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

Color symmetry and altermagneticlike spin textures in noncollinear antiferromagnets

Paolo G. Radaelli*

Gautam Gurung†

  • *Contact author: p.g.radaelli@physics.ox.ac.uk
  • †Contact author: gautam.gurung@trinity.ox.ac.uk

Phys. Rev. B 112, 014431 – Published 17 July, 2025

DOI: https://doi.org/10.1103/r34k-xjpx

Abstract

We present a formalism based on color symmetry to analyze the momentum-space spin textures of noncollinear antiferromagnets. We show that, out of the spin textures allowed by the magnetic point group, one can extract a component that is invariant by general rotations in spin space, and can exist in the absence of spin-orbit coupling, in complete analogy to spin textures in altermagnets. We demonstrate this approach in the case of three complex, noncollinear magnets, Mn3Ir(Ge,Si), Pb2MnO4, and Mn3GaN. For Mn3GaN, we also show that the predictions of color-symmetry analysis are consistent with density functional theory calculations performed on the same system both with and without spin-orbit coupling.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (41)

  1. 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).
  2. L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
  3. P. G. Radaelli, Tensorial approach to altermagnetism, Phys. Rev. B 110, 214428 (2024).
  4. S. W. Cheong and F. T. Huang, Altermagnetism with non-collinear spins, npj Quantum Mater. 9, 13 (2024).
  5. A. B. Hellenes, T. Jungwirth, R. Jaeschke-Ubiergo, A. Chakraborty, J. Sinova, and L. Šmejkal, p-wave magnets, arXiv:2309.01607.
  6. S. Hayami, Y. Yanagi, and H. Kusunose, Spontaneous antisymmetric spin splitting in noncollinear antiferromagnets without spin-orbit coupling, Phys. Rev. B 101, 220403(R) (2020).
  7. Here “k/−ksymmetric/antisymmetric” means that the spin texture, defined as snk=〈Ψnk|σ|Ψnk〉 (see below), is the same/changes sign by exchanging k and −k. “Time-reversal odd/even” means that the spin texture in the time-reversed magnetic domain (i.e., the domain obtained by flipping all the magnetic moments) is opposite/the same for a given k.
  8. G. Dresselhaus, Spin-orbit coupling effects in zinc blende structures, Phys. Rev. 100, 580 (1955).
  9. E. I. Rashba and V. I. Sheka, Symmetry of energy bands in crystals of Wurtzite type II. Symmetry of bands with spin-orbit interaction included, Fiz. Tverd. Tela: Collected Papers 2, 62 (1959) [New. J. Phys. 17, 050202 (2015)].
  10. J. Železný, Y. Zhang, C. Felser, and B. Yan, Spin-polarized current in noncollinear antiferromagnets, Phys. Rev. Lett. 119, 187204 (2017).
  11. J. Sticht, K. H. Höck, and J. Kübler, Non-collinear itinerant magnetism: The case of Mn3Sn, J. Phys.: Condens. Matter 1, 8155 (1989).
  12. As explained in the remainder, the CG approach can be employed to describe the magnetic structures of k/−k-antisymmetric magnets, but colored tensors as defined here would require some modifications. For this reason, we will exclude k/−k-antisymmetric magnets from our treatment.
  13. B. Brekke, P. Sukhachov, H. G. Giil, A. Brataas, and J. Linder, Minimal models and transport properties of unconventional p-wave magnets, Phys. Rev. Lett. 133, 236703 (2024).
  14. D. Harker, The three-colored three-dimensional space groups, Acta Crystallogr. Sect. A 37, 286 (1981).
  15. J. Sivardière, Sous-groupes des groupes d'espace et groupes à trois couleurs, Acta Crystallogr. Sect. A 40, 573 (1984).
  16. R. L. Roth, Coloring p4m with two, four, and six colors, Acta Crystallogr. Sect. A 41, 484 (1985).
  17. J. Sivardière, Groupes d'espace à quatre et six couleurs, Acta Crystallogr. 44, 735 (1988).
  18. J. N. Kotzev and D. A. Alexandrova, Full tables of colour space groups with colour-preserving translations, Acta Crystallogr. Sect. A 44, 1082 (1988).
  19. D. B. Litvin, J. N. Kotzev, and J. L. Birman, Physical applications of crystallographic color groups: Landau theory of phase transitions, Phys. Rev. B 26, 6947 (1982).
  20. Z. Jirák, Group-theoretical approach to orbital ordering in crystals with Eg and T2g ions, Phys. Rev. B 46, 8725 (1992).
  21. E. F. Bertaut, Representation analysis of magnetic structures, Acta Crystallogr. Sect. A 24, 217 (1968).
  22. Y. A. Izyumov, Exchange multiplets in the theory of magnetic structures of crystals, J. Magn. Magn. Mater. 15-18, 497 (1980).
  23. D. B. Litvin, Spin point groups, Acta Crystallogr. Sect. A 33, 279 (1977).
  24. T. Eriksson, L. Bergqvist, P. Nordblad, O. Eriksson, and Y. Andersson, Structural and magnetic characterization of Mn3IrGe and Mn3Ir(Si1−xGex): Experiments and theory, J. Solid State Chem. 177, 4058 (2004).
  25. T. Eriksson, R. Lizárraga, S. Felton, L. Bergqvist, Y. Andersson, P. Nordblad, and O. Eriksson, Crystal and magnetic structure of Mn3IrSi, Phys. Rev. B 69, 054422 (2004).
  26. M. Hu, O. Janson, C. Felser, P. McClarty, J. van den Brink, and M. G. Vergniory, Spin Hall and Edelstein effects in novel chiral noncollinear altermagnets, arXiv:2410.17993.
  27. S. A. Kimber and J. P. Attfield, Magnetic order in acentric Pb2MnO4, J. Mater. Chem. 17, 4885 (2007).
  28. D. C. Kakarla, H. C. Wu, D. J. Hsieh, P. J. Sun, G. J. Dai, J. Y. Lin, J. L. Her, Y. H. Matsuda, L. Z. Deng, M. Gooch, C. W. Chu, and H. D. Yang, Metamagnetic transitions and magnetoelectric coupling in acentric and nonpolar Pb2MnO4, Phys. Rev. B 99, 195129 (2019).
  29. S.-W. Cheong and F.-T. Huang, Kinetomagnetism and altermagnetism, arXiv:2503.16277.
  30. E. F. Bertaut, D. Fruchart, J. P. Bouchaud, and R. Fruchart, Diffraction neutronique de Mn3GaN, Solid State Commun. 6, 251 (1968).
  31. K. Shi, Y. Sun, J. Yan, S. Deng, L. Wang, H. Wu, P. Hu, H. Lu, M. I. Malik, Q. Huang, and C. Wang, Baromagnetic effect in antiperovskite Mn3Ga0.95N0.94 by neutron powder diffraction analysis, Adv. Mater. 28, 3761 (2016).
  32. T. Nan, C. X. Quintela, J. Irwin, G. Gurung, D. F. Shao, J. Gibbons, N. Campbell, K. Song, S. Y. Choi, L. Guo, R. D. Johnson, P. Manuel, R. V. Chopdekar, I. Hallsteinsen, T. Tybell, P. J. Ryan, J. W. Kim, Y. Choi, P. G. Radaelli, D. C. Ralph et al., Controlling spin current polarization through non-collinear antiferromagnetism, Nat. Commun. 11, 4671 (2020).
  33. H. K. Singh, I. Samathrakis, N. M. Fortunato, J. Zemen, C. Shen, O. Gutfleisch, and H. Zhang, Multifunctional antiperovskites driven by strong magnetostructural coupling, npj Comput. Mater. 7, 98 (2021).
  34. Note that the Γ4g magnetic structure is the same as for the compound Mn3Ir reported in Ref. [10]. The schematic spin texture reported in their Fig. 3 is very similar to the one we calculate here.
  35. P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buongiorno Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. Dal Corso, S. De Gironcoli, P. Delugas, R. A. Distasio, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo et al., Advanced capabilities for materials modelling with Quantum ESPRESSO, J. Phys.: Condens. Matter 29, 465901 (2017).
  36. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  37. See Supplemental Material at http://link.aps.org/supplemental/10.1103/r34k-xjpx for I. Further discussion of the relation between color groups and spin groups; II. Spin-resolved band dispersions of Mn3GaN; III. Fermi surfaces of Mn3GaN; IV. Decompositions of the Fermi surfaces (Bands 0, 2, 3) spin textures of Mn3GaN onto tensorial expansions.
  38. Note that the net magnetization in the absence of SOC is identically zero for collinear altermagnets and also for noncollinear magnets where each color has a corresponding anticolor, since the magnetization of anticolored sublattices cancels.
  39. Very briefly, magnets with k/−kantisymmetric splitting are characterized by bond-type multipolar ordering [6], and the staggered magnetization (in the collinear case) or the one-color axial unit vectors (noncollinear case) need to be replaced in the tensorial treatment by the cross product S1×S2, where sites 1 and 2 are those connected by the specific bond. This approach will be fully described in a future paper.
  40. A. Richards, University of Oxford Advanced Research Computing, Zenodo (2015), see https://doi.org/10.5281/zenodo.22558.
  41. P. Radaelli and G. Gurung, Data linked to the publication “Color symmetry and altermagneticlike spin textures in noncollinear antiferromagnets” (University of Oxford, 2025), see https://dx.doi.org/10.5287/ora-ng7pyddap.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation