Giant Dzyaloshinskii-Moriya interaction, strong XXZ-type biquadratic coupling, and bimeronic excitations in the two-dimensional CrMnI6 magnet
Source abstract
Abstract
Abstract Two-dimensional magnets have been discovered recently as a new class of quantum matter exhibiting a broad wealth of exotic phenomena, including notably various topological excitations rooted in emergent exchange couplings between the localized magnetic moments. By analyzing the anisotropies in the single-ion magnetization and two-body exchange couplings obtained from first-principles calculations, we reveal coexistence of both giant Dzyaloshinskii–Moriya interaction and strong anisotropic XXZ-type biquadratic coupling in a recently predicted monolayer CrMnI6 magnet. The former is induced by the spontaneous in-plane inversion symmetry breaking in the bipartite system, the latter is inherently tied to the distinct high-spin state of the Mn sublattice, while the large magnitudes of both stem from the significant spin-orbit coupling. Next, we use atomistic magnetics simulations to demonstrate the vital role of Dzyaloshinskii–Moriya interaction in harboring topological bimeronic excitations, and show that the biquadratic coupling favors a Berezinskii–Kosterlitz–Thouless-like transition as the system reduces its temperature from the paramagnetic phase. These findings substantially enrich our understanding of the microscopic couplings in 2D magnets, with appealing application potentials.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Advanced Condensed Matter Physics · Topological Materials and Phenomena · 2D Materials and Applications
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (60)
Show source-provided references
1. Mermin, N. D. & Wagner, H. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys. Rev. Lett. 17, 1133–1136 (1966).10.1103/PhysRevLett.17.1133 ↗
2. Hohenberg, P. C. Existence of long-range order in one and two dimensions. Phys. Rev. 158, 383–386 (1967).10.1103/PhysRev.158.383 ↗
3. Berezinsky, V. L. Destruction of long range order in one-dimensional and two-dimensional systems having a continuous symmetry group. I. Classical systems. Sov. Phys. JETP 32, 493–500 (1971).
4. Berezinsky, V. L. Destruction of Long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group. II. Quantum systems. Sov. Phys. JETP 34, 610 (1972).
5. Kosterlitz, J. M. & Thouless, D. J. Long range order and metastability in two dimensional solids and superfluids. (application of dislocation theory). J. Phys. C: Solid State Phys. 5, L124–L126 (1972).10.1088/0022-3719/5/11/002 ↗
6. Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017).10.1038/nature22391 ↗
7. Gong, C. et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature 546, 265–269 (2017).10.1038/nature22060 ↗
8. Dzyaloshinsky, I. A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958).10.1016/0022-3697(58)90076-3 ↗
9. Moriya, T. New mechanism of anisotropic superexchange interaction. Phys. Rev. Lett. 4, 228–230 (1960).10.1103/PhysRevLett.4.228 ↗
10. Parkin, S. & Yang, S.-H. Memory on the racetrack. Nat. Nanotechnol. 10, 195–198 (2015).10.1038/nnano.2015.41 ↗
11. Mühlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009).10.1126/science.1166767 ↗
12. Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010).10.1038/nature09124 ↗
13. Tokura, Y. & Kanazawa, N. Magnetic skyrmion materials. Chem. Rev. 121, 2857 (2021).10.1021/acs.chemrev.0c00297 ↗
14. Yu, X. Z. et al. Transformation between meron and skyrmion topological spin textures in a chiral magnet. Nature 564, 95–98 (2018).10.1038/s41586-018-0745-3 ↗
15. Xu, C., Feng, J., Xiang, H. & Bellaiche, L. Interplay between Kitaev interaction and single ion anisotropy in ferromagnetic CrI3 and CrGeTe3 monolayers. npj Comput. Mater. 4, 57 (2018).10.1038/s41524-018-0115-6 ↗
16. Zhu, F. et al. Topological magnon insulators in two-dimensional van der waals ferromagnets CrSiTe3 and CrGeTe3: Toward intrinsic gap-tunability. Sci. Adv. 7, eabi7532 (2021).10.1126/sciadv.abi7532 ↗
17. Liu, J., Shi, M., Lu, J. & Anantram, M. P. Analysis of electrical-field-dependent Dzyaloshinskii-Moriya interaction and magnetocrystalline anisotropy in a two-dimensional ferromagnetic monolayer. Phys. Rev. B 97, 054416 (2018).10.1103/PhysRevB.97.054416 ↗
18. Cui, Q., Liang, J., Shao, Z., Cui, P. & Yang, H. Strain-tunable ferromagnetism and chiral spin textures in two-dimensional Janus chromium dichalcogenides. Phys. Rev. B 102, 094425 (2020).10.1103/PhysRevB.102.094425 ↗
19. Xu, C. et al. Topological spin texture in Janus monolayers of the chromium trihalides Cr(I, X)3. Phys. Rev. B 101, 060404 (2020).10.1103/PhysRevB.101.060404 ↗
20. Yuan, J. et al. Intrinsic skyrmions in monolayer Janus magnets. Phys. Rev. B 101, 094420 (2020).10.1103/PhysRevB.101.094420 ↗
21. Sun, W. et al. Controlling bimerons as skyrmion analogues by ferroelectric polarization in 2D van der Waals multiferroic heterostructures. Nat. Commun. 11, 5930 (2020).10.1038/s41467-020-19779-6 ↗
22. Zhang, H., Yang, W., Cui, P., Xu, X. & Zhang, Z. Prediction of monolayered ferromagnetic CrMnI6 as an intrinsic high-temperature quantum anomalous Hall system. Phys. Rev. B 102, 115413 (2020).10.1103/PhysRevB.102.115413 ↗
23. Lee, J.-H. et al. Multiple spin-orbit excitons in α-RuCl3 from bulk to atomically thin layers. npj Quantum Mater. 6, 43 (2021).10.1038/s41535-021-00340-7 ↗
24. Xiang, H., Kan, E., Wei, S.-H., Whangbo, M. H. & Gong, X. Predicting the spin-lattice order of frustrated systems from first principles. Phys. Rev. B 84, 224429 (2011).10.1103/PhysRevB.84.224429 ↗
25. Xiang, H., Lee, C., Koo, H.-J., Gong, X. & Whangbo, M.-H. Magnetic properties and energy-mapping analysis. Dalton. Trans. 42, 823–853 (2013).10.1039/C2DT31662E ↗
26. Šabani, D., Bacaksiz, C. & Milošević, M. V. Ab initio methodology for magnetic exchange parameters: generic four-state energy mapping onto a Heisenberg spin Hamiltonian. Phys. Rev. B 102, 014457 (2020).10.1103/PhysRevB.102.014457 ↗
27. Xu, C. et al. Possible Kitaev quantum spin liquid state in 2D materials with S=3/2. Phys. Rev. Lett. 124, 087205 (2020).10.1103/PhysRevLett.124.087205 ↗
28. Xu, C. et al. Electric-field switching of magnetic topological charge in Type-I multiferroics. Phys. Rev. Lett. 125, 037203 (2020).10.1103/PhysRevLett.125.037203 ↗
29. Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98 (1960).10.1103/PhysRev.120.91 ↗
30. Liang, J. et al. Very large Dzyaloshinskii-Moriya interaction in two-dimensional Janus manganese dichalcogenides and its application to realize skyrmion states. Phys. Rev. B 101, 184401 (2020).10.1103/PhysRevB.101.184401 ↗
31. Fert, A., Cros, V. & Sampaio, J. Skyrmions on the track. Nat. Nanotechnol. 8, 152–156 (2013).10.1038/nnano.2013.29 ↗
32. Heinze, S. et al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713–718 (2011).10.1038/nphys2045 ↗
33. Brinker, S., dos Santos Dias, M. & Lounis, S. Prospecting chiral multisite interactions in prototypical magnetic systems. Phys. Rev. Res. 2, 033240 (2020).10.1103/PhysRevResearch.2.033240 ↗
34. Mila, F. & Zhang, F.-C. On the origin of biquadratic exchange in spin 1 chains. Eur. Phys. J. B 16, 7–10 (2000).10.1007/s100510070242 ↗
35. Wysocki, A. L., Belashchenko, K. D. & Antropov, V. P. Consistent model of magnetism in ferropnictides. Nat. Phys. 7, 485–489 (2011).10.1038/nphys1933 ↗
36. Zhu, H.-F. et al. Giant biquadratic interaction-induced magnetic anisotropy in the iron-based superconductor AxFe2−ySe2. Phys. Rev. B 93, 024511 (2016).10.1103/PhysRevB.93.024511 ↗
37. Kartsev, A., Augustin, M., Evans, R. F. L., Novoselov, K. S. & Santos, E. J. G. Biquadratic exchange interactions in two-dimensional magnets. npj Comput. Mater. 6, 150 (2020).10.1038/s41524-020-00416-1 ↗
38. Paul, S., Haldar, S., von Malottki, S. & Heinze, S. Role of higher-order exchange interactions for skyrmion stability. Nat. Commun. 11, 4756 (2020).10.1038/s41467-020-18473-x ↗
39. Ni, J. et al. Giant biquadratic exchange in 2D magnets and its role in stabilizing ferromagnetism of NiCl2 monolayers. Phys. Rev. Lett. 127, 247204 (2021).10.1103/PhysRevLett.127.247204 ↗
40. Brinker, S., dos Santos Dias, M. & Lounis, S. The chiral biquadratic pair interaction. N. J. Phys. 21, 083015 (2019).10.1088/1367-2630/ab35c9 ↗
41. Rachel, S. & Le Hur, K. Topological insulators and Mott physics from the Hubbard interaction. Phys. Rev. B 82, 075106 (2010).10.1103/PhysRevB.82.075106 ↗
42. Vaezi, A., Mashkoori, M. & Hosseini, M. Phase diagram of the strongly correlated Kane-Mele-Hubbard model. Phys. Rev. B 85, 195126 (2012).10.1103/PhysRevB.85.195126 ↗
43. Gilbert, T. L. A phenomenological theory of damping in ferromagnetic materials. IEEE Trans. Magn. 40, 3443–3449 (2004).10.1109/TMAG.2004.836740 ↗
44. Berg, B. & Lüscher, M. Definition and statistical distributions of a topological number in the lattice O(3) σ-model. Nucl. Phys. B 190, 412–424 (1981).10.1016/0550-3213(81)90568-X ↗
45. Göbel, B., Mertig, I. & Tretiakov, O. A. Beyond skyrmions: review and perspectives of alternative magnetic quasiparticles. Phys. Rep. 895, 1–28 (2021).10.1016/j.physrep.2020.10.001 ↗
46. Bramwell, S. T. & Holdsworth, P. C. W. Magnetization and universal sub-critical behaviour in two-dimensional XY magnets. J. Phys. Condens. Matter 5, L53 (1993).10.1088/0953-8984/5/4/004 ↗
47. Bedoya-Pinto, A. et al. Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer. Science 374, 616–620 (2021).10.1126/science.abd5146 ↗
48. Zhou, J. et al. Composition and phase engineering of metal chalcogenides and phosphorous chalcogenides. Nat. Mater. 22, 450–458 (2023).10.1038/s41563-022-01291-5 ↗
49. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).10.1103/PhysRevB.54.11169 ↗
50. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).10.1103/PhysRevB.50.17953 ↗
51. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).10.1103/PhysRevB.59.1758 ↗
52. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).10.1103/PhysRevLett.77.3865 ↗
53. Ma, P.-W. & Dudarev, S. L. Constrained density functional for noncollinear magnetism. Phys. Rev. B 91, 054420 (2015).10.1103/PhysRevB.91.054420 ↗
54. Dudarev, S. L., Botton, G. A., Savrasov, S. Y., Humphreys, C. J. & Sutton, A. P. Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998).10.1103/PhysRevB.57.1505 ↗
55. Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).10.1107/S0021889811038970 ↗
56. Zhang, S. PyASD: python-based atomistic spin dynamics and Monte Carlo simulators. https://pypi.org/project/pyasd (2023) .
57. Depondt, P. & Mertens, F. G. Spin dynamics simulations of two-dimensional clusters with Heisenberg and dipole-dipole interactions. J. Phys. Condens. Matter 21, 336005 (2009).10.1088/0953-8984/21/33/336005 ↗
58. Lee, K. J., Park, N. Y. & Lee, T. D. Numerical study of spin relaxation by thermal fluctuation: effect of shape anisotropy. J. Appl. Phys. 89, 7460–7462 (2001).10.1063/1.1355348 ↗
59. Chubykalo, O., Hannay, J. D., Wongsam, M., Chantrell, R. W. & Gonzalez, J. M. Langevin dynamic simulation of spin waves in a micromagnetic model. Phys. Rev. B 65, 184428 (2002).10.1103/PhysRevB.65.184428 ↗
60. Müller, G. P. et al. Spirit: multifunctional framework for atomistic spin simulations. Phys. Rev. B 99, 224414 (2019).10.1103/PhysRevB.99.224414 ↗