- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

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

Activation of anomalous Hall effect and orbital magnetization by domain walls in altermagnets

Sopheak Sorn1,2,* and Yuriy Mokrousov3,4

  • *Contact author: sopheak.sorn@kit.edu
PDF

Phys. Rev. B 112, 245115 – Published 5 December, 2025

DOI: https://doi.org/10.1103/vzmh-mxlz

Abstract

Altermagnets are an emerging class of unconventional antiferromagnets, characterized by a Néel ordering that does not break the translational symmetry of the underlying lattice. Depending on the orientation of the Néel vector, the anomalous Hall effect (AHE) may or may not exist. In the so-called pure altermagnets, the AHE is forbidden by magnetic symmetry. Here, we demonstrate that in pure altermagnets, domain walls can lift the symmetry constraints, thereby activating the AHE and orbital magnetization. Taking a representative example of a rutile-lattice tight-binding minimal model in slab geometry, we use linear response theory to demonstrate the emergence of the domain-wall AHE, finding that it is closely related to the orbital magnetization, while the spin magnetization does not play a significant role. Using Landau theory, we argue that, while for a random arrangement of π domain walls, the contributions from the individual domain walls will cancel one another, an external magnetic field will favor domain-wall arrangements with specific chirality giving rise to a net AHE signal. Using group theory, we discuss how these findings can be straightforwardly generalized to certain other classes of altermagnets. Our work reveals a crucial role for domain walls in understanding Hall transport and orbital magnetism of altermagnets. Our work generally calls for a rigorous analysis of Hall-transport data for an altermagnet, ideally in conjunction with imaging data, in order to unambiguously assign an observed Hall effect to magnetic domains or to domain walls.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (50)

  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. L. Bai, W. Feng, S. Liu, L. Šmejkal, Y. Mokrousov, and Y. Yao, Altermagnetism: Exploring new frontiers in magnetism and spintronics, Adv. Funct. Mater. 34, 2409327 (2024).
  4. Y. Noda, K. Ohno, and S. Nakamura, Momentum-dependent band spin splitting in semiconducting MnO2: A density functional calculation, Phys. Chem. Chem. Phys. 18, 13294 (2016).
  5. K.-H. Ahn, A. Hariki, K.-W. Lee, and J. Kuneš, Antiferromagnetism in RuO2 as d-wave pomeranchuk instability, Phys. Rev. B 99, 184432 (2019).
  6. S. Hayami, Y. Yanagi, and H. Kusunose, Momentum-dependent spin splitting by collinear antiferromagnetic ordering, J. Phys. Soc. Jpn. 88, 123702 (2019).
  7. M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Motome, and H. Seo, Spin current generation in organic antiferromagnets, Nat. Commun. 10, 4305 (2019).
  8. S. Hayami, Y. Yanagi, and H. Kusunose, Bottom-up design of spin-split and reshaped electronic band structures in antiferromagnets without spin-orbit coupling: Procedure on the basis of augmented multipoles, Phys. Rev. B 102, 144441 (2020).
  9. R. M. Fernandes, V. S. de Carvalho, T. Birol, and R. G. Pereira, Topological transition from nodal to nodeless Zeeman splitting in altermagnets, Phys. Rev. B 109, 024404 (2024).
  10. C. Ederer and N. A. Spaldin, Towards a microscopic theory of toroidal moments in bulk periodic crystals, Phys. Rev. B 76, 214404 (2007).
  11. N. A. Spaldin, M. Fiebig, and M. Mostovoy, The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect, J. Phys.: Condens. Matter 20, 434203 (2008).
  12. Y. Kuramoto, H. Kusunose, and A. Kiss, Multipole orders and fluctuations in strongly correlated electron systems, J. Phys. Soc. Jpn. 78, 072001 (2009).
  13. P. Santini, S. Carretta, G. Amoretti, R. Caciuffo, N. Magnani, and G. H. Lander, Multipolar interactions in f-electron systems: The paradigm of actinide dioxides, Rev. Mod. Phys. 81, 807 (2009).
  14. P. A. McClarty and J. G. Rau, Landau theory of altermagnetism, Phys. Rev. Lett. 132, 176702 (2024).
  15. S. Bhowal and N. A. Spaldin, Ferroically ordered magnetic octupoles in d-wave altermagnets, Phys. Rev. X 14, 011019 (2024).
  16. C. R. W. Steward, R. M. Fernandes, and J. Schmalian, Dynamic paramagnon-polarons in altermagnets, Phys. Rev. B 108, 144418 (2023).
  17. D. S. Antonenko, R. M. Fernandes, and J. W. F. Venderbos, Mirror chern bands and Weyl nodal loops in altermagnets, Phys. Rev. Lett. 134, 096703 (2025).
  18. S. Sorn, Antichiral surface states and Su-Schrieffer-Heeger physics in rutile altermagnets, Phys. Rev. B 111, L161109 (2025).
  19. X. Zhou, W. Feng, R.-W. Zhang, L. Šmejkal, J. Sinova, Y. Mokrousov, and Y. Yao, Crystal thermal transport in altermagnetic RuO2, Phys. Rev. Lett. 132, 056701 (2024).
  20. S. Sorn and A. S. Patri, Signatures of hidden octupolar order from nonlinear Hall effects, Phys. Rev. B 110, 125127 (2024).
  21. Y. Fang, J. Cano, S. Ali, and A. Ghorashi, Quantum geometry induced nonlinear transport in altermagnets, Phys. Rev. Lett. 133, 106701 (2024).
  22. J. Ōiké, K. Shinada, and R. Peters, Nonlinear magnetoelectric effect under magnetic octupole order: Application to a d-wave altermagnet and a pyrochlore lattice with all-in/all-out magnetic order, Phys. Rev. B 110, 184407 (2024).
  23. T. Farajollahpour, R. Ganesh, and K. V. Samokhin, Light-induced charge and spin Hall currents in materials with C4K symmetry, npj Quantum Mater. 10, 29 (2025).
  24. 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).
  25. K. Takahashi, C. R. W. Steward, M. Ogata, R. M. Fernandes, and J. Schmalian, Elasto-Hall conductivity and the anomalous Hall effect in altermagnets, Phys. Rev. B 111, 184408 (2025).
  26. 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).
  27. R. P. Rao, R. C. Sherwood, and N. Bartlett, “Weak” ferromagnetism in PDF, J. Chem. Phys. 49, 3728 (1968).
  28. Z. H. Zhu, J. Strempfer, R. R. Rao, C. A. Occhialini, J. Pelliciari, Y. Choi, T. Kawaguchi, H. You, J. F. Mitchell, Y. Shao-Horn, and R. Comin, Anomalous antiferromagnetism in metallic RuO2 determined by resonant x-ray scattering, Phys. Rev. Lett. 122, 017202 (2019).
  29. Z. Feng, X. Zhou, L. Šmejkal, L. Wu, Z. Zhu, H. Guo, R. González-Hernández, X. Wang, H. Yan, P. Qin et al., An anomalous Hall effect in altermagnetic ruthenium dioxide, Nat. Electron. 5, 735 (2022).
  30. L. Šmejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji, and T. Jungwirth, Anomalous Hall antiferromagnets, Nat. Rev. Mater. 7, 482 (2022).
  31. M. Wang, K. Tanaka, S. Sakai, Z. Wang, K. Deng, Y. Lyu, C. Li, D. Tian, S. Shen, N. Ogawa, N. Kanazawa, P. Yu, R. Arita, and F. Kagawa, Emergent zero-field anomalous Hall effect in a reconstructed rutile antiferromagnetic metal, Nat. Commun. 14, 8240 (2023).
  32. K. P. Kluczyk, K. Gas, M. J. Grzybowski, P. Skupinski, M. A. Borysiewicz, T. Fas, J. Suffczynski, J. Z. Domagala, K. Grasza, A. Mycielski, M. Baj, K. H. Ahn, K. Vyborny, M. Sawicki, and M. Gryglas-Borysiewicz, Coexistence of anomalous Hall effect and weak magnetization in a nominally collinear antiferromagnet MnTe, Phys. Rev. B 110, 155201 (2024).
  33. D. Jo, D. Go, Y. Mokrousov, P. M. Oppeneer, S.-W. Cheong, and H.-W. Lee, Weak ferromagnetism in altermagnets from alternating g-tensor anisotropy, Phys. Rev. Lett. 134, 196703 (2025).
  34. O. Gomonay, V. P. Kravchuk, R. Jaeschke-Ubiergo, K. V. Yershov, T. Jungwirth, L. Šmejkal, J. van den Brink, and J. Sinova, Structure, control, and dynamics of altermagnetic textures, npj Spintronics 2, 35 (2024).
  35. W. Xia, B. Bai, X. Chen, Y. Yang, Y. Zhang, J. Yuan, Q. Li, K. Yang, X. Liu, Y. Shi, H. Ma, H. Yang, M. He, L. Li, C. Xi, L. Pi, X. Lv, X. Wang, X. Liu, S. Li et al., Giant domain wall anomalous Hall effect in a layered antiferromagnet EuAl2Si2, Phys. Rev. Lett. 133, 216602 (2024).
  36. F. R. Lux, F. Freimuth, S. Blügel, and Y. Mokrousov, Chiral Hall effect in noncollinear magnets from a cyclic cohomology approach, Phys. Rev. Lett. 124, 096602 (2020).
  37. S. Sorn and A. Paramekanti, Domain wall skew scattering in ferromagnetic Weyl metals, Phys. Rev. B 103, 104413 (2021).
  38. M. M. Piva, J. C. Souza, V. Brousseau-Couture, S. Sorn, K. R. Pakuszewski, J. K. John, C. Adriano, M. Côté, P. G. Pagliuso, A. Paramekanti, and M. Nicklas, Topological features in the ferromagnetic Weyl semimetal CeAlSi: Role of domain walls, Phys. Rev. Res. 5, 013068 (2023).
  39. In the mixed altermagnetic cases, incorporating weak ferromagnetism can lead to a slight deviation from a perfect collinearity. In that case, the term “collinear” refers to the collinearity of the sublattice exchange terms that enter the tight-binding Hamiltonian.
  40. M.è Roig, A. Kreisel, Y. Yu, B. M. Andersen, and D. F. Agterberg, Minimal models for altermagnetism, Phys. Rev. B 110, 144412 (2024).
  41. T. Adamantopoulos, M. Merte, F. Freimuth, D. Go, L. Zhang, M. Ležaić, W. Feng, Y. Yao, J. Sinova, L. Šmejkal, S. Blügel, and Y. Mokrousov, Spin and orbital magnetism by light in rutile altermagnets, npj Spintronics 2, 46 (2024).
  42. T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Orbital magnetization in periodic insulators, Phys. Rev. Lett. 95, 137205 (2005).
  43. D. Xiao, J. Shi, and Q. Niu, Berry phase correction to electron density of states in solids, Phys. Rev. Lett. 95, 137204 (2005).
  44. D. Ceresoli, T. Thonhauser, D. Vanderbilt, and R. Resta, Orbital magnetization in crystalline solids: Multi-band insulators, chern insulators, and metals, Phys. Rev. B 74, 024408 (2006).
  45. J. Shi, G. Vignale, D. Xiao, and Q. Niu, Quantum theory of orbital magnetization and its generalization to interacting systems, Phys. Rev. Lett. 99, 197202 (2007).
  46. The effective mass of the electrons is of the order of ℏ2/a2W, where W denotes the bandwidth, and a is the lattice constant. This means that one can vary the tight-binding parameters in order to change W and the effective mass. Assuming the unit where ℏ=a=me=1, the bandwidth W as seen in Fig.  4 produces the effective mass comparable with the bare mass me. Therefore, we can indeed compare the order of magnitude between M⃗orb and M⃗sp with the choice of the tight-binding parameters.
  47. H. Schiff, P. McClarty, J. G Rau, and J. Romhanyi, Collinear altermagnets and their Landau theories, Phys. Rev. Res. 7, 033301 (2025).
  48. The origin of the x component of M⃗sp can also be understood this way, but the spin magnetization is dominated by the nonrelativistic contribution, i.e., the x component is masked by the z component that has a nonrelativistic and a non-altermagnetic origin, as discussed in the Appendix  pp4. For this reason, the Landau theory appears less relevant for M⃗sp.
  49. In practice, one needs to consider symmetry operations of the space group, but each of such operations can be identified unambiguously with an operation of the point group.
  50. C. Chen Ye, K. Tenzin, J. Slawińska, and C. Autieri, Dominant orbital magnetization in the prototypical altermagnet MnTe, arXiv:2505.08675.

Outline

Information

Phys. Rev. B 112, 245115– Published 5 December, 2025
  • Received 31 May 2025
  • Revised 3 October 2025
  • Accepted 5 November 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation