Gutiérrez-Lezama, N. Ubrig, M. Kroner, M. Gibertini, T. Taniguchi, K. Watanabe, A. Imamoğlu, E. Giannini, A. F. Morpurgo. Very large tunneling magnetoresistance in layered magnetic semiconductor CrI3. Nat. Commun., 2018, 9(1): 2516
CrossRef
ADS
Google scholar
|
[80] |
H. H. Kim, B. Yang, T. Patel, F. Sfigakis, C. Li, S. Tian, H. Lei, A. W. Tsen. One million percent tunnel magnetoresistance in a magnetic van der Waals heterostructure. Nano Lett., 2018, 18(8): 4885
CrossRef
ADS
Google scholar
|
[81] |
S. Jiang, L. Li, Z. Wang, K. F. Mak, J. Shan. Controlling magnetism in 2D CrI3 by electrostatic doping. Nat. Nanotechnol., 2018, 13(7): 549
CrossRef
ADS
Google scholar
|
[82] |
S. Jiang, J. Shan, K. F. Mak. Electric-field switching of two-dimensional van der Waals magnets. Nat. Mater., 2018, 17(5): 406
CrossRef
ADS
Google scholar
|
[83] |
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, X. Xu. Electrical control of 2D magnetism in bilayer CrI3. Nat. Nanotechnol., 2018, 13(7): 544
CrossRef
ADS
Google scholar
|
[84] |
H. H. Kim, B. Yang, S. Li, S. Jiang, C. Jin, Z. Tao, G. Nichols, F. Sfigakis, S. Zhong, C. Li, S. Tian, D. G. Cory, G. X. Miao, J. Shan, K. F. Mak, H. Lei, K. Sun, L. Zhao, A. W. Tsen. Evolution of interlayer and intralayer magnetism in three atomically thin chromium trihalides. Proc. Natl. Acad. Sci. USA, 2019, 116(23): 11131
CrossRef
ADS
Google scholar
|
[85] |
R. Xu, X. Zhou. Electric field-modulated magnetic phase transition in van der Waals CrI3 bilayers. J. Phys. Chem. Lett., 2020, 11(8): 3152
CrossRef
ADS
Google scholar
|
[86] |
N. Sivadas, S. Okamoto, X. Xu, C. J. Fennie, D. Xiao. Stacking-dependent magnetism in bilayer CrI3. Nano Lett., 2018, 18(12): 7658
CrossRef
ADS
Google scholar
|
[87] |
P. Jiang, C. Wang, D. Chen, Z. Zhong, Z. Yuan, Z. Y. Lu, W. Ji. Stacking tunable interlayer magnetism in bilayer CrI3. Phys. Rev. B, 2019, 99(14): 144401
CrossRef
ADS
Google scholar
|
[88] |
W. Chen, Z. Sun, Z. Wang, L. Gu, X. Xu, S. Wu, C. Gao. Direct observation of van der Waals stacking-dependent interlayer magnetism. Science, 2019, 366(6468): 983
CrossRef
ADS
Google scholar
|
[89] |
J. Xiao, B. Yan. An electron-counting rule to determine the interlayer magnetic coupling of the van der Waals materials. 2D Mater., 2020, 7: 045010
CrossRef
ADS
Google scholar
|
[90] |
T. Li, S. Jiang, N. Sivadas, Z. Wang, Y. Xu, D. Weber, J. E. Goldberger, K. Watanabe, T. Taniguchi, C. J. Fennie, K. Fai Mak, J. Shan. Pressure-controlled interlayer magnetism in atomically thin CrI3. Nat. Mater., 2019, 18(12): 1303
CrossRef
ADS
Google scholar
|
[91] |
Y. Xu, A. Ray, Y. T. Shao, S. Jiang, K. Lee, D. Weber, J. E. Goldberger, K. Watanabe, T. Taniguchi, D. A. Muller, K. F. Mak, J. Shan. Coexisting ferromagnetic–antiferromagnetic state in twisted bilayer CrI3. Nat. Nanotechnol., 2022, 17(2): 143
CrossRef
ADS
Google scholar
|
[92] |
C. Wang, X. Zhou, L. Zhou, Y. Pan, Z. Y. Lu, X. G. Wan, X. Q. Wang, W. Ji. Bethe−Slater-curve-like behavior and interlayer spin-exchange coupling mechanisms in two-dimensional magnetic bilayers. Phys. Rev. B, 2020, 102: 020402(R)
CrossRef
ADS
Google scholar
|
[93] |
L. Wu, L. Zhou, X. Zhou, C. Wang, W. Ji. In-plane epitaxy-strain-tuning intralayer and interlayer magnetic coupling in CrSe2 and CrTe2 monolayers and bilayers. Phys. Rev. B, 2022, 106(8): L081401
CrossRef
ADS
Google scholar
|
[94] |
J. C. Slonczewski. Fluctuation mechanism for biquadratic exchange coupling in magnetic multilayers. Phys. Rev. Lett., 1991, 67(22): 3172
CrossRef
ADS
Google scholar
|
[95] |
N. S. Fedorova, C. Ederer, N. A. Spaldin, A. Scaramucci. Biquadratic and ring exchange interactions in orthorhombic perovskite manganites. Phys. Rev. B, 2015, 91(16): 165122
CrossRef
ADS
Google scholar
|
[96] |
A. Kartsev, M. Augustin, R. F. L. Evans, K. S. Novoselov, E. J. G. Santos. Biquadratic exchange interactions in two-dimensional magnets. npj Comput. Mater., 2020, 6: 150
CrossRef
ADS
Google scholar
|
[97] |
L. Chen, J. H. Chung, B. Gao, T. Chen, M. B. Stone, A. I. Kolesnikov, Q. Huang, P. Dai. Topological spin excitations in honeycomb ferromagnet CrI3. Phys. Rev. X, 2018, 8(4): 041028
CrossRef
ADS
Google scholar
|
[98] |
L. Chen, J. H. Chung, M. B. Stone, A. I. Kolesnikov, B. Winn, V. O. Garlea, D. L. Abernathy, B. Gao, M. Augustin, E. J. G. Santos, P. Dai. Magnetic field effect on topological spin excitations in CrI3. Phys. Rev. X, 2021, 11(3): 031047
CrossRef
ADS
Google scholar
|
[99] |
D. A. Wahab, M. Augustin, S. M. Valero, W. Kuang, S. Jenkins, E. Coronado, I. V. Grigorieva, I. J. Vera-Marun, E. Navarro-Moratalla, R. F. L. Evans, K. S. Novoselov, E. J. G. Santos. Quantum rescaling, domain metastability, and hybrid domain‐walls in 2D CrI3 magnets. Adv. Mater., 2021, 33(5): 2004138
CrossRef
ADS
Google scholar
|
[100] |
P. A. Lindgard, R. J. Birgeneau, J. Als-Nielsen, H. J. Guggenheim. Spin-wave dispersion and sublattice magnetization in NiCl2. J. Phys. Chem., 1975, 8: 1059
|
[101] |
Z. Jiang, Y. Li, W. Duan, S. Zhang. Half-excitonic insulator: A single-spin Bose−Einstein condensate. Phys. Rev. Lett., 2019, 122(23): 236402
CrossRef
ADS
Google scholar
|
[102] |
S. Paul, S. Haldar, S. von Malottki, S. Heinze. Role of higher-order exchange interactions for skyrmion stability. Nat. Commun., 2020, 11(1): 4756
CrossRef
ADS
Google scholar
|
[103] |
B. Ding, Z. Li, G. Xu, H. Li, Z. Hou, E. Liu, X. Xi, F. Xu, Y. Yao, W. Wang. Observation of magnetic skyrmion bubbles in a van der Waals ferromagnet Fe3GeTe2. Nano Lett., 2020, 20(2): 868
CrossRef
ADS
Google scholar
|
[104] |
M. T. Birch, L. Powalla, S. Wintz, O. Hovorka, K. Litzius, J. C. Loudon, L. A. Turnbull, V. Nehruji, K. Son, C. Bubeck, T. G. Rauch, M. Weigand, E. Goering, M. Burghard, G. Schütz. History-dependent domain and skyrmion formation in 2D van der Waals magnet Fe3GeTe2. Nat. Commun., 2022, 13(1): 3035
CrossRef
ADS
Google scholar
|
[105] |
C. Xu, X. Li, P. Chen, Y. Zhang, H. Xiang, L. Bellaiche. Assembling diverse skyrmionic phases in Fe3GeTe2 monolayers. Adv. Mater., 2022, 34(12): 2107779
CrossRef
ADS
Google scholar
|
[106] |
X. Y. Li, F. Lou, X. G. Gong, H. Xiang. Constructing realistic effective spin Hamiltonians with machine learning approaches. New J. Phys., 2020, 22(5): 053036
CrossRef
ADS
Google scholar
|
[107] |
H. Yu, C. Xu, X. Li, F. Lou, L. Bellaiche, Z. Hu, X. Gong, H. Xiang. Complex spin Hamiltonian represented by an artificial neural network. Phys. Rev. B, 2022, 105(17): 174422
CrossRef
ADS
Google scholar
|
[108] |
I. Dzyaloshinsky. A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids, 1958, 4(4): 241
CrossRef
ADS
Google scholar
|
[109] |
T. Moriya. New mechanism of anisotropic superexchange interaction. Phys. Rev. Lett., 1960, 4(5): 228
CrossRef
ADS
Google scholar
|
[110] |
T. Moriya. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev., 1960, 120(1): 91
CrossRef
ADS
Google scholar
|
[111] |
A. Fert, P. M. Levy. Role of anisotropic exchange interactions in determining the properties of spin-glasses. Phys. Rev. Lett., 1980, 44(23): 1538
CrossRef
ADS
Google scholar
|
[112] |
P. M. Levy, A. Fert. Anisotropy induced by nonmagnetic impurities in Cu Mn spin-glass alloys. Phys. Rev. B, 1981, 23(9): 4667
CrossRef
ADS
Google scholar
|
[113] |
A. Kundu, S. Zhang. Dzyaloshinskii−Moriya interaction mediated by spin-polarized band with Rashba spin−orbit coupling. Phys. Rev. B, 2015, 92(9): 094434
CrossRef
ADS
Google scholar
|
[114] |
A. Fert, N. Reyren, V. Cros. Magnetic skyrmions: Advances in physics and potential applications. Nat. Rev. Mater., 2017, 2(7): 17031
CrossRef
ADS
Google scholar
|
[115] |
S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, P. Böni. Skyrmion lattice in a chiral magnet. Science, 2009, 323(5916): 915
CrossRef
ADS
Google scholar
|
[116] |
X. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagaosa, Y. Tokura. Real-space observation of a two-dimensional skyrmion crystal. Nature, 2010, 465(7300): 901
CrossRef
ADS
Google scholar
|
[117] |
X. Yu, N. Kanazawa, Y. Onose, K. Kimoto, W. Z. Zhang, S. Ishiwata, Y. Matsui, Y. Tokura. Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. Nat. Mater., 2011, 10(2): 106
CrossRef
ADS
Google scholar
|
[118] |
C. Moreau-Luchaire, C. Moutafis, N. Reyren, J. Sampaio, C. A. F. Vaz, N. Van Horne, K. Bouzehouane, K. Garcia, C. Deranlot, P. Warnicke, P. Wohlhüter, J. M. George, M. Weigand, J. Raabe, V. Cros, A. Fert. Additive interfacial chiral interaction in multilayers for stabilization of small individual skyrmions at room temperature. Nat. Nanotechnol., 2016, 11(5): 444
CrossRef
ADS
Google scholar
|
[119] |
A. Soumyanarayanan, M. Raju, A. L. Gonzalez Oyarce, A. K. C. Tan, M. Y. Im, A. P. Petrović, P. Ho, K. H. Khoo, M. Tran, C. K. Gan, F. Ernult, C. Panagopoulos. Tunable room-temperature magnetic skyrmions in Ir/Fe/Co/Pt multilayers. Nat. Mater., 2017, 16(9): 898
CrossRef
ADS
Google scholar
|
[120] |
O. Boulle, J. Vogel, H. Yang, S. Pizzini, D. de Souza Chaves, A. Locatelli, T. O. Menteş, A. Sala, L. D. Buda-Prejbeanu, O. Klein, M. Belmeguenai, Y. Roussigné, A. Stashkevich, S. M. Chérif, L. Aballe, M. Foerster, M. Chshiev, S. Auffret, I. M. Miron, G. Gaudin. Room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures. Nat. Nanotechnol., 2016, 11(5): 449
CrossRef
ADS
Google scholar
|
[121] |
H. Yang, O. Boulle, V. Cros, A. Fert, M. Chshiev. Controlling Dzyaloshinskii−Moriya interaction via chirality dependent atomic-layer stacking, insulator capping and electric field. Sci. Rep., 2018, 8(1): 12356
CrossRef
ADS
Google scholar
|
[122] |
A. Kundu, S. Zhang. Dzyaloshinskii−Moriya interaction mediated by spin-polarized band with Rashba spin-orbit coupling. Phys. Rev. B, 2015, 92(9): 094434
CrossRef
ADS
Google scholar
|
[123] |
A. A. Ado, A. Qaiumzadeh, R. A. Duine, A. Brataas, M. Titov. Asymmetric and symmetric exchange in a generalized 2D Rashba ferromagnet. Phys. Rev. Lett., 2018, 121(8): 086802
CrossRef
ADS
Google scholar
|
[124] |
H. Yang, G. Chen, A. A. C. Cotta, A. T. N’Diaye, S. A. Nikolaev, E. A. Soares, W. A. A. Macedo, K. Liu, A. K. Schmid, A. Fert, M. Chshiev. Significant Dzyaloshinskii−Moriya interaction at graphene-ferromagnet interfaces due to the Rashba effect. Nat. Mater., 2018, 17(7): 605
CrossRef
ADS
Google scholar
|
[125] |
A. Hallal, J. Liang, F. Ibrahim, H. Yang, A. Fert, M. Chshiev. Rashba-type Dzyaloshinskii−Moriya interaction, perpendicular magnetic anisotropy, and skyrmion states at 2D materials/Co interfaces. Nano Lett., 2021, 21(17): 7138
CrossRef
ADS
Google scholar
|
[126] |
J. Liang, W. Wang, H. Du, A. Hallal, K. Garcia, M. Chshiev, A. Fert, H. Yang. Very large Dzyaloshinskii-Moriya interaction in two-dimensional Janus manganese dichalcogenides and its application to realize skyrmion states. Phys. Rev. B, 2020, 101(18): 184401
CrossRef
ADS
Google scholar
|
[127] |
S. Heinze, K. von Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G. Bihlmayer, S. Blügel. Spontaneous atomic scale magnetic skyrmion lattice in two dimensions. Nat. Phys., 2011, 7(9): 713
CrossRef
ADS
Google scholar
|
[128] |
A. Belabbes, G. Bihlmayer, F. Bechstedt, S. Blügel, A. Manchon. Hund’s rule-driven Dzyaloshinskii−Moriya interaction at 3d−5d interfaces. Phys. Rev. Lett., 2016, 117(24): 247202
CrossRef
ADS
Google scholar
|
[129] |
C. Xu, J. Feng, S. Prokhorenko, Y. Nahas, H. Xiang, L. Bellaiche. Topological spin texture in Janus monolayers of the chromium trihalides Cr(I,X)3. Phys. Rev. B, 2020, 101(6): 060404
CrossRef
ADS
Google scholar
|
[130] |
Y. Zhang, C. Xu, P. Chen.
CrossRef
ADS
Google scholar
|
[131] |
S.LarefV. GoliI.Smaili,
|
[132] |
J. Jiang, X. Liu, R. Li, W. Mi. Topological spin textures in a two-dimensional MnBi2(Se,Te)4 Janus material. Appl. Phys. Lett., 2021, 119(7): 072401
CrossRef
ADS
Google scholar
|
[133] |
Q. Cui, Y. Zhu, J. Jiang, J. Liang, D. Yu, P. Cui, H. Yang. Ferroelectrically controlled topological magnetic phase in a Janus-magnet-based multiferroic heterostructure. Phys. Rev. Res., 2021, 3(4): 043011
CrossRef
ADS
Google scholar
|
[134] |
W. Du, K. Dou, Z. He, Y. Dai, B. Huang, Y. Ma, Spontaneous magnetic skyrmions in single-layer CrInX3 (X = Te. Se). Nano Lett., 2022, 22(8): 3440
CrossRef
ADS
Google scholar
|
[135] |
P. Li, Q. Cui, Y. Ga, J. Liang, H. Yang. Large Dzyaloshinskii−Moriya interaction and field-free topological chiral spin states in two-dimensional alkali-based chromium chalcogenides. Phys. Rev. B, 2022, 106(2): 024419
CrossRef
ADS
Google scholar
|
[136] |
F. Zhang, W. Mi, X. Wang, Spin-dependent electronic structure, magnetic anisotropy of 2D ferromagnetic Janus Cr2I3X3 (X = Br. Cl) monolayers. Adv. Electron. Mater., 2019,
CrossRef
ADS
Google scholar
|
[137] |
F. Zhang, H. Zhang, W. Mi, X. Wang, Electronic structure, magnetic anisotropy, Dzyaloshinskii–Moriya interaction in Janus Cr2I3X3 (X = Br. Cl) bilayers. Phys. Chem. Chem. Phys., 2020, 22(16): 8647
CrossRef
ADS
Google scholar
|
[138] |
R. Li, J. Jiang, X. Shi, W. Mi, H. Bai, Two-dimensional Janus FeXY (X, Y = Cl. Br, and I, X ≠ Y) monolayers: Half-metallic ferromagnets with tunable magnetic properties under strain. ACS Appl. Mater. Interfaces, 2021, 13(32): 38897
CrossRef
ADS
Google scholar
|
[139] |
J. Jiang, R. Li, W. Mi. Electrical control of topological spin textures in two-dimensional multiferroics. Nanoscale, 2021, 13(48): 20609
CrossRef
ADS
Google scholar
|
[140] |
Y. Xu, S. Qi, W. Mi, Electronic structure, magnetic properties of two-dimensional h-BN/Janus 2H-VSeX (X = S. Te) van der Waals heterostructures. Appl. Surf. Sci., 2021, 537: 147898
CrossRef
ADS
Google scholar
|
[141] |
S. Qi, J. Jiang, X. Wang, W. Mi. Valley polarization, magnetic anisotropy and Dzyaloshinskii−Moriya interaction of two-dimensional graphene/Janus 2H-VSeX (X = S, Te) heterostructures. Carbon, 2021, 174: 540
CrossRef
ADS
Google scholar
|
[142] |
Q. Cui, Y. Zhu, Y. Ga, J. Liang, P. Li, D. Yu, P. Cui, H. Yang. Anisotropic Dzyaloshinskii–Moriya interaction and topological magnetism in two-dimensional magnets protected by P4¯m2 crystal symmetry. Nano Lett., 2022, 22(6): 2334
CrossRef
ADS
Google scholar
|
[143] |
Y. Ga, Q. Cui, Y. Zhu, D. Yu, L. Wang, J. Liang, H. Yang. Anisotropic Dzyaloshinskii−Moriya interaction protected by D2d crystal symmetry in two-dimensional ternary compounds. npj Comput. Mater., 2022, 8: 128
CrossRef
ADS
Google scholar
|
[144] |
F. Matsukura, Y. Tokura, H. Ohno. Control of magnetism by electric fields. Nat. Nanotechnol., 2015, 10(3): 209
CrossRef
ADS
Google scholar
|
[145] |
P. J. Hsu, A. Kubetzka, A. Finco, N. Romming, K. von Bergmann, R. Wiesendanger. Electric-field-driven switching of individual magnetic skyrmions. Nat. Nanotechnol., 2017, 12(2): 123
CrossRef
ADS
Google scholar
|
[146] |
C. Tang, L. Zhang, S. Sanvito, A. Du. Electric-controlled half-metallicity in magnetic van der Waals heterobilayer. J. Mater. Chem. C, 2020, 8(21): 7034
CrossRef
ADS
Google scholar
|
[147] |
L. Zhang, C. Tang, S. Sanvito, Y. Gu, A. Du. Hydrogen-intercalated 2D magnetic bilayer: Controlled magnetic phase transition and half-metallicity via ferroelectric switching. ACS Appl. Mater. Interfaces, 2022, 14(1): 1800
CrossRef
ADS
Google scholar
|
[148] |
C. Xu, P. Chen, H. Tan, Y. Yang, H. Xiang, L. Bellaiche. Electric-field switching of magnetic topological charge in type-I multiferroics. Phys. Rev. Lett., 2020, 125(3): 037203
CrossRef
ADS
Google scholar
|
[149] |
J. Liang, Q. Cui, H. Yang. Electrically switchable Rashba-type Dzyaloshinskii−Moriya interaction and skyrmion in two-dimensional magnetoelectric multiferroics. Phys. Rev. B, 2020, 102(22): 220409
CrossRef
ADS
Google scholar
|
[150] |
Z. Shao, J. Liang, Q. Cui, M. Chshiev, A. Fert, T. Zhou, H. Yang. Multiferroic materials based on transition-metal dichalcogenides: Potential platform for reversible control of Dzyaloshinskii−Moriya interaction and skyrmion via electric field. Phys. Rev. B, 2022, 105(17): 174404
CrossRef
ADS
Google scholar
|
[151] |
Y. Wu, S. Zhang, J. Zhang, W. Wang, Y. L. Zhu, J. Hu, G. Yin, K. Wong, C. Fang, C. Wan, X. Han, Q. Shao, T. Taniguchi, K. Watanabe, J. Zang, Z. Mao, X. Zhang, K. L. Wang. Néel-type skyrmion in WTe2/Fe3GeTe2 van der Waals heterostructure. Nat. Commun., 2020, 11(1): 3860
CrossRef
ADS
Google scholar
|
[152] |
T. E. Park, L. Peng, J. Liang, A. Hallal, F. S. Yasin, X. Zhang, K. M. Song, S. J. Kim, K. Kim, M. Weigand, G. Schütz, S. Finizio, J. Raabe, K. Garcia, J. Xia, Y. Zhou, M. Ezawa, X. Liu, J. Chang, H. C. Koo, Y. D. Kim, M. Chshiev, A. Fert, H. Yang, X. Yu, S. Woo. Néel-type skyrmions and their current-induced motion in van der Waals ferromagnet-based heterostructures. Phys. Rev. B, 2021, 103(10): 104410
CrossRef
ADS
Google scholar
|
[153] |
Y.WuB.FranciscoW.Wang,
|
[154] |
W. Sun, W. Wang, H. Li, G. Zhang, D. Chen, J. Wang, Z. Cheng. Controlling bimerons as skyrmion analogues by ferroelectric polarization in 2D van der Waals multiferroic heterostructures. Nat. Commun., 2020, 11(1): 5930
CrossRef
ADS
Google scholar
|
[155] |
C. K. Li, X. P. Yao, G. Chen. Writing and deleting skyrmions with electric fields in a multiferroic heterostructure. Phys. Rev. Res., 2021, 3(1): L012026
CrossRef
ADS
Google scholar
|
[156] |
K. Dou, W. Du, Y. Dai, B. Huang, Y. Ma. Two-dimensional magnetoelectric multiferroics in a MnSTe/In2Se3 heterobilayer with ferroelectrically controllable skyrmions. Phys. Rev. B, 2022, 105(20): 205427
CrossRef
ADS
Google scholar
|
[157] |
W. Sun, W. Wang, J. Zang, H. Li, G. Zhang, J. Wang, Z. Cheng. Manipulation of magnetic skyrmion in a 2D van der Waals heterostructure via both electric and magnetic fields. Adv. Funct. Mater., 2021, 31(47): 2104452
CrossRef
ADS
Google scholar
|
[158] |
W. Sun, W. Wang, H. Li, X. Li, Z. Yu, Y. Bai, G Zhang, Z. Cheng. LaBr2 bilayer multiferroic moiré superlattice with robust magnetoelectric coupling and magnetic bimerons. npj Comput. Mater., 2022, 8: 159
CrossRef
ADS
Google scholar
|
[159] |
J. Chen, S. Dong. Manipulation of magnetic domain walls by ferroelectric switching: Dynamic magnetoelectricity at the nanoscale. Phys. Rev. Lett., 2021, 126: 117603
CrossRef
ADS
Google scholar
|
[160] |
Y. Onose, T. Ideue, H. Katsura, Y. Shiomi, N. Nagaosa, Y. Tokura. Observation of the magnon Hall effect. Science, 2010, 329(5989): 297
CrossRef
ADS
Google scholar
|
[161] |
R. Matsumoto, S. Murakami. Theoretical prediction of a rotating magnon wave packet in ferromagnets. Phys. Rev. Lett., 2011, 106(19): 197202
CrossRef
ADS
Google scholar
|
[162] |
R. Chisnell, J. S. Helton, D. E. Freedman, D. K. Singh, R. I. Bewley, D. G. Nocera, Y. S. Lee. Topological magnon bands in a kagome lattice ferromagnet. Phys. Rev. Lett., 2015, 115(14): 147201
CrossRef
ADS
Google scholar
|
[163] |
F. Zhu, L. Zhang, X. Wang, F. J. dos Santos, J. Song, T. Mueller, K. Schmalzl, W. F. Schmidt, A. Ivanov, J. T. Park, J. Xu, J. Ma, S. Lounis, S. Blügel, Y. Mokrousov, Y. Su, T. Brückel. Topological magnon insulators in two-dimensional van der Waals ferromagnets CrSiTe3 and CrGeTe3: Toward intrinsic gap-tunability. Sci. Adv., 2021, 7(37): eabi7532
CrossRef
ADS
Google scholar
|
[164] |
X. Yu, X. Zhang, Q. Shi, S. Tian, H. Lei, K. Xu, H. Hosono. Large magnetocaloric effect in van der Waals crystal CrBr3. Front. Phys., 2019, 14(4): 43501
CrossRef
ADS
Google scholar
|
[165] |
Q. Pei, X. C. Wang, J. J. Zou, W. B. Mi. Tunable electronic structure and magnetic coupling in strained two-dimensional semiconductor MnPSe3. Front. Phys., 2018, 13(4): 137105
CrossRef
ADS
Google scholar
|
/
〈 | 〉 |