Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Chiral magnetic excitations and domain textures of g-wave altermagnets

Volodymyr P. Kravchuk1,2,3,*, Kostiantyn V. Yershov1,3, Jorge I. Facio4, Yaqian Guo1, Oleg Janson1, Olena Gomonay5, Jairo Sinova5,6, and Jeroen van den Brink1,2,7

  • *Contact author: v.kravchuk@ifw-dresden.de

Phys. Rev. B 112, 144421 – Published 14 October, 2025

DOI: https://doi.org/10.1103/zn8d-ft9b

Abstract

Altermagnets (AMs) constitute a novel class of spin-compensated materials in which opposite-spin sublattices are connected by a crystal rotation, causing their electronic isoenergy surfaces to be spin split. While cubic and tetragonal crystal symmetries tend to produce AMs in which the splitting of electronic isoenergy surfaces has d-wave symmetry, hexagonal AMs, such as CrSb and MnTe, are g-wave AMs. Here we investigate the purely magnetic modes and spin textures of g-wave AMs and show that they are drastically different for easy-axial (CrSb) and easy-planar (MnTe) materials. We show that in CrSb the splitting of the chiral magnon branches possesses g-wave symmetry, with each branch carrying a fixed momentum-independent magnetic moment. The altermagnetic splitting is not affected by the easy-axial anisotropy and is the same as that in the nonrelativistic limit. The magnon splitting of MnTe, however, does not strictly possess g-wave symmetry due to its easy-planar anisotropy. Instead, the magnetic moment of each branch becomes momentum dependent, with a distribution that is of g-wave symmetry. To generalize the concept of the altermagnetic splitting beyond the nonrelativistic limit, we introduce an alternative, directly observable splitting parameter that encompasses both the magnon eigenenergy and its magnetic moment (a component along the ground-state Néel vector), and exhibits g-wave symmetry in both easy-axial and easy-planar cases. The associated altermagnetic domain walls in easy-axial CrSb possess a net magnetization with an amplitude that depends on their orientation.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (42)

  1. L. Šmejkal, R. González-Hernández, T. Jungwirth, and J. Sinova, Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets, Sci. Adv. 6, eaaz8809 (2020).
  2. M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Motome, and H. Seo, Spin current generation in organic antiferromagnets, Nat. Commun. 10, 4305 (2019).
  3. L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and A. Zunger, Giant momentum-dependent spin splitting in centrosymmetric low-z antiferromagnets, Phys. Rev. B 102, 014422 (2020).
  4. M. Naka, Y. Motome, and H. Seo, Perovskite as a spin current generator, Phys. Rev. B 103, 125114 (2021).
  5. Y. Guo, H. Liu, O. Janson, I. C. Fulga, J. van den Brink, and J. I. Facio, Spin-split collinear antiferromagnets: A large-scale ab-initio study, Mater. Today Phys. 32, 100991 (2023).
  6. L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
  7. L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond conventional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X 12, 031042 (2022).
  8. L. Šmejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji, and T. Jungwirth, Anomalous Hall antiferromagnets, Nat. Rev. Mater. 7, 482 (2022).
  9. T. Sato, S. Haddad, I. C. Fulga, F. F. Assaad, and J. van den Brink, Altermagnetic anomalous Hall effect emerging from electronic correlations, Phys. Rev. Lett. 133, 086503 (2024).
  10. O. Gomonay, V. P. Kravchuk, R. Jaeschke-Ubiergo, K. V. Yershov, T. Jungwirth, L. Šmejkal, J. v. d. Brink, and J. Sinova, Structure, control, and dynamics of altermagnetic textures, npj Spintronics 2, 35 (2024).
  11. P. M. Cônsoli, M. Fornoville, and M. Vojta, Fluctuation-induced ferrimagnetism in sublattice-imbalanced antiferromagnets with application to SrCu2(BO3)2 under pressure, Phys. Rev. B 104, 064422 (2021).
  12. K. V. Yershov, V. P. Kravchuk, M. Daghofer, and J. van den Brink, Fluctuation-induced piezomagnetism in local moment altermagnets, Phys. Rev. B 110, 144421 (2024).
  13. K. V. Yershov, O. Gomonay, J. Sinova, J. van den Brink, and V. P. Kravchuk, Curvature-induced magnetization of altermagnetic films, Phys. Rev. Lett. 134, 116701 (2025).
  14. S. Reimers, L. Odenbreit, L. Šmejkal, V. N. Strocov, P. Constantinou, A. B. Hellenes, R. Jaeschke Ubiergo, W. H. Campos, V. K. Bharadwaj, A. Chakraborty, T. Denneulin, W. Shi, R. E. Dunin-Borkowski, S. Das, M. Kläui, J. Sinova, and M. Jourdan, Direct observation of altermagnetic band splitting in CrSb thin films, Nat. Commun. 15, 2116 (2024).
  15. C. Li, M. Hu, Z. Li, Y. Wang, W. Chen, B. Thiagarajan, M. Leandersson, C. Polley, T. Kim, H. Liu, C. Fulga, M. G. Vergniory, O. Janson, O. Tjernberg, and J. van den Brink, Topological weyl altermagnetism in CrSb, Commun. Phys. 8, 311 (2025).
  16. G. Yang, Z. Li, S. Yang, J. Li, H. Zheng, W. Zhu, Z. Pan, Y. Xu, S. Cao, W. Zhao, A. Jana, J. Zhang, M. Ye, Y. Song, L.-H. Hu, L. Yang, J. Fujii, I. Vobornik, M. Shi, H. Yuan et al., Three-dimensional mapping of the altermagnetic spin splitting in CrSb, Nat. Commun. 16, 1442 (2025).
  17. M. Zeng, M. Zhu, Y. Zhu, X. Liu, X. Ma, Y. Hao, P. Liu, G. Qu, Y. Yang, Z. Jiang, K. Yamagami, M. Arita, X. Zhang, T. Shao, Y. Dai, K. Shimada, Z. Liu, M. Ye, Y. Huang, Q. Liu et al., Observation of spin splitting in room temperature metallic antiferromagnet crsb, Adv. Sci. 11, 2406529 (2024).
  18. J. Ding, Z. Jiang, X. Chen, Z. Tao, Z. Liu, T. Li, J. Liu, J. Sun, J. Cheng, J. Liu, Y. Yang, R. Zhang, L. Deng, W. Jing, Y. Huang, Y. Shi, M. Ye, S. Qiao, Y. Wang, Y. Guo et al., Large band splitting in g-wave altermagnet crsb, Phys. Rev. Lett. 133, 206401 (2024).
  19. I. I. Mazin, Altermagnetism in mnte: Origin, predicted manifestations, and routes to detwinning, Phys. Rev. B 107, L100418 (2023).
  20. J. Krempaský, L. Šmejkal, S. W. D'Souza, M. Hajlaoui, G. Springholz, K. Uhlířová, F. Alarab, P. C. Constantinou, V. Strocov, D. Usanov, W. R. Pudelko, R. González-Hernández, A. Birk Hellenes, Z. Jansa, H. Reichlová, Z. Šobáň, R. D. Gonzalez Betancourt, P. Wadley, J. Sinova, D. Kriegner et al., Altermagnetic lifting of kramers spin degeneracy, Nature (London) 626, 517 (2024).
  21. S. Lee, S. Lee, S. Jung, J. Jung, D. Kim, Y. Lee, B. Seok, J. Kim, B. G. Park, L. Šmejkal, C.-J. Kang, and C. Kim, Broken kramers degeneracy in altermagnetic mnte, Phys. Rev. Lett. 132, 036702 (2024).
  22. T. Osumi, S. Souma, T. Aoyama, K. Yamauchi, A. Honma, K. Nakayama, T. Takahashi, K. Ohgushi, and T. Sato, Observation of a giant band splitting in altermagnetic mnte, Phys. Rev. B 109, 115102 (2024).
  23. H.-H. Yang, L. Desplat, V. P. Kravchuk, M. Hervé, T. Balashov, S. Gerber, M. Garst, B. Dupé, and W. Wulfhekel, Observation of the sliding phason mode of the incommensurate magnetic texture in fe/ir(111), npj Quantum Mater. 9, 54 (2024).
  24. Z. Liu, M. Ozeki, S. Asai, S. Itoh, and T. Masuda, Chiral split magnon in altermagnetic mnte, Phys. Rev. Lett. 133, 156702 (2024).
  25. S. Polesya, G. Kuhn, S. Mankovsky, H. Ebert, M. Regus, and W. Bensch, Structural and magnetic properties of CrSb compounds: Nias structure, J. Phys.: Condens. Matter 24, 036004 (2012).
  26. W. J. Takei, D. E. Cox, and G. Shirane, Magnetic structures in the MnSb-CrSb system, Phys. Rev. 129, 2008 (1963).
  27. I. I. Mazin and K. D. Belashchenko, Origin of the gossamer ferromagnetism in mnte, Phys. Rev. B 110, 214436 (2024).
  28. S. Greenwald, The antiferromagnetic structure deformations in CoO and MnTe, Acta Crystallogr. 6, 396 (1953).
  29. Mnte Crystal Structure: Datasheet from “Pauling File Multinaries Edition, 2022” (Springer, Berlin, 2023)
  30. A. N. Bogdanov, A. V. Zhuravlev, and U. K. Rößler, Spin-flop transition in uniaxial antiferromagnets: Magnetic phases, reorientation effects, and multidomain states, Phys. Rev. B 75, 094425 (2007).
  31. S. V. Tyablikov, Methods in the Quantum Theory of Magnetism, 2nd ed. (Nauka, Moscow, 1975) [translation of 1st Russian edition (Plenum, New York, 1967)].
  32. T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940).
  33. S. M. Rezende, A. Azevedo, and R. L. Rodríguez-Suárez, Introduction to antiferromagnetic magnons, J. Appl. Phys. 126, 151101 (2019).
  34. N. W. Ashcroft and N. Mermin, Solid State Physics (Dover, New York, 1976).
  35. Y. Nambu, J. Barker, Y. Okino, T. Kikkawa, Y. Shiomi, M. Enderle, T. Weber, B. Winn, M. Graves-Brook, J. M. Tranquada, T. Ziman, M. Fujita, G. Bauer, E. Saitoh, and K. Kakurai, Observation of magnon polarization, Phys. Rev. Lett. 125, 027201 (2020).
  36. O. J. Amin, A. Dal Din, E. Golias, Y. Niu, A. Zakharov, S. C. Fromage, C. J. B. Fields, S. L. Heywood, R. B. Cousins, F. Maccherozzi, J. Krempaský, J. H. Dil, D. Kriegner, B. Kiraly, R. P. Campion, A. W. Rushforth, K. W. Edmonds, S. S. Dhesi, L. Šmejkal, T. Jungwirth et al., Nanoscale imaging and control of altermagnetism in mnte, Nature (London) 636, 348 (2024).
  37. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  38. K. Koepernik and H. Eschrig, Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme, Phys. Rev. B 59, 1743 (1999).
  39. S. P. Bommanaboyena, C. Müller, M. Jarošová, K. Wolk, S. Telkamp, P. Zeng, F. Krizek, T. Uchimura, A. Badura, K. Olejník, D. Scheffler, K. Beranová, S. Banerjee, M. Ledinský, H. Reichlová, T. Jungwirth, L. Horák, and D. Kriegner, Single-crystalline CrSb(0001) thin films grown by dc magnetron co-sputtering, Phys. Rev. Mater. 9, 064402 (2025).
  40. S. Abe, T. Kaneko, M. Ohashi, H. Yoshida, and K. Kamigaki, Magnetic Properties of CrSb, J. Phys. Soc. Jpn. 53, 2703 (1984).
  41. G. Kuhn, S. Polesya, S. Mankovsky, J. Minár, H. Ebert, M. Regus, and W. Bensch, Magnetic properties of CrSb compounds with zinc-blende and wurtzite structures, J. Phys.: Condens. Matter 24, 306005 (2012).
  42. Y.-F. Zhang, X.-S. Ni, K. Chen, and K. Cao, Chiral magnon splitting in altermagnetic CrSb from first principles, Phys. Rev. B 111, 174451 (2025).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation