journal article·2024-09-14Open access

Unconventional spin textures emerging from a universal symmetry theory of spin-momentum locking

Yuntian Liu, Jiayu Li, Pengfei Liu, Qihang Liu

npj Quantum Materials· Volume 9· Issue 1

Abstract

Spin textures, i.e., the distribution of spin polarization vectors in reciprocal space, exhibit diverse patterns determined by symmetry constraints, resulting in a variety of spintronic phenomena. Here, we propose a universal theory to comprehensively describe the nature of spin textures by incorporating three symmetry flavors of reciprocal wavevector, atomic orbital, and atomic site. Such an approach enables us to establish a complete classification of spin textures constrained by the little co-group and predict some exotic spin texture types, such as Zeeman-type spin splitting in antiferromagnets and quadratic spin texture. To illustrate the influence of atomic orbitals and sites on spin textures, we predict orbital-dependent spin texture and anisotropic spin-momentum-site locking effects, and corresponding material candidates validated through first-principles calculations. The comprehensive classification and the predicted new spin textures in realistic materials are expected to trigger future spin-based functionalities in electronics.
Source: openalex_inverted_index · Quality: baseline

Research context

OpenAlex topics: Magnetic properties of thin films · Topological Materials and Phenomena · Quantum many-body systems

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (71)

Show source-provided references
1. Ohno, H. et al. Electric-field control of ferromagnetism. Nature 408, 944 (2000).10.1038/35050040 ↗
2. Chappert, C., Fert, A. & Van Dau, F. N. The emergence of spin electronics in data storage. Nat. Mater. 6, 813 (2007).10.1038/nmat2024 ↗
3. Wunderlich, J. et al. Spin hall effect transistor. Science 330, 1801 (2010).10.1126/science.1195816 ↗
4. Wang, K. L. et al. Electric-field control of spin-orbit interaction for low-power spintronics. Proc. IEEE 104, 1974 (2016).10.1109/JPROC.2016.2573836 ↗
5. R. Winkler. Spin-orbit coupling effects in two-dimensional electron and hole systems (Springer, Berlin, Heidelberg, 2003).10.1007/b13586 ↗
6. Datta, S. & Das, B. Electronic analog of the electro‐optic modulator,. Appl. Phys. Lett. 56, 665 (1990).10.1063/1.102730 ↗
7. Koo, H. C. et al. Control of spin precession in a spin-injected field effect transistor. Science 325, 1515 (2009).10.1126/science.1173667 ↗
8. Ganichev, S. D. Spin-galvanic effect and spin orientation by current in non-magnetic semiconductors. Int. J. Mod. Phys. B 22, 1 (2008).10.1142/S0217979208046001 ↗
9. Murakami, S., Nagaosa, N. & Zhang, S. C. Dissipationless quantum spin current at room temperature. Science 301, 1348 (2003).10.1126/science.1087128 ↗
10. Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Experimental observation of the spin-Hall effect in a two-dimensional spin-orbit coupled semiconductor system. Phys. Rev. Lett. 94, 047204 (2005).10.1103/PhysRevLett.94.047204 ↗
11. Bernevig, B. A. & Vafek, O. Piezo-magnetoelectric effects in p-doped semiconductors. Phys. Rev. B 72, 033203 (2005).10.1103/PhysRevB.72.033203 ↗
12. Manchon, A. & Zhang, S. Theory of nonequilibrium intrinsic spin torque in a single nanomagnet. Phys. Rev. B 78, 212405 (2008).10.1103/PhysRevB.78.212405 ↗
13. Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature 476, 189 (2011).10.1038/nature10309 ↗
14. Dresselhaus, G. Spin-orbit coupling effects in zinc blende structures. Phys. Rev. 100, 580 (1955).10.1103/PhysRev.100.580 ↗
15. Rashba, E. I. Properties of semiconductors with an extremum loop .1. Cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop. Sov. Phys. Sol. State 2, 1109 (1960).
16. Ishizaka, K. et al. Giant Rashba-type spin splitting in bulk BiTeI. Nat. Mater. 10, 521 (2011).10.1038/nmat3051 ↗
17. Zhao, H. J. et al. Purely cubic spin splittings with persistent spin textures. Phys. Rev. Lett. 125, 216405 (2020).10.1103/PhysRevLett.125.216405 ↗
18. Li, Y. L. et al. Valley splitting and polarization by the Zeeman effect in monolayer MoSe2. Phys. Rev. Lett. 113, 266804 (2014).10.1103/PhysRevLett.113.266804 ↗
19. Acosta, C. M., Fazzio, A. & Dalpian, G. M. Zeeman-type spin splitting in nonmagnetic three-dimensional compounds. Npj Quantum Mater. 4, 41 (2019).10.1038/s41535-019-0182-z ↗
20. Bernevig, B. A., Orenstein, J. & Zhang, S. C. Exact SU(2) symmetry and persistent spin helix in a spin-orbit coupled system. Phys. Rev. Lett. 97, 236601 (2006).10.1103/PhysRevLett.97.236601 ↗
21. Koralek, J. D. et al. Emergence of the persistent spin helix in semiconductor quantum wells. Nature 458, 610 (2009).10.1038/nature07871 ↗
22. Tao, L. L. & Tsymbal, E. Y. Persistent spin texture enforced by symmetry. Nat. Commun. 9, 2763 (2018).10.1038/s41467-018-05137-0 ↗
23. Liu, Q. H., Guo, Y. Z. & Freeman, A. J. Tunable Rashba effect in two-dimensional LaOBiS2 films: ultrathin candidates for spin field effect transistors. Nano. Lett. 13, 5264 (2013).10.1021/nl4027346 ↗
24. Zhang, X. W., Liu, Q. H., Luo, J. W., Freeman, A. J. & Zunger, A. Hidden spin polarization in inversion-symmetric bulk crystals. Nat. Phys. 10, 387 (2014).10.1038/nphys2933 ↗
25. Železný, J. et al. Relativistic Néel-order fields induced by electrical current in antiferromagnets. Phys. Rev. Lett. 113, 157201 (2014).10.1103/PhysRevLett.113.157201 ↗
26. Wadley, P. et al. Electrical switching of an antiferromagnet. Science 351, 587 (2016).10.1126/science.aab1031 ↗
27. Zhang, K. et al. Observation of spin-momentum-layer locking in a centrosymmetric crystal. Phys. Rev. Lett. 127, 126402 (2021).10.1103/PhysRevLett.127.126402 ↗
28. Chen, W. Z., Gu, M. Q., Li, J. Y., Wang, P. S. & Liu, Q. H. Role of hidden spin polarization in nonreciprocal transport of antiferromagnets. Phys. Rev. Lett. 129, 276601 (2022).10.1103/PhysRevLett.129.276601 ↗
29. Zak, J. Band representations of space-groups. Phys. Rev. B 26, 3010 (1982).10.1103/PhysRevB.26.3010 ↗
30. Bradlyn, B. et al. Topological quantum chemistry. Nature 547, 298 (2017).10.1038/nature23268 ↗
31. Kruthoff, J., de Boer, J., van Wezel, J., Kane, C. L. & Slager, R. J. Topological classification of crystalline insulators through band structure combinatorics. Phys. Rev. X 7, 041069 (2017).
32. Cano, J. et al. Building blocks of topological quantum chemistry: elementary band representations. Phys. Rev. B 97, 035139 (2018).10.1103/PhysRevB.97.035139 ↗
33. Acosta, C. M., Yuan, L. D., Dalpian, G. M. & Zunger, A. Different shapes of spin textures as a journey through the Brillouin zone. Phys. Rev. B 104, 104408 (2021).10.1103/PhysRevB.104.104408 ↗
34. Jain, A. et al. Commentary: the materials project: a materials genome approach to accelerating materials innovation. APL Mater. 1, 011002 (2013).10.1063/1.4812323 ↗
35. Chen, H., Niu, Q. & MacDonald, A. H. Anomalous hall effect arising from noncollinear antiferromagnetism. Phys. Rev. Lett. 112, 017205 (2014).10.1103/PhysRevLett.112.017205 ↗
36. Šmejkal, L., González-Hernández, R., Jungwirth, T. & Sinova, J. Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets. Sci. Adv. 6, eaaz8809 (2020).10.1126/sciadv.aaz8809 ↗
37. Krempaský, J. et al. Altermagnetic lifting of Kramers spin degeneracy. Nature 626, 517 (2024).10.1038/s41586-023-06907-7 ↗
38. Ramazashvili, R. Kramers degeneracy in a magnetic field and Zeeman spin-orbit coupling in antiferromagnetic conductors. Phys. Rev. Lett. 101, 137202 (2008).10.1103/PhysRevLett.101.137202 ↗
39. Ramazashvili, R. Zeeman spin-orbit coupling in antiferromagnetic conductors. J. Phys. Chem. Solids 128, 65 (2019).10.1016/j.jpcs.2018.09.033 ↗
40. Ramazashvili, R. Kramers degeneracy in a magnetic field and Zeeman spin-orbit coupling in antiferromagnetic conductors. Phys. Rev. B 79, 184432 (2009).10.1103/PhysRevB.79.184432 ↗
41. Ramazashvili, R. Quantum oscillations in antiferromagnetic conductors with small carrier pockets. Phys. Rev. Lett. 105, 216404 (2010).10.1103/PhysRevLett.105.216404 ↗
42. Ramazashvili, R. et al. Experimental evidence for Zeeman spin-orbit coupling in layered antiferromagnetic conductors. Npj Quantum Mater. 6, 11 (2021).10.1038/s41535-021-00309-6 ↗
43. Šmejkal, L., Sinova, J. & Jungwirth, T. Beyond conventional ferromagnetism and antiferromagnetism: a phase with nonrelativistic spin and crystal rotation symmetry. Phys. Rev. X 12, 031042 (2022).
44. Zhang, H. J., Liu, C. X. & Zhang, S. C. Spin-orbital texture in topological insulators. Phys. Rev. Lett. 111, 066801 (2013).10.1103/PhysRevLett.111.066801 ↗
45. Hayami, S. & Kusunose, H. Spin-orbital-momentum locking under odd-parity magnetic quadrupole ordering. Phys. Rev. B 104, 045117 (2021).10.1103/PhysRevB.104.045117 ↗
46. Schulz, S. et al. Classical and cubic Rashba effect in the presence of in-plane 4f magnetism at the iridium silicide surface of the antiferromagnet GdIr2Si2. Phys. Rev. B 103, 035123 (2021).10.1103/PhysRevB.103.035123 ↗
47. Park, S. R. et al. Chiral orbital-angular momentum in the surface states of Bi2Se3. Phys. Rev. Lett. 108, 046805 (2012).10.1103/PhysRevLett.108.046805 ↗
48. Cao, Y. et al. Mapping the orbital wavefunction of the surface states in three-dimensional topological insulators. Nat. Phys. 9, 499 (2013).10.1038/nphys2685 ↗
49. Zhu, Z. H. et al. Layer-by-layer entangled spin-orbital texture of the topological surface state in Bi2Se3. Phys. Rev. Lett. 110, 216401 (2013).10.1103/PhysRevLett.110.216401 ↗
50. Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45 (1984).10.1098/rspa.1984.0023 ↗
51. Xiao, D., Chang, M. C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959 (2010).10.1103/RevModPhys.82.1959 ↗
52. Hayami, S., Yanagi, Y. & Kusunose, H. Momentum-dependent spin splitting by collinear antiferromagnetic ordering. J. Phys. Soc. Jpn. 88, 123702 (2019).10.7566/JPSJ.88.123702 ↗
53. Hayami, S., Yanagi, Y. & Kusunose, H. Spontaneous antisymmetric spin splitting in noncollinear antiferromagnets without spin-orbit coupling. Phys. Rev. B 101, 220403 (2020).10.1103/PhysRevB.101.220403 ↗
54. Yuan, L. D., Wang, Z., Luo, J. W., Rashba, E. I. & Zunger, A. Giant momentum-dependent spin splitting in centrosymmetric low-Z antiferromagnets. Phys. Rev. B 102, 014422 (2020).10.1103/PhysRevB.102.014422 ↗
55. Yuan, L. D., Wang, Z., Luo, J. W. & Zunger, A. Prediction of low-Z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling. Phys. Rev. Mater. 5, 014409 (2021).10.1103/PhysRevMaterials.5.014409 ↗
56. Mazin, I. I., Koepernik, K., Johannes, M. D., González-Hernández, R. & Šmejkal, L. Prediction of unconventional magnetism in doped FeSb. PNAS 118, e2108924118 (2021).10.1073/pnas.2108924118 ↗
57. Zhu, Y.-P. et al. Observation of plaid-like spin splitting in a noncoplanar antiferromagnet. Nature 626, 523 (2024).10.1038/s41586-024-07023-w ↗
58. Litvin, D. B. Spin point groups. Acta Crystallogr. Sect. A 33, 279 (1977).10.1107/S0567739477000709 ↗
59. Liu, P., Li, J., Han, J., Wan, X. & Liu, Q. Spin-group symmetry in magnetic materials with negligible spin-orbit coupling. Phys. Rev. X 12, 021016 (2022).
60. Chen, X. et al. Enumeration and representation theory of spin space groups. Phys. Rev. X 14, 031038 (2024).
61. Xiao, Z., Zhao, J., Li, Y., Shindou, R. & Song, Z.-D. Spin space groups: full classification and applications. Phys. Rev. X 14, 031037 (2024).
62. Jiang, Y. et al. Enumeration of spin-space groups: towards a complete description of symmetries of magnetic orders. Phys. Rev. X 14, 031039 (2024).
63. Yao, W. et al. Direct observation of spin-layer locking by local Rashba effect in monolayer semiconducting PtSe2 film. Nat. Commun. 8, 14216 (2017).10.1038/ncomms14216 ↗
64. Kresse, G. & Furthmuller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).10.1103/PhysRevB.54.11169 ↗
65. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).10.1103/PhysRevB.59.1758 ↗
66. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).10.1103/PhysRev.136.B864 ↗
67. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, 1133 (1965).10.1103/PhysRev.140.A1133 ↗
68. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).10.1103/PhysRevLett.77.3865 ↗
69. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple (vol 77, pg 3865, 1996). Phys. Rev. Lett. 78, 1396 (1997).10.1103/PhysRevLett.78.1396 ↗
70. Ast, C. R. et al. Giant spin splitting through surface alloying. Phys. Rev. Lett. 98, 186807 (2007).10.1103/PhysRevLett.98.186807 ↗
71. Luo, J. W., Bester, G. & Zunger, A. Full-zone spin splitting for electrons and holes in bulk GaAs and GaSb. Phys. Rev. Lett. 102, 056405 (2009).10.1103/PhysRevLett.102.056405 ↗