- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

X-ray magnetic circular dichroism of altermagnet α−Fe2O3 based on multiplet ligand-field theory using Wannier orbitals

Ruiwen Xie, Hamza Zerdoumi, and Hongbin Zhang*

  • *Contact author: hzhang@tmm.tu-darmstadt.de
PDF

Phys. Rev. B 113, 214445 – Published 18 June, 2026

DOI: https://doi.org/10.1103/4cbj-w8wd

Abstract

Hematite α−Fe2O3 is a g-wave altermagnetic material which has an easy-axis phase and easy-plane weak ferromagnetic phase below and above the Morin transition temperature, respectively. The presence of these phases renders it a good candidate to study the characteristic spin splitting in altermagnets under the impacts of the relativistic effect and finite temperature. In this regard, we calculate the band structure of α−Fe2O3 based on density functional theory (DFT) which also considers the Hubbard U correction and spin-orbit coupling (SOC) effects. Additionally, charge self-consistent DFT plus dynamical mean-field theory (DMFT) calculations are performed at finite temperatures. We find that the altermagnetic spin splitting in α−Fe2O3 is preserved by taking either SOC or the temperature effect into account. Furthermore, we present a numerical simulation of the x-ray magnetic circular dichroism (XMCD) of the L2,3 edge of Fe using a combination of DFT and multiplet ligand-field theory. In terms of the different Néel vectors present in α−Fe2O3, we calculate the x-ray absorption spectroscopy of the L2,3 edge of Fe in the form of a conductivity tensor and analyze the XMCD response from the perspective of symmetry. A characteristic XMCD line shape is expected when the Néel vector is along the [010] direction (magnetic point group 2′/m′) and the light propagation vector is perpendicular to the Néel vector, which can be further distinguished from the XMCD response originating from weak ferromagnetism with the light propagation vector parallel to the Néel vector.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (48)

  1. 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).
  2. L. Šmejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji, and T. Jungwirth, Anomalous Hall antiferromagnets, Nat. Rev. Mater. 7, 482 (2022).
  3. R. D. Gonzalez Betancourt, J. Zubáč, R. Gonzalez-Hernandez, K. Geishendorf, Z. Šobáň, G. Springholz, K. Olejník, L. Šmejkal, J. Sinova, T. Jungwirth, et al., Spontaneous anomalous Hall effect arising from an unconventional compensated magnetic phase in a semiconductor, Phys. Rev. Lett. 130, 036702 (2023).
  4. M. Naka, Y. Motome, and H. Seo, Anomalous Hall effect in antiferromagnetic perovskites, Phys. Rev. B 106, 195149 (2022).
  5. K. Samanta, M. Ležaić, M. Merte, F. Freimuth, S. Blügel, and Y. Mokrousov, Crystal Hall and crystal magneto-optical effect in thin films of SrRuO3, J. Appl. Phys. 127, 213904 (2020).
  6. A. Hariki, A. Dal Din, O. Amin, T. Yamaguchi, A. Badura, D. Kriegner, K. W. Edmonds, R. P. Campion, P. Wadley, D. Backes, et al., X-ray magnetic circular dichroism in altermagnetic α-MnTe, Phys. Rev. Lett. 132, 176701 (2024).
  7. A. Hariki, Y. Takahashi, and J. Kuneš, X-ray magnetic circular dichroism in RuO2, Phys. Rev. B 109, 094413 (2024).
  8. N. Sasabe, M. Mizumaki, T. Uozumi, and Y. Yamasaki, Ferroic order for anisotropic magnetic dipole term in collinear antiferromagnets of (t2g)4 system, Phys. Rev. Lett. 131, 216501 (2023).
  9. M. Hu, O. Janson, C. Felser, P. McClarty, J. van den Brink, and M. G. Vergniory, Spin Hall and Edelstein effects in chiral non-collinear altermagnets, Nat. Commun. 16, 8529 (2025).
  10. 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).
  11. I. Dzyaloshinsky, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4, 241 (1958).
  12. I. E. Dzialoshinskii, The problem of piezomagnetism, J. Exptl. Theoret. Phys. 33, 807 (1958) [Sov. Phys. JETP 6, 621 (1958)].
  13. I. Dzyaloshinskii, On the magneto-electrical effect in antiferromagnets, J. Exptl. Theoret. Phys. 37, 881 (1959) [Sov. Phys. JETP 37, 628 (1959)].
  14. E. Turov, Kinetic, Optical, and Acoustic Properties of Antiferromagnets (Izd. Ural. Otd. Akad. Nauk, Sverdlovsk, USSR, 1990).
  15. I. Solovyev, Hidden ferromagnetism of centrosymmetric antiferromagnets, arXiv:2509.00369.
  16. J. Kuneš, Néel vector dependence of x-ray magnetic circular dichroism in altermagnets, Phys. Rev. B 112, 184415 (2025).
  17. A. Hariki, T. Okauchi, Y. Takahashi, and J. Kuneš, Determination of the Néel vector in rutile altermagnets through x-ray magnetic circular dichroism: The case of MnF2, Phys. Rev. B 110, L100402 (2024).
  18. A. Hariki, K. Sakurai, T. Okauchi, and J. Kuneš, Separating altermagnetic and ferromagnetic effects in x-ray magnetic dichroism of rutile NiF2, npj Quantum Mater. 10, 49 (2025).
  19. X. Wan, S. Mandal, Y. Guo, and K. Haule, High-throughput search for metallic altermagnets by embedded dynamical mean field theory, Phys. Rev. Lett. 135, 106501 (2025).
  20. F. Morin, Magnetic susceptibility of α−Fe2o3 and α−Fe2o3 with added titanium, Phys. Rev. 78, 819 (1950).
  21. T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120, 91 (1960).
  22. 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).
  23. X. Chen, Y. Liu, P. Liu, Y. Yu, J. Ren, J. Li, A. Zhang, and Q. Liu, Unconventional magnons in collinear magnets dictated by spin space groups, Nature (London) 641, E1 (2025).
  24. R. Hoyer, P. P. Stavropoulos, A. Razpopov, R. Valentí, L. Šmejkal, and A. Mook, Altermagnetic splitting of magnons in hematite α−Fe2o3, Phys. Rev. B 112, 064425 (2025).
  25. V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, Antiferromagnetic spintronics, Rev. Mod. Phys. 90, 015005 (2018).
  26. R. Lebrun, A. Ross, S. Bender, A. Qaiumzadeh, L. Baldrati, J. Cramer, A. Brataas, R. Duine, and M. Kläui, Tunable long-distance spin transport in a crystalline antiferromagnetic iron oxide, Nature (London) 561, 222 (2018).
  27. A. Ross, R. Lebrun, O. Gomonay, D. A. Grave, A. Kay, L. Baldrati, S. Becker, A. Qaiumzadeh, C. Ulloa, G. Jakob, et al., Propagation length of antiferromagnetic magnons governed by domain configurations, Nano Lett. 20, 306 (2020).
  28. M. W. Haverkort, M. Zwierzycki, and O. O. Andersen, Multiplet ligand-field theory using Wannier orbitals, Phys. Rev. B 85, 165113 (2012).
  29. P. Blaha, K. Schwarz, F. Tran, R. Laskowski, G. K. Madsen, and L. D. Marks, WIEN2k: An APW+ lo program for calculating the properties of solids, J. Chem. Phys. 152, 074101 (2020).
  30. K. Haule, C.-H. Yee, and K. Kim, Dynamical mean-field theory within the full-potential methods: Electronic structure of CeIrIn5, CeCoIn5, and CeRhIn5, Phys. Rev. B 81, 195107 (2010).
  31. K. Haule, Quantum Monte Carlo impurity solver for cluster dynamical mean-field theory and electronic structure calculations with adjustable cluster base, Phys. Rev. B 75, 155113 (2007).
  32. 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).
  33. 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).
  34. K. Koepernik and H. Eschrig, Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme, Phys. Rev. B 59, 1743 (1999).
  35. I. Opahle, K. Koepernik, and H. Eschrig, Full-potential band-structure calculation of iron pyrite, Phys. Rev. B 60, 14035 (1999).
  36. K. Koepernik, O. Janson, Y. Sun, and J. van den Brink, Symmetry-conserving maximally projected Wannier functions, Phys. Rev. B 107, 235135 (2023).
  37. L. Šmejkal, A. Marmodoro, K.-H. Ahn, R. González-Hernández, I. Turek, S. Mankovsky, H. Ebert, S. W. D'Souza, O. Šipr, J. Sinova, et al., Chiral magnons in altermagnetic RuO2, Phys. Rev. Lett. 131, 256703 (2023).
  38. M. Tahir, M. Fakhar-e Alam, M. Atif, G. Mustafa, and Z. Ali, Investigation of optical, electrical and magnetic properties of hematite α−Fe2O3 nanoparticles via sol-gel and co-precipitation method, J. King Saud Univ. Sci. 35, 102695 (2023).
  39. A. Hill, F. Jiao, P. Bruce, A. Harrison, W. Kockelmann, and C. Ritter, Neutron diffraction study of mesoporous and bulk hematite, α−Fe2O3, Chem. Mater. 20, 4891 (2008).
  40. A. S. Belozerov, I. Leonov, and V. I. Anisimov, Magnetism of iron and nickel from rotationally invariant Hirsch-Fye quantum Monte Carlo calculations, Phys. Rev. B 87, 125138 (2013).
  41. A. Borovik-Romanov and H. Grimmer, Magnetic properties, in International Tables for Crystallography, Vol. D: Physical Properties of Crystals, edited by A. Authier (Springer, Dordrecht, 2006), pp. 105–149.
  42. M. Winder, A. Hariki, and J. Kuneš, X-ray spectroscopy of the rare-earth nickelate LuNio3: LDA+DMFT study, Phys. Rev. B 102, 085155 (2020).
  43. P. Kuiper, B. G. Searle, P. Rudolf, L. H. Tjeng, and C. T. Chen, X-ray magnetic dichroism of antiferromagnet Fe2O3: The orientation of magnetic moments observed by Fe 2p x-ray absorption spectroscopy, Phys. Rev. Lett. 70, 1549 (1993).
  44. H. Jani, J. Linghu, S. Hooda, R. V. Chopdekar, C. Li, G. J. Omar, S. Prakash, Y. Du, P. Yang, A. Banas, et al., Reversible hydrogen control of antiferromagnetic anisotropy in α−Fe2O3, Nat. Commun. 12, 1668 (2021).
  45. Y. Lu, M. Höppner, O. Gunnarsson, and M. W. Haverkort, Efficient real-frequency solver for dynamical mean-field theory, Phys. Rev. B 90, 085102 (2014).
  46. A. E. Bocquet, T. Mizokawa, T. Saitoh, H. Namatame, and A. Fujimori, Electronic structure of 3d-transition-metal compounds by analysis of the 2p core-level photoemission spectra, Phys. Rev. B 46, 3771 (1992).
  47. Y. Ishii, N. Sasabe, and Y. Yamasaki, Altermagnetic XMCD in hematite distinct from weak ferromagnetic contributions, arXiv:2603.00442.
  48. www.nhr-verein.de/unserepartner.

Outline

Information

Phys. Rev. B 113, 214445– Published 18 June, 2026
  • Received 18 December 2025
  • Revised 12 April 2026
  • Accepted 15 May 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation