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Emergent Altermagnetism at Surfaces of Antiferromagnets: Full Symmetry Classification and Material Identification

Colin Lange1,*, Rodrigo Jaeschke-Ubiergo1,*, Atasi Chakraborty1, Xanthe H. Verbeek1, Libor Šmejkal2,3, Jairo Sinova1,4, and Alexander Mook5,†

  • *These authors contributed equally to this work.
  • †Contact author: amook@uni-muenster.de
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Phys. Rev. X 16, 031066 – Published 11 September, 2026

DOI: https://doi.org/10.1103/6j6l-kb6x

Abstract

We demonstrate the emergence of altermagnetism at the surfaces of antiferromagnets, vastly expanding the number of material candidates with altermagnetic characteristics and establishing a route towards two-dimensional altermagnetism through surface-induced symmetry breaking. We do so by developing a surface spin group formalism that fully classifies all surface magnetic states and identifies altermagnetic surface spin groups that can arise at the surfaces of antiferromagnets. We use this formalism to identify over 150 antiferromagnetic entries from the MAGNDATA database with at least one altermagnetic surface, often times with multiple such surfaces in the same material, and clarify the role of surface roughness and terraces. We illustrate this emergent phenomenon in a realistic Lieb lattice-based minimal model and present ab initio calculations on two representative material candidates, NaMnP and FeGe2, exhibiting d-wave and g-wave surface altermagnetism, respectively. Our theory naturally resolves the contradiction of recent experimental reports of d-wave spin splitting from ARPES measurements on metallic Lieb lattice compounds such as KV2Se2O that have been shown to be antiferromagnetic in the bulk. Hence, we establish a new paradigm for generating effectively two-dimensional altermagnetism by functionalizing the abundant material class of collinear antiferromagnets as viable platforms for controlled surface altermagnetism.

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Popular Summary

Discovering two-dimensional altermagnetic materials, despite being particularly promising for device application, remains a major challenge in condensed matter physics because candidate systems with the desired spin-splitting and vanishing net magnetization are rare. We addressed this limitation by developing a surface spin-group framework showing that two-dimensional altermagnetism naturally emerges at the surfaces of ordinary antiferromagnets due to surface symmetry breaking.

We used this formalism to systematically classify surface spin symmetries, identifying the specific structural conditions that lift bulk spin degeneracies without generating stray magnetic fields. Applying our approach to an electronic materials database revealed more than 150 conventional antiferromagnets that host altermagnetic surface states. Our work establishes surfaces of many conventional antiferromagnets as a versatile platform for designing two-dimensional spintronic components from abundant bulk materials.

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References (86)

  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. T. Jungwirth, R. M. Fernandes, E. Fradkin, A. H. MacDonald, J. Sinova, and L. Šmejkal, Altermagnetism: An unconventional spin-ordered phase of matter, Newton 1, 100162 (2025).
  4. T. Jungwirth, J. Sinova, R. M. Fernandes, Q. Liu, H. Watanabe, S. Murakami, S. Nakatsuji, and L. Šmejkal, Symmetry, microscopy and spectroscopy signatures of altermagnetism, Nature (London) 649, 837 (2026).
  5. D. B. Litvin and W. Opechowski, Spin groups, Physica 76, 538 (1974).
  6. D. B. Litvin, Spin point groups, Acta Crystallogr. Sect. A 33, 279 (1977).
  7. T. Jungwirth, J. Sinova, P. Wadley, D. Kriegner, H. Reichlova, F. Krizek, H. Ohno, and L. Smejkal, Altermagnetic spintronics, Nat. Phys. 22, 1012 (2026).
  8. J. Krempaský et al., Altermagnetic lifting of Kramers spin degeneracy, Nature (London) 626, 517 (2024).
  9. S. S. Lee, S. 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).
  10. 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).
  11. M. Hajlaoui, S. Wilfred D’souza, L. Šmejkal, D. Kriegner, G. Krizman, T. Zakusylo, N. Olszowska, O. Caha, J. Michalička, J. Sánchez-Barriga, A. Marmodoro, K. Výborný, A. Ernst, M. Cinchetti, J. Minar, T. Jungwirth, and G. Springholz, Temperature dependence of relativistic valence band splitting induced by an altermagnetic phase transition, Adv. Mater. 36, 2314076 (2024).
  12. M. Chilcote et al., Stoichiometry-Induced ferromagnetism in altermagnetic candidate MnTe, Adv. Funct. Mater. 34, 2405829 (2024).
  13. O. J. Amin et al., Nanoscale imaging and control of altermagnetism in MnTe, Nature (London) 636, 348 (2024).
  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. G. Yang et al., Three-dimensional mapping of the altermagnetic spin splitting in CrSb, Nat. Commun. 16, 1442 (2025).
  16. J. Ding et al., Large band splitting in g-wave altermagnet CrSb, Phys. Rev. Lett. 133, 206401 (2024).
  17. M. Zeng et al., Observation of spin splitting in room-temperature metallic antiferromagnet CrSb, Adv. Sci. 11, 2406529 (2024).
  18. 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).
  19. Z. Liu, M. Ozeki, S. Asai, S. Itoh, and T. Masuda, Chiral-split magnon in altermagnetic MnTe, Phys. Rev. Lett. 133, 156702 (2024).
  20. B. Jiang et al., A metallic room-temperature d-wave altermagnet, Nat. Phys. 21, 754 (2025).
  21. F. Zhang et al., Crystal-symmetry-paired spin–valley locking in a layered room-temperature metallic altermagnet candidate, Nat. Phys. 21, 760 (2025).
  22. I. I. Mazin, Notes on altermagnetism and superconductivity, AAPPS Bull. 35, 18 (2025).
  23. P. Chatterjee and V. Juričić, Interplay between altermagnetism and topological superconductivity on an unconventional superconducting platform, Phys. Rev. B 112, 054503 (2025).
  24. G. Yang et al., Observation of hidden altermagnetism in CsV2Te2O, arXiv:2512.00972.
  25. R. M. Sattigeri, X. Gong, A. Fakhredine, C. Autieri, and G. Cuono, Dirac edge states of two-dimensional altermagnetic topological crystalline insulators, Appl. Phys. Lett. 127, 243103 (2025).
  26. Z. Jin, Z. Zeng, Y. Cao, and P. Yan, Skyrmion Hall effect in altermagnets, Phys. Rev. Lett. 133, 196701 (2024).
  27. K. Dou, Z. He, W. Du, Y. Dai, B. Huang, and Y. Ma, Altermagnetic skyrmions in 2D lattices exhibiting anisotropic skyrmion Hall effect, arXiv:2505.05154.
  28. L. Šmejkal, Altermagnetic multiferroics and altermagnetoelectric effect, arXiv:2411.19928.
  29. 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).
  30. D. Wang, H. Wang, L. Liu, J. Zhang, and H. Zhang, Electric-field-induced switchable two-dimensional altermagnets, Nano Lett. 25, 498 (2024).
  31. H. Zhu, J. Li, X. Chen, Y. Yu, and Q. Liu, Magnetic geometry induced quantum geometry and nonlinear transports, Nat. Commun. 16, 4882 (2025).
  32. A. Urru and N. A. Spaldin, Magnetic octupole tensor decomposition and second-order magnetoelectric effect, Ann. Phys. (N. Y) 447, 168964 (2022).
  33. I. Mazin, R. González-Hernández, and L. Šmejkal, Induced monolayer altermagnetism in MnP(S,Se)3 and FeSe, Ann. Phys. (Amsterdam) 447, 16896 (2022) [arXiv:2309.02355].
  34. N. Jana, A. Chakraborty, A. Mukherjee, and A. Agarwal, Layered topological antiferromagnetic metal at room temperature—YbMn2Ge2, Phys. Rev. B 112, 075127 (2025).
  35. S.-D. Guo, External-field-induced altermagnetism in experimentally synthesized monolayer CrX3 (x=Cl,Br, and I), arXiv:2503.23036.
  36. D. Liu, S. Zeng, J.-H. Liao, and Y.-J. Zhao, Unlocking altermagnetism in antiferromagnetic 2D films via adsorption, arXiv:2507.09518.
  37. S. V. Gallego, J. Manuel 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, J. Appl. Crystallogr. 49, 1750 (2016).
  38. X. Chen, J. Ren, Y. Zhu, Y. Yu, A. Zhang, P. Liu, J. Li, Y. Liu, C. Li, and Q. Liu, Enumeration and representation theory of spin space groups, Phys. Rev. X 14, 031038 (2024).
  39. M. Tian, C. Cui, Z. Zhang, J. Duan, W. Feng, and R.-W. Zhang, Symmetry classification of altermagnetism and emergence of type-IV magnetism in two dimensions, arXiv:2508.17864.
  40. S. Zeng and Y. J. Zhao, Description of two-dimensional altermagnetism: Categorization using spin group theory, Phys. Rev. B 110, 054406 (2024).
  41. Y. Sun, Y. Huang, J. Cheng, S. Zhang, Z. Li, H. Luo, X. Ma, W. Yang, J. Yang, D. Chen, K. Sun, M. Gutmann, S. C. Capelli, F. Shen, J. Hao, L. He, G. Chen, and S. Li, Antiferromagnetic structure of KV2Se2O: A neutron diffraction study, Phys. Rev. B 112, 184416 (2025).
  42. L. Šmejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji, and T. Jungwirth, Anomalous Hall antiferromagnets, Nat. Rev. Mater. 7, 482 (2022).
  43. 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, National electronics review 5, 735 (2022).
  44. 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).
  45. S. Noh, G.-H. Kim, J. Lee, H. Jung, U. Seo, G. So, J. Lee, S. Lee, M. Park, S. Yang, Y. S. Oh, H. Jin, C. Sohn, and J.-W. Yoo, Tunneling magnetoresistance in altermagnetic RuO2-based magnetic tunnel junctions, Phys. Rev. Lett. 134, 246703 (2025).
  46. R. Jaeschke-Ubiergo, V.-K. Bharadwaj, W. Campos, R. Zarzuela, N. Biniskos, R. M. Fernandes, T. Jungwirth, J. Sinova, and L. Šmejkal, Atomic altermagnetism, arXiv:2503.10797.
  47. N. Kaushal and M. Franz, Altermagnetism in modified Lieb lattice Hubbard model, arXiv:2412.16421.
  48. M. Dürrnagel, H. Hohmann, A. Maity, J. Seufert, M. Klett, L. Klebl, and R. Thomale, Altermagnetic phase transition in a Lieb metal, Phys. Rev. Lett. 135, 036502 (2025).
  49. P.-H. Chang, I. I. Mazin, and K. D. Belashchenko, Inverse Lieb materials: Altermagnetism and more, arXiv:2508.04839.
  50. W. Bronger, P. Müller, R. Höppner, and H. Schuster, Zur Charakterisierung der magnetischen Eigenschaften von NaMnP, NaMnAs, NaMnSb, NaMnBi, LiMnAs und KMnAs über Neutronenbeugungsexperimente, Z. Anorg. Allg. Chem. 539, 175 (1986).
  51. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
  52. M. P. Lopez Sancho, J. M. Lopez Sancho, and J. Rubio, Quick iterative scheme for the calculation of transfer matrices: Application to Mo (100), J. Phys. F 14, 1205 (1984).
  53. M. P. Lopez Sancho, J. M. Lopez Sancho, and J. Rubio, Highly convergent schemes for the calculation of bulk and surface Green functions, J. Phys. F 15, 851 (1985).
  54. J. Henk and W. Schattke, Computer physics A subroutine package for computing Green’s functions of relaxed surfaces by the renormalization method, Comput. Phys. Commun. 77, 69 (1993).
  55. S. F. Weber, A. Urru, S. Bhowal, C. Ederer, and N. A. Spaldin, Surface magnetization in antiferromagnets: Classification, example materials, and relation to magnetoelectric responses, Phys. Rev. X 14, 021033 (2024).
  56. H. A. Kramers, Théorie générale de la rotation paramagnétique dans les cristaux, Proc. Amsterdam Acad. 33 (1930), https://www.dwc.knaw.nl/DL/publications/PU00015981.pdf.
  57. E. Wigner, Ueber die Operation der Zeitumkehr in der Quantenmechanik, Nachr. Ges. Wiss. Gött. Math. Klasse 1932, 546 (1932), http://www.digizeitschriften.de/dms/img/?PPN=GDZPPN002509032.
  58. L. Bai, R.-W. Zhang, W. Feng, and Y. Yao, Anomalous Hall effect in type IV 2D collinear magnets, Phys. Rev. Lett. 135, 036702 (2025).
  59. 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).
  60. P. A. McClarty and J. G. Rau, Landau theory of altermagnetism, Phys. Rev. Lett. 132, 176702 (2024).
  61. K. Shinohara, A. Togo, H. Watanabe, T. Nomoto, I. Tanaka, and R. Arita, Algorithm for spin symmetry operation search, Acta Crystallogr. Sect. A 80, 94 (2024).
  62. MAGNDATA: A collection of magnetic structures with portable cif-type files, https://cryst.ehu.es/magndata/.
  63. E. Krén, G. Kádár, L. Pál, J. Sólyom, and P. Szabó, Magnetic structures and magnetic transformations in ordered Mn3(Rh, Pt) alloys, Phys. Lett. 20, 331 (1966).
  64. W. Tian, C. Svoboda, M. Ochi, M. Matsuda, H. B. Cao, J.-G. Cheng, B. C. Sales, D. G. Mandrus, R. Arita, N. Trivedi, and J.-Q. Yan, High antiferromagnetic transition temperature of the honeycomb compound SrRu2O6, Phys. Rev. B 92, 100404(R) (2015).
  65. M. Guillot, M. El-Ghozzi, D. Avignant, G. Andre, F. Bouree, and A. Cousson, Magnetic properties of a mixed-valence (III/IV) terbium fluoride KTb3F12, J. Appl. Phys. 91, 8519 (2002).
  66. M. Fiebig, D. Fröhlich, and H. J. Thiele, Determination of spin direction in the spin-flop phase of Cr2O3, Phys. Rev. B 54, R12681 (1996).
  67. V. M. Barthem, C. V. Colin, H. Mayaffre, M. H. Julien, and D. Givord, Revealing the properties of Mn2 au for antiferromagnetic spintronics, Nat. Commun. 4, 2892 (2013).
  68. M. H. Karigerasi, K. Kang, J. Huang, V. K. Peterson, K. C. Rule, A. J. Studer, A. Schleife, P. Y. Huang, and D. P. Shoemaker, High-resolution diffraction reveals magnetoelastic coupling and coherent phase separation in tetragonal CuMnAs, Phys. Rev. Mater. 6, 094405 (2022).
  69. S. A. J. Kimber, D. N. Argyriou, F. Yokaichiya, K. Habicht, S. Gerischer, T. Hansen, T. Chatterji, R. Klingeler, C. Hess, G. Behr, A. Kondrat, and B. Büchner, Magnetic ordering and negative thermal expansion in PrFeAsO, Phys. Rev. B 78, 140503(R) (2008).
  70. M. Reehuis, C. Ulrich, K. Prokeš, A. Gozar, G. Blumberg, S. Komiya, Y. Ando, P. Pattison, and B. Keimer, Crystal structure and high-field magnetism of La2CuO4, Phys. Rev. B 73, 144513 (2006).
  71. C. Lane, J. W. Furness, I. G. Buda, Y. Zhang, R. S. Markiewicz, B. Barbiellini, J. Sun, and A. Bansil, Antiferromagnetic ground state of La2CuO4: A parameter-free ab initio description, Phys. Rev. B 98, 125140 (2018).
  72. D. Chakraborty and A. M. Black-Schaffer, Constraints on superconducting pairing in altermagnets, arXiv:2408.03999.
  73. Y. Fukaya, B. Lu, K. Yada, Y. Tanaka, and J. Cayao, Superconducting phenomena in systems with unconventional magnets, J. Phys. Condens. Matter 37, 313003 (2025).
  74. N. S. S. Murthy, R. J. Begum, C. S. Somanathan, and M. R. L. N. Murthy, Magnetic structure in the Iron-Germanium system, Solid State Commun. 3, 113 (1965).
  75. Y. Chen, J. Ji, L. Hong, X. Wan, and H. Xiang, Generation of pure spin current with insulating antiferromagnetic materials, Phys. Rev. Lett. 135, 146703 (2025).
  76. P. Zhou, X. N. Peng, Y. Z. Hu, B. R. Pan, S. M. Liu, P. B. Lyu, and L. Z. Sun, Transition from antiferromagnets to altermagnets: Symmetry-breaking theory, Phys. Rev. B 112, 144419 (2025).
  77. W. Xie, C. Liu, F. Zhang, Z. Tan, W. Ji, N. Zhao, L. Bao, D. Zhang, F. Shen, L. He, H. Wang, R. Du, G. Cao, C. Chen, and P. Miao, G-type antiferromagnetic structure in Rb1−xV2Te2O, arXiv:2604.17365.
  78. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  79. P. E. Blöchl, Projector augmented-wave method, J. Chem. Phys. 141, 234102 (2014).
  80. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  81. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  82. N. Marzari and D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997).
  83. A. A. Mostofi, J. R. Yates, G. Pizzi, Y. S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, An updated version of Wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 185, 2309 (2014).
  84. Q. S. Wu, S. N. Zhang, H.-F. F. Song, M. Troyer, and A. A. Soluyanov, WannierTools: An open-source software package for novel topological materials, Comput. Phys. Commun. 224, 405 (2017).
  85. A. Zangwill, Physics at Surfaces (1988), 10.1017/cbo9780511622564.
  86. K. Oura, Surface Science: An Introduction (Springer, New York, 2011), p. 440.

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Phys. Rev. X 16, 031066– Published 11 September, 2026
  • Received 9 February 2026
  • Revised 30 July 2026
  • Accepted 11 August 2026
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