Altermagnetic lifting of Kramers spin degeneracy

Abstract

Lifted Kramers spin degeneracy (LKSD) has been among the central topics of condensed-matter physics since the dawn of the band theory of solids 1,2 . It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology 3–7 to topological quantum matter 8–14 . Traditionally, LKSD has been considered to originate from two possible internal symmetry-breaking mechanisms. The first refers to time-reversal symmetry breaking by magnetization of ferromagnets and tends to be strong because of the non-relativistic exchange origin 15 . The second applies to crystals with broken inversion symmetry and tends to be comparatively weaker, as it originates from the relativistic spin–orbit coupling (SOC) 16–19 . A recent theory work based on spin-symmetry classification has identified an unconventional magnetic phase, dubbed altermagnetic 20,21 , that allows for LKSD without net magnetization and inversion-symmetry breaking. Here we provide the confirmation using photoemission spectroscopy and ab initio calculations. We identify two distinct unconventional mechanisms of LKSD generated by the altermagnetic phase of centrosymmetric MnTe with vanishing net magnetization 20–23 . Our observation of the altermagnetic LKSD can have broad consequences in magnetism. It motivates exploration and exploitation of the unconventional nature of this magnetic phase in an extended family of materials, ranging from insulators and semiconductors to metals and superconductors 20,21 , that have been either identified recently or perceived for many decades as conventional antiferromagnets 21,24,25 .

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References 64

1. 1.

   Kramers HA. Théorie générale de la rotation paramagnétique dans les cristaux. Proc. Amsterdam Akad. 1930;33:959-972.

   Not in our library

2. 2.

   Wigner EP. Über die Operation der Zeitumkehr in der Quantenmechanik. Nachr. Ges. Wiss. Gottingen, Math. Phys. Kl. 1932;1932:546-559.

   Not in our library

3. 3.

   Chappert C, Fert A, Van Dau FN. The emergence of spin electronics in data storage. Nat. Mater. 2007;6:813-823.

   Not in our library10.1038/nmat2024

4. 4.

   Ralph DC, Stiles MD. Spin transfer torques. J. Magn. Magn. Mater. 2008;320:1190-1216.

   Not in our library10.1016/j.jmmm.2007.12.019

5. 5.

   Bader SD, Parkin S. Spintronics. Annu. Rev. Condens. Matter Phys. 2010;1:71-88.

   Not in our library10.1146/annurev-conmatphys-070909-104123

6. 6.

   Bhatti S, et al. Spintronics based random access memory: a review. Mater. Today. 2017;20:530-548.

   Not in our library10.1016/j.mattod.2017.07.007

7. 7.

   Manchon A, et al. Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys. 2019;91:035004.

   Not in our library10.1103/revmodphys.91.035004

8. 8.

   Nagaosa N, Sinova J, Onoda S, MacDonald AH, Ong NP. Anomalous Hall effect. Rev. Mod. Phys. 2010;82:1539-1592.

   Not in our library10.1103/revmodphys.82.1539

9. 9.

   Franz, M. & Molenkamp, L. (eds) Topological Insulators Vol. 6 (Elsevier, 2013).

   Not in our library

10. 10.

    Šmejkal L, Mokrousov Y, Yan B, MacDonald AH. Topological antiferromagnetic spintronics. Nat. Phys. 2018;14:242-251.

    Not in our library10.1038/s41567-018-0064-5

11. 11.

    Zang, J., Cros, V. & Hoffmann, A. (eds) Topology in Magnetism (Springer, 2018).

    Not in our library

12. 12.

    Tokura Y, Yasuda K, Tsukazaki A. Magnetic topological insulators. Nat. Rev. Phys. 2019;1:126-143.

    Not in our library10.1038/s42254-018-0011-5

13. 13.

    Vergniory MG, et al. A complete catalogue of high-quality topological materials. Nature. 2019;566:480-485.

    Not in our library10.1038/s41586-019-0954-4

14. 14.

    Šmejkal L, MacDonald AH, Sinova J, Nakatsuji S, Jungwirth T. Anomalous Hall antiferromagnets. Nat. Rev. Mater. 2022;7:482-496.

    Not in our library10.1038/s41578-022-00430-3

15. 15.

    Landau, L. D. & Lifshitz, E. M. Electrodynamics of Continuous Media 2nd edn (Pergamon Press, Oxford, 1984).

    Not in our library

16. 16.

    Winkler, R. Spin–Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, 2003).

    Not in our library

17. 17.

    Armitage NP, Mele EJ, Vishwanath A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 2018;90:015001.

    Not in our library10.1103/revmodphys.90.015001

18. 18.

    Krempaský J, et al. Disentangling bulk and surface Rashba effects in ferroelectric α-GeTe. Phys. Rev. B. 2016;94:205111.

    Not in our library10.1103/physrevb.94.205111

19. 19.

    Sante DD, Barone P, Bertacco R, Picozzi S. Electric control of the giant Rashba effect in bulk GeTe. Adv. Mater. 2013;25:509-513.

    Not in our library10.1002/adma.201203199

20. 20.

    Šmejkal L, Sinova J, Jungwirth T. Beyond conventional ferromagnetism and antiferromagnetism: a phase with nonrelativistic spin and crystal rotation symmetry. Phys. Rev. 2022;12:031042.

    Not in our library10.1103/physrevx.12.031042

21. 21.

    Šmejkal L, Sinova J, Jungwirth T. Emerging research landscape of altermagnetism. Phys. Rev. 2022;12:040501.

    Not in our library10.1103/physrevx.12.040501

22. 22.

    Gonzalez Betancourt RD, et al. Spontaneous anomalous Hall effect arising from an unconventional compensated magnetic phase in a semiconductor. Phys. Rev. Lett. 2023;130:036702.

    Not in our library10.1103/physrevlett.130.036702

23. 23.

    Mazin II. Altermagnetism in MnTe: origin, predicted manifestations, and routes to detwinning. Phys. Rev. B. 2023;107:L100418.

    Not in our library10.1103/physrevb.107.l100418

24. 24.

    Néel L. Magnetism and local molecular field. Science. 1971;174:985-992.

    Not in our library10.1126/science.174.4013.985

25. 25.

    Kunitomi N, Hamaguchi Y, Anzai S. Neutron diffraction study on manganese telluride. J. Phys. 1964;25:568-574.

    Not in our library10.1051/jphys:01964002505056800

26. 26.

    Šmejkal L, Železný J, Sinova J, Jungwirth T. Electric control of Dirac quasiparticles by spin-orbit torque in an antiferromagnet. Phys. Rev. Lett. 2017;118:106402.

    Not in our library10.1103/physrevlett.118.106402

27. 27.

    Naka M, et al. Spin current generation in organic antiferromagnets. Nat. Commun. 2019;10:4305.

    Not in our library10.1038/s41467-019-12229-y

28. 28.

    González-Hernández R, et al. Efficient electrical spin splitter based on nonrelativistic collinear antiferromagnetism. Phys. Rev. Lett. 2021;126:127701.

    Not in our library10.1103/physrevlett.126.127701

29. 29.

    Naka M, Motome Y, Seo H. Perovskite as a spin current generator. Phys. Rev. B. 2021;103:125114.

    Not in our library10.1103/physrevb.103.125114

30. 30.
    Multifunctional antiferromagnetic materials with giant piezomagnetism and noncollinear spin current · 2021

    No notice
31. 31.

    Šmejkal L, Hellenes AB, González-Hernández R, Sinova J, Jungwirth T. Giant and tunneling magnetoresistance in unconventional collinear antiferromagnets with nonrelativistic spin-momentum coupling. Phys. Rev. X. 2022;12:011028.

    Not in our library

32. 32.

    Šmejkal L, González-Hernández R, Jungwirth T, Sinova J. Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets. Sci. Adv. 2020;6:eaaz8809.

    Not in our library10.1126/sciadv.aaz8809

33. 33.

    Samanta K, et al. Crystal Hall and crystal magneto-optical effect in thin films of SrRuO3. J. Appl. Phys. 2020;127:213904.

    Not in our library10.1063/5.0005017

34. 34.

    Naka M, et al. Anomalous Hall effect in κ-type organic antiferromagnets. Phys. Rev. B. 2020;102:075112.

    Not in our library10.1103/physrevb.102.075112

35. 35.

    Hayami S, Kusunose H. Essential role of the anisotropic magnetic dipole in the anomalous Hall effect. Phys. Rev. B. 2021;103:L180407.

    Not in our library10.1103/physrevb.103.l180407

36. 36.

    Mazin II, Koepernik K, Johannes MD, González-Hernández R, Šmejkal L. Prediction of unconventional magnetism in doped FeSb2. Proc. Natl Acad. Sci. 2021;118:e2108924118.

    Not in our library10.1073/pnas.2108924118

37. 37.

    Naka M, Motome Y, Seo H. Anomalous Hall effect in antiferromagnetic perovskites. Phys. Rev. B. 2022;106:195149.

    Not in our library10.1103/physrevb.106.195149

38. 38.

    Feng Z, et al. An anomalous Hall effect in altermagnetic ruthenium dioxide. Nat. Electron. 2022;5:735-743.

    Not in our library10.1038/s41928-022-00866-z

39. 39.

    Bose A, et al. Tilted spin current generated by an antiferromagnet. Nat. Electron. 2022;5:263-264.

    Not in our library10.1038/s41928-022-00758-2

40. 40.

    Bai H, et al. Observation of spin splitting torque in a collinear antiferromagnet RuO2. Phys. Rev. Lett. 2022;128:197202.

    Not in our library10.1103/physrevlett.128.197202

41. 41.

    Karube S, et al. Observation of spin-splitter torque in collinear antiferromagnetic RuO2. Phys. Rev. Lett. 2022;129:137201.

    Not in our library10.1103/physrevlett.129.137201

42. 42.

    Strocov VN, et al. Soft-X-ray ARPES facility at the ADRESS beamline of the SLS: concepts, technical realisation and scientific applications. J. Synchrotron Radiat. 2014;21:32-44.

    Not in our library10.1107/s1600577513019085

43. 43.
    Multiple-stable anisotropic magnetoresistance memory in antiferromagnetic MnTe · 2016

    Not checked
44. 44.

    Ebert H, Ködderitzsch D, Minár J. Calculating condensed matter properties using the KKR-Green’s function method—recent developments and applications. Rep. Prog. Phys. 2011;74:096501.

    Not in our library10.1088/0034-4885/74/9/096501

45. 45.

    Braun J, Minár J, Ebert H. Correlation, temperature and disorder: recent developments in the one-step description of angle-resolved photoemission. Phys. Rep. 2018;740:1-34.

    Not in our library10.1016/j.physrep.2018.02.007

46. 46.

    Zhang P, et al. A precise method for visualizing dispersive features in image plots. Rev. Sci. Instrum. 2011;82:043712.

    Not in our library10.1063/1.3585113

47. 47.

    Kriegner D, et al. Magnetic anisotropy in antiferromagnetic hexagonal MnTe. Phys. Rev. B. 2017;96:214418.

    Not in our library10.1103/physrevb.96.214418

48. 48.

    Ishizaka K, et al. Giant Rashba-type spin splitting in bulk BiTeI. Nat. Mater. 2011;10:521-526.

    Not in our library10.1038/nmat3051

49. 49.

    Braun J, et al. Exploring the XPS limit in soft and hard x-ray angle-resolved photoemission using a temperature-dependent one-step theory. Phys. Rev. B. 2013;88:205409.

    Not in our library10.1103/physrevb.88.205409

50. 50.

    Hoesch M, et al. Spin-polarized Fermi surface mapping. J. Electron. Spectrosc. Relat. Phenom. 2002;124:263-279.

    Not in our library10.1016/s0368-2048(02)00058-0

51. 51.

    Kriegner D, Wintersberger E, Stangl J. Xrayutilities: a versatile tool for reciprocal space conversion of scattering data recorded with linear and area detectors. J. Appl. Crystallogr. 2013;46:1162-1170.

    Not in our library10.1107/s0021889813017214

52. 52.

    Damascelli A, Hussain Z, Shen Z-X. Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 2003;75:473-541.

    Not in our library10.1103/revmodphys.75.473

53. 53.

    Strocov V. Photoemission response of 2D electron states. J. Electron. Spectrosc. Relat. Phenom. 2018;229:100-107.

    Not in our library10.1016/j.elspec.2018.09.001

54. 54.

    Powell CJ, Jablonski A. Surface sensitivity of Auger-electron spectroscopy and X-ray photoelectron spectroscopy. J. Surf. Anal. 2011;17:170-176.

    Not in our library10.1384/jsa.17.170

55. 55.

    Strocov VN, et al. Three-dimensional electron realm in VSe2 by soft-x-ray photoelectron spectroscopy: origin of charge-density waves. Phys. Rev. Lett. 2012;109:086401.

    Not in our library10.1103/physrevlett.109.086401

56. 56.

    Weber F, et al. Three-dimensional Fermi surface of 2H–NbSe2: implications for the mechanism of charge density waves. Phys. Rev. B. 2018;97:235122.

    Not in our library10.1103/physrevb.97.235122

57. 57.

    Schröter N, et al. Observation and control of maximal Chern numbers in a chiral topological semimetal. Science. 2020;369:179-183.

    Not in our library10.1126/science.aaz3480

58. 58.
    High-resolution soft X-ray beamline ADRESS at the Swiss Light Source for resonant inelastic X-ray scattering and angle-resolved photoelectron spectroscopies · 2010

    No notice
59. 59.

    Dil JH. Spin and angle resolved photoemission on non-magnetic low-dimensional systems. J. Phys. Condens. Matter. 2009;21:403001.

    Not in our library10.1088/0953-8984/21/40/403001

60. 60.

    Kresse G, Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B. 1996;54:11169-11186.

    Not in our library10.1103/physrevb.54.11169

61. 61.

    Perdew JP, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996;78:1396-1396.

    Not in our library10.1103/physrevlett.78.1396

62. 62.

    Minár J. Correlation effects in transition metals and their alloys studied using the fully self-consistent KKR-based LSDA + DMFT scheme. J. Phys. Condens. Matter. 2011;23:253201.

    Not in our library10.1088/0953-8984/23/25/253201

63. 63.

    Lloyd P. Wave propagation through an assembly of spheres: II. The density of single-particle eigenstates. Proc. Phys. Soc. 1967;90:207.

    Not in our library10.1088/0370-1328/90/1/323

64. 64.

    Lloyd P, Smith P. Multiple scattering theory in condensed materials. Adv. Phys. 1972;21:69-142.

    Not in our library10.1080/00018737200101268

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