- Open Access
Electric-Field-Induced X-Ray Nonreciprocal Dichroism in Hematite
Phys. Rev. X 16, 041015 – Published 14 October, 2026
DOI: https://doi.org/10.1103/p5ry-x2wr
Abstract
Hematite () is a prototypical room-temperature antiferromagnet whose time-reversal-odd magnetic structure has recently attracted renewed attention. While such magnetic symmetry can be characterized in terms of higher-order multipoles beyond the magnetic dipole, their manifestation in measurable physical phenomena has remained largely elusive. In this work, we investigate x-ray absorption near the Fe -edge of hematite under an applied electric field, which explicitly breaks space-inversion symmetry. We observe an electric-field-induced x-ray nonreciprocal linear dichroism that reflects the time-reversal-odd nature of the magnetic order. A symmetry-resolved multipole analysis attributes this response to the electric-field-induced magnetic quadrupole and the magnetic toroidal octupole induced by the applied electric field. Furthermore, numerical simulations based on ab initio density functional theory reproduce the observed spectra, including their dependence on the antiferromagnetic domain and x-ray polarization. These results indicate that electric-field-modulated x-ray absorption measurements, combined with simulations, provide a framework for identifying the higher-order multipoles contributing to measurable physical responses in time-reversal-odd antiferromagnets, thereby facilitating the investigation of hidden symmetry properties in magnetic materials.
Physics Subject Headings (PhySH)
Popular Summary
Detecting higher-order multipoles in common antiferromagnets like hematite () remains an experimental hurdle because these subtle magnetic configurations are typically invisible to standard spectroscopic probes. We addressed this challenge by using x-ray absorption measurements under an applied electric field to render these hidden multipolar states observable. We demonstrated that the applied field induces femtometer-scale ionic displacements between iron and oxygen sites, breaking inversion symmetry and generating nonreciprocal x-ray absorption signatures. Combined with theoretical calculations, these measurements reveal how otherwise compensated multipolar components can contribute to the material’s response to an electric field. Our work establishes a spectroscopic approach for investigating hidden multipoles through their response to external fields in a broader class of magnetic materials.
Article Text
References (73)
- L. Néel, Propriétés magnétiques des ferrites; ferrimagnétisme et antiferromagnétisme, Ann. Phys. (Berlin) 3, 137 (1948).
- L. Néel, Essai d’interprétation des propriétés magnétiques du sesquioxyde de fer rhomboédrique, Ann. Phys. (Berlin) 4, 249 (1949).
- I. Dzyaloshinsky, Thermodynamic theory of weak ferromagnetism in antiferromagnetic substances, Sov. Phys. JETP 5, 1259 (1958).
- I. Dzyaloshinsky, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4, 241 (1958).
- T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120, 91 (1960).
- F. J. Morin, Magnetic susceptibility of and with added titanium, Phys. Rev. 78, 819 (1950).
- A. H. Morish, Canted Antiferromagnetism: Hematite (World Scientific, Singapore, 1994).
- Y. Cheng, S. Yu, M. Zhu, J. Hwang, and F. Yang, Electrical switching of tristate antiferromagnetic Néel order in epitaxial films, Phys. Rev. Lett. 124, 027202 (2020).
- E. Cogulu, N. N. Statuto, Y. Cheng, F. Yang, R. V. Chopdekar, H. Ohldag, and A. D. Kent, Direct imaging of electrical switching of antiferromagnetic Néel order in epitaxial films, Phys. Rev. B 103, L100405 (2021).
- E. Galindez-Ruales, R. Gonzalez-Hernandez, C. Schmitt, S. Das, F. Fuhrmann, A. Ross, E. Golias, A. Akashdeep, L. Lünenbürger, E. Baek, W. Yang, L. Šmejkal, V. Krishna, R. Jaeschke-Ubiergo, J. Sinova, A. Rothschild, C.-Y. You, G. Jakob, and M. Kläui, Revealing the altermagnetism in hematite via XMCD imaging and anomalous Hall electrical transport, Adv. Mater. 37, e05019 (2025).
- H. Pan, R.-C. Xiao, J. Han, H. Zhu, J. Li, Q. Niu, Y. Gao, and D. Hou, Experimental evidence of Néel-order-driven magneto-optical Kerr effect in an altermagnetic insulator, Phys. Rev. Lett. 136, 036701 (2026).
- J. Luo, X. Zhou, J. Liang, L. Wang, Q. Zhou, Y. Jiang, W. Wang, Y. Yao, L. Yang, and W. Jiang, Symmetry-driven giant magneto-optical Kerr effects in altermagnetic insulator, Chin. Phys. Lett. 43, 020713 (2026).
- H. Yoshimochi, K. Yoshida, R. Oiwa, T. Nomoto, N. D. Khanh, A. Kitaori, R. Takagi, R. Arita, and S. Seki, Large magneto-optical Kerr effect induced by collinear antiferromagnetic order, Sci. Rep. 16, 26745 (2026).
- Q. Sun, J. Guo, D. Wang, D. L. Abernathy, W. Tian, and C. Li, Observation of chiral magnon band splitting in altermagnetic hematite, Phys. Rev. Lett. 135, 186703 (2025).
- L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
- 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).
- X. H. Verbeek, A. Urru, and N. A. Spaldin, Hidden orders and (anti-)magnetoelectric effects in and , Phys. Rev. Res. 5, L042018 (2023).
- X. H. Verbeek, D. Voderholzer, S. Schären, Y. Gachnang, N. A. Spaldin, and S. Bhowal, Nonrelativistic ferromagnetotriakontadipolar order and spin splitting in hematite, Phys. Rev. Res. 6, 043157 (2024).
- S. Bhowal and N. A. Spaldin, Ferroically ordered magnetic octupoles in -wave altermagnets, Phys. Rev. X 14, 011019 (2024).
- A. Hariki, A. Dal Din, O. J. Amin, T. Yamaguchi, A. Badura, D. Kriegner, K. W. Edmonds, R. P. Campion, P. Wadley, D. Backes, L. S. I. Veiga, S. S. Dhesi, G. Springholz, L. Šmejkal, K. Výborný, T. Jungwirth, and J. Kuneš, X-ray magnetic circular dichroism in altermagnetic -MnTe, Phys. Rev. Lett. 132, 176701 (2024).
- N. Sasabe, Y. Ishii, and Y. Yamasaki, X-ray magnetic circular dichroism originating from the anisotropic magnetic dipole operator in collinear altermagnets under trigonal crystal field, Phys. Rev. B 112, 224401 (2025).
- S. Di Matteo, Y. Joly, and C. R. Natoli, Detection of electromagnetic multipoles by x-ray spectroscopies, Phys. Rev. B 72, 144406 (2005).
- S. Di Matteo, Resonant x-ray diffraction: Multipole interpretation, J. Phys. D 45, 163001 (2012).
- S. W. Lovesey and E. Balcar, A theoretical framework for absorption (dichroism) and the resonance-enhanced scattering of x-rays by magnetic materials: I, J. Phys. Condens. Matter 8, 10983 (1996).
- S. W. Lovesey, A theoretical framework for dichroism and the resonance-enhanced scattering of x-rays by magnetic materials: II. Quadrupolar absorption events, J. Phys. Condens. Matter 8, 11009 (1996).
- G. Schütz, W. Wagner, W. Wilhelm, P. Kienle, R. Zeller, R. Frahm, and G. Materlik, Absorption of circularly polarized x rays in iron, Phys. Rev. Lett. 58, 737 (1987).
- J. Stöhr, Exploring the microscopic origin of magnetic anisotropies with x-ray magnetic circular dichroism (XMCD) spectroscopy, J. Magn. Magn. Mater. 200, 470 (1999).
- Y. Yamasaki, H. Nakao, and T.-H. Arima, Augmented magnetic octupole in kagomé 120-degree antiferromagnets detectable via x-ray magnetic circular dichroism, J. Phys. Soc. Jpn. 89, 083703 (2020).
- M. Kimata, N. Sasabe, K. Kurita, Y. Yamasaki, C. Tabata, Y. Yokoyama, Y. Kotani, M. Ikhlas, T. Tomita, K. Amemiya, H. Nojiri, S. Nakatsuji, T. Koretsune, H. Nakao, T.-H. Arima, and T. Nakamura, X-ray study of ferroic octupole order producing anomalous Hall effect, Nat. Commun. 12, 5582 (2021).
- M. Ceolín, S. Goberna-Ferrón, and J. R. Galán-Mascarós, Strong hard x-ray magnetochiral dichroism in paramagnetic enantiopure molecules, Adv. Mater. 24, 3120 (2012).
- M. Kubota, T. Arima, Y. Kaneko, J. P. He, X. Z. Yu, and Y. Tokura, X-ray directional dichroism of a polar ferrimagnet, Phys. Rev. Lett. 92, 137401 (2004).
- H. Schmid, On ferrotoroidics and electrotoroidic, magnetotoroidic and piezotoroidic effects, Ferroelectrics 252, 41 (2001).
- S. Hayami and H. Kusunose, Time-reversal switching responses in antiferromagnets, Phys. Rev. B 108, L140409 (2023).
- T. Hayashida, K. Matsumoto, and T. Kimura, Electric field-induced nonreciprocal directional dichroism in a time-reversal-odd antiferromagnet, Adv. Mater. 37, e2414876 (2025).
- K. Kobayashi, T. Hayashida, and T. Kimura, Imaging of altermagnetic domains in orthoferrite using electric field-induced nonreciprocal directional dichroism, npj Quantum Mater. 11, 38 (2026).
- L. Pauling and S. B. Hendricks, The crystal structures of hematite and corundum, J. Am. Chem. Soc. 47, 781 (1925).
- R. J. Harrison, S. A. McEnroe, P. Robinson, and C. J. Howard, Spin orientation in a natural Ti-bearing hematite: Evidence for an out-of-plane component, Am. Mineral. 95, 974 (2010).
- L. Oravova, Z. Zhang, N. Church, R. J. Harrison, C. J. Howard, and M. A. Carpenter, Elastic and anelastic relaxations accompanying magnetic ordering and spin-flop transitions in hematite, , J. Phys. Condens. Matter 25, 116006 (2013).
- P. Kuiper, B. G. Searle, P. Rudolf, L. H. Tjeng, and C. T. Chen, X-ray magnetic dichroism of antiferromagnet : The orientation of magnetic moments observed by Fe x-ray absorption spectroscopy, Phys. Rev. Lett. 70, 1549 (1993).
- S. M. Suturin, A. M. Korovin, S. V. Gastev, P. A. Dvortsova, M. P. Volkov, M. Valvidares, and N. S. Sokolov, X-ray magnetic linear dichroism study of field-manipulated canted antiferromagnetism in epitaxial films, Phys. Rev. Mater. 5, 044408 (2021).
- Y. Ishii, N. Sasabe, and Y. Yamasaki, Altermagnetic XMCD in hematite distinct from weak ferromagnetic contributions, arXiv:2603.00442.
- R. Yamamoto et al., Nanoscale imaging of spin textures with locally varying altermagnetic response in , arXiv:2603.09934.
- J. Kokubun, A. Watanabe, M. Uehara, Y. Ninomiya, H. Sawai, N. Momozawa, K. Ishida, and V. E. Dmitrienko, Chiral and magnetic effects in forbidden x-ray scattering from antiferromagnetic hematite and eskolaite , Phys. Rev. B 78, 115112 (2008).
- S. W. Lovesey, A. Rodríguez-Fernández, and J. A. Blanco, Parity-odd multipoles, magnetic charges, and chirality in hematite , Phys. Rev. B 83, 054427 (2011).
- A. Rodríguez-Fernández, J. A. Blanco, S. W. Lovesey, V. Scagnoli, U. Staub, H. C. Walker, D. K. Shukla, and J. Strempfer, Chiral properties of hematite inferred from resonant Bragg diffraction using circularly polarized x rays, Phys. Rev. B 88, 094437 (2013).
- N. A. Spaldin, M. Fiebig, and M. Mostovoy, The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect, J. Phys. Condens. Matter 20, 434203 (2008).
- N. A. Spaldin, M. Fechner, E. Bousquet, A. Balatsky, and L. Nordström, Monopole-based formalism for the diagonal magnetoelectric response, Phys. Rev. B 88, 094429 (2013).
- S. Hayami, M. Yatsushiro, Y. Yanagi, and H. Kusunose, Classification of atomic-scale multipoles under crystallographic point groups and application to linear response tensors, Phys. Rev. B 98, 165110 (2018).
- R. R. Birss, Symmetry & Magnetism (North-Holland Publishing Company, Amsterdam, 1966).
- R. E. Newnham, Properties of Materials (Oxford University Press, New York, 2005).
- M. Yabashi, T. Mochizuki, H. Yamazaki, S. Goto, H. Ohashi, K. Takeshita, T. Ohata, T. Matsushita, K. Tamasaku, Y. Tanaka, and T. Ishikawa, Design of a beamline for the SPring-8 long undulator source 1, Nucl. Instrum. Methods Phys. Res., Sect. A 467–468, 678 (2001).
- O. Bunău and Y. Joly, Self-consistent aspects of x-ray absorption calculations, J. Phys. Condens. Matter 21, 345501 (2009).
- K. D. Finkelstein, Q. Shen, and S. Shastri, Resonant x-ray diffraction near the iron K edge in hematite (), Phys. Rev. Lett. 69, 1612 (1992).
- M. Ramakrishnan, Y. Joly, Q. N. Meier, M. Fechner, M. Porer, S. Parchenko, Y. W. Windsor, E. M. Bothschafter, F. Lichtenberg, and U. Staub, Antiferromagnetic spin canting and magnetoelectric multipoles in , Phys. Rev. Res. 5, 013203 (2023).
- Z. Liu, M. Wei, W. Peng, D. Hou, Y. Gao, and Q. Niu, Multipolar anisotropy in anomalous Hall effect from spin-group symmetry breaking, Phys. Rev. X 15, 031006 (2025).
- R.-C. Xiao, H. Li, H. Han, W. Gan, M. Yang, D.-F. Shao, S.-H. Zhang, Y. Gao, M. Tian, and J. Zhou, Anomalous-Hall Néel textures in altermagnetic materials, Sci. China Phys. Mech. Astron. 69, 217511 (2026).
- W. Peng, Z. Liu, H. Pan, P. Wang, Y. Chen, J. Zhang, X. Yu, J. Shen, M. Yang, J. Han, Q. Niu, Y. Gao, and D. Hou, Uncovering the magnetization multipolar anisotropy of the anomalous Hall effect in conventional ferromagnets, Chin. Phys. Lett. 43, 060704 (2026).
- U. Staub, Y. Bodenthin, C. Piamonteze, S. P. Collins, S. Koohpayeh, D. Fort, and S. W. Lovesey, Magnetoelectric effects studied by resonant x-ray diffraction in ferrimagnetic , Phys. Rev. B 82, 104411 (2010).
- H. Watanabe and Y. Yanase, Nonlinear electric transport in odd-parity magnetic multipole systems: Application to Mn-based compounds, Phys. Rev. Res. 2, 043081 (2020).
- M. Yatsushiro, R. Oiwa, H. Kusunose, and S. Hayami, Analysis of model-parameter dependences on the second-order nonlinear conductivity in -symmetric collinear antiferromagnetic metals with magnetic toroidal moment on zigzag chains, Phys. Rev. B 105, 155157 (2022).
- S. Hayami, Effect of external fields and currents on electronic nematic ordering with quadrupole moments, J. Magn. Magn. Mater. 604, 172274 (2024).
- K. Momma and F. Izumi, VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).
- T. Hayashida, Source data for “Electric-field-induced x-ray nonreciprocal dichroism in hematite” Zenodo, 10.5281/zenodo.22142610 (2026).
- D. Szaller, S. Bordács, and I. Kézsmárki, Symmetry conditions for nonreciprocal light propagation in magnetic crystals, Phys. Rev. B 87, 014421 (2013).
- Y. Tokura and N. Nagaosa, Nonreciprocal responses from non-centrosymmetric quantum materials, Nat. Commun. 9, 3740 (2018).
- K. Kimura, T. Katsuyoshi, Y. Sawada, S. Kimura, and T. Kimura, Imaging switchable magnetoelectric quadrupole domains via nonreciprocal linear dichroism, Commun. Mater. 1, 39 (2020).
- K. Kimura and T. Kimura, Visualization of antiferromagnetic domains by nonreciprocal directional dichroism and related optical responses, APL Mater. 11, 100902 (2023).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- U. v. Barth and L. Hedin, A local exchange-correlation potential for the spin polarized case. I, J. Phys. 5, 1629 (1972).
- B. Cros, Phase equilibriums in vanadium-metal-oxygen systems, V. The vanadium-iron-oxygen system at 1,273 K, Bull. Soc. Chim. Fr. 36, 1381 (1976).
- J. C. Papaioannou, G. S. Patermarakis, and H. S. Karayianni, Electron hopping mechanism in hematite , J. Phys. Chem. Solids 66, 839 (2005).
- V. Aji and C. M. Varma, Spin order accompanying loop-current order in cuprate superconductors, Phys. Rev. B 75, 224511 (2007).
- D. Go, D. Jo, H.-W. Lee, M. Kläui, and Y. Mokrousov, Orbitronics: Orbital currents in solids, Europhys. Lett. 135, 37001 (2021).
