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Magnetic excitation spectrum and the hierarchy of the magnetic interactions in ErFeO3

Dnyaneshwar R. Bhosale1,*, Piotr Fabrykiewicz1,2, Devashibhai Adroja3,4, Martin Meven1,2, Astrid Schneidewind1, and Michał Stękiel1,†

  • *Contact author: d.bhosale@fz-juelich.de
  • †Contact author: m.stekiel@fz-juelich.de
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Phys. Rev. B 114, 094403 – Published 3 August, 2026

DOI: https://doi.org/10.1103/m41l-7jkp

Abstract

We report a comprehensive investigation of the excitation spectrum of ErFeO3 orthoferrite by means of time-of-flight neutron spectroscopy. The spectrum consists of two distinct components: strongly dispersive spin wave excitations of the Fe3+ sublattice spanning ≈9–65 meV, and crystal electric field (CEF) excitations of Er3+ ions below 36 meV. The observed spin wave dispersions and spectral weight are well captured within linear spin wave theory, enabling extraction of the key Fe-Fe exchange parameters. Low-energy incident neutrons with their enhanced energy resolution, further revealed the dispersive character and splitting of Kramers-degenerate CEF levels. We show that the dispersion is caused by the exchange coupling between Er3+ ions, while the degeneracy is lifted by interactions between the Er3+ and Fe3+ sublattices. We further explore the influence of dipolar and antisymmetric exchange interactions with the focus on the magnetic ground state of ErFeO3, with particular attention to the low-temperature spin arrangement. Taken together, our results provide a detailed account of the spin dynamics in ErFeO3 and reveal a hierarchy of interactions scales characteristic for orthoferrites.

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References (61)

  1. W. Lin, J. He, B. Ma, M. Matzelle, J. Xu, J. Freeland, Y. Choi, D. Haskel, B. Barbiellini, A. Bansil, G. A. Fiete, J. Zhou, and C. L. Chien, Evidence for spin swapping in an antiferromagnet, Nat. Phys. 18, 800 (2022).
  2. J. R. Hortensius, D. Afanasiev, M. Matthiesen, R. Leenders, R. Citro, A. V. Kimel, R. V. Mikhaylovskiy, B. A. Ivanov, and A. D. Caviglia, Coherent spin-wave transport in an antiferromagnet, Nat. Phys. 17, 1001 (2021).
  3. X. Ma, W. Fan, G. Zhao, H. Chen, C. Wang, B. Kang, Z. Feng, J.-Y. Ge, W. Ren, and S. Cao, Low field control of spin switching and continuous magnetic transition in an ErFeO3 single crystal, Phys. Chem. Chem. Phys. 24, 735 (2022).
  4. X. X. Zhang, Z. C. Xia, Y. J. Ke, X. Q. Zhang, Z. H. Cheng, Z. W. Ouyang, J. F. Wang, S. Huang, F. Yang, Y. J. Song, G. L. Xiao, H. Deng, and D. Q. Jiang, Magnetic behavior and complete high-field magnetic phase diagram of the orthoferrite ErFeO3, Phys. Rev. B 100, 054418 (2019).
  5. M. P. Zic, W. T. Fuhrman, K. Wang, S. Ran, J. Paglione, and N. P. Butch, Coupled spin waves and crystalline electric field levels in candidate multiferroic ErFeO3, J. Appl. Phys. 130, 014102 (2021).
  6. H. Adachi, K.-i. Uchida, E. Saitoh, and S. Maekawa, Theory of the spin Seebeck effect, Rep. Prog. Phys. 76, 036501 (2013).
  7. V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, Antiferromagnetic spintronics, Rev. Mod. Phys. 90, 015005 (2018).
  8. T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich, Antiferromagnetic spintronics, Nat. Nanotechnol. 11, 231 (2016).
  9. J. Xu, J. He, J.-S. Zhou, D. Qu, S.-Y. Huang, and C. L. Chien, Observation of vector spin Seebeck effect in a noncollinear antiferromagnet, Phys. Rev. Lett. 129, 117202 (2022).
  10. D. Kim, S. Dasgupta, X. Ma, J.-M. Park, H.-T. Wei, X. Li, L. Luo, J. Doumani, W. Yang, D. Cheng, R. H. J. Kim, H. O. Everitt, S. Kimura, H. Nojiri, J. Wang, S. Cao, M. Bamba, K. R. A. Hazzard, and J. Kono, Observation of the magnonic Dicke superradiant phase transition, Sci. Adv. 11, eadt1691 (2025).
  11. A. Kumar, A. K. Bera, C. Balz, I. Da Silva, and S. M. Yusuf, Exchange interactions, anisotropy, and low-temperature magnetization reversal in NdFeO3, Phys. Rev. B 112, 094444 (2025).
  12. S. E. Nikitin, L. S. Wu, A. S. Sefat, K. A. Shaykhutdinov, Z. Lu, S. Meng, E. V. Pomjakushina, K. Conder, G. Ehlers, M. D. Lumsden, A. I. Kolesnikov, S. Barilo, S. A. Guretskii, D. S. Inosov, and A. Podlesnyak, Decoupled spin dynamics in the rare-earth orthoferrite YbFeO3: Evolution of magnetic excitations through the spin-reorientation transition, Phys. Rev. B 98, 064424 (2018).
  13. X. Li, D. Kim, Y. Liu, and J. Kono, Terahertz spin dynamics in rare-earth orthoferrites, Photonics Insights 1, R05 (2022).
  14. G. Gorodetsky, R. M. Hornreich, I. Yaeger, H. Pinto, G. Shachar, and H. Shaked, Magnetic structure of ErFeO3 below 4.5°K, Phys. Rev. B 8, 3398 (1973).
  15. G. Deng, P. Guo, W. Ren, S. Cao, H. E. Maynard-Casely, M. Avdeev, and G. J. McIntyre, The magnetic structures and transitions of a potential multiferroic orthoferrite ErFeO3, J. Appl. Phys. 117, 164105 (2015).
  16. I. Fita, R. Puzniak, E. E. Zubov, P. Iwanowski, and A. Wisniewski, Temperature-driven spin switching and exchange bias in the ErFeO3 ferrimagnet, Phys. Rev. B 105, 094424 (2022).
  17. D. G. Oh, J. H. Kim, H. J. Shin, Y. J. Choi, and N. Lee, Anisotropic and nonlinear magnetodielectric effects in orthoferrite ErFeO3 single crystals, Sci. Rep. 10, 11825 (2020).
  18. H. Yokota, T. Nozue, S. Nakamura, H. Hojo, M. Fukunaga, P.-E. Janolin, J.-M. Kiat, and A. Fuwa, Ferroelectricity and weak ferromagnetism of hexagonal ErFeO3 thin films, Phys. Rev. B 92, 054101 (2015).
  19. D. M. Juraschek, M. Fechner, A. V. Balatsky, and N. A. Spaldin, Dynamical multiferroicity, Phys. Rev. Mater. 1, 014401 (2017).
  20. M. Marezio, J. P. Remeika, and P. D. Dernier, The crystal chemistry of the rare earth orthoferrites, Acta Cryst. B 26, 2008 (1970).
  21. E. O. Wollan and W. C. Koehler, Neutron diffraction study of the magnetic properties of the series of perovskite-type compounds [(1−x)La,xCa]MnO3, Phys. Rev. 100, 545 (1955).
  22. W. C. Koehler, E. O. Wollan, and M. K. Wilkinson, Neutron diffraction study of the magnetic properties of rare-earth-iron perovskites, Phys. Rev. 118, 58 (1960).
  23. The notation follows Koehler [22] and Bertaut [61] works. The capitalized symbol denotes the type of ordering F (ferromagnetic) A/G/C (antiferromagnetic) and the subscript denotes the direction of the moment's component. The bold component is the one with the highest amplitude.
  24. K. P. Belov, A. M. Kadomtseva, N. M. Kovtun, V. N. Derkachenko, V. N. Melov, and V. A. Khokhlov, On the character of phase transitions in ErFeO3, Phys. Stat. Sol. (a) 36, 415 (1976).
  25. R. Faulhaber, S. Hüfner, E. Orlich, and H. Schuchert, Optical investigation of ErFeO3, Z. Phys. 204, 101 (1967).
  26. D. L. Wood, J. P. Remeika, L. M. Holmes, and E. M. Gyorgy, Effect of Y and Bi substitution on spin reorientation and optical absorption in ErFeO3, J. Appl. Phys. 40, 1245 (1969).
  27. D. L. Wood, L. M. Holmes, and J. P. Remeika, Exchange fields and optical Zeeman effect in ErFeO3, Phys. Rev. 185, 689 (1969).
  28. K. Yamaguchi, T. Kurihara, Y. Minami, M. Nakajima, and T. Suemoto, Terahertz time-domain observation of spin reorientation in orthoferrite ErFeO3 through magnetic free induction decay, Phys. Rev. Lett. 110, 137204 (2013).
  29. R. V. Mikhaylovskiy, T. J. Huisman, R. V. Pisarev, T. Rasing, and A. V. Kimel, Selective excitation of terahertz magnetic and electric dipoles in Er3+ ions by femtosecond laser pulses in ErFeO3, Phys. Rev. Lett. 118, 017205 (2017).
  30. S. E. Hahn, A. A. Podlesnyak, G. Ehlers, G. E. Granroth, R. S. Fishman, A. I. Kolesnikov, E. Pomjakushina, and K. Conder, Inelastic neutron scattering studies of YFeO3, Phys. Rev. B 89, 014420 (2014).
  31. A. K. Ovsianikov, O. V. Usmanov, I. A. Zobkalo, W. Schmidt, A. Maity, V. Hutanu, E. Ressouche, K. A. Shaykhutdinov, K. Y. Terentjev, S. V. Semenov, M. Meven, G. Roth, and L. Peters, Inelastic neutron studies and diffraction in magnetic fields of TbFeO3 and YbFeO3, J. Magn. Magn. Mater. 563, 170025 (2022).
  32. A. K. Ovsyanikov, I. A. Zobkalo, W. Schmidt, S. N. Barilo, S. A. Guretskii, and V. Hutanu, Neutron inelastic scattering study of rare-earth orthoferrite HoFeO3, J. Magn. Magn. Mater. 507, 166855 (2020).
  33. S. A. Skorobogatov, S. E. Nikitin, K. A. Shaykhutdinov, A. D. Balaev, K. Y. Terentjev, G. Ehlers, G. Sala, E. V. Pomjakushina, K. Conder, and A. Podlesnyak, Low-temperature spin dynamics in the TmFeO3 orthoferrite with a non-Kramers ion, Phys. Rev. B 101, 014432 (2020).
  34. A. Podlesnyak, S. E. Nikitin, and G. Ehlers, Low-energy spin dynamics in rare-earth perovskite oxides, J. Phys.: Condens. Matter 33, 403001 (2021).
  35. R. Przeniosło, I. Sosnowska, M. Loewenhaupt, and A. Taylor, Crystal field excitations of NdFeO3, J. Magn. Magn. Mater. 140-144, 2151 (1995).
  36. S. M. Shapiro, J. D. Axe, and J. P. Remeika, Neutron-scattering studies of spin waves in rare-earth orthoferrites, Phys. Rev. B 10, 2014 (1974).
  37. J. O'Brien, G. Deng, X. Ma, Z. Feng, W. Ren, S. Cao, D. Yu, G. J. McIntyre, and C. Ulrich, Giant shifts of crystal-field excitations in ErFeO3 driven by internal magnetic fields, arXiv:2109.07667.
  38. A. Ovsianikov,The role of exchange interactions in the formation of the magnetic structure in rare-earth orthoferrites RFeO3 (R = Ho, Tb, Yb), Dissertation/Ph.D. Thesis, Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, 2023, https://doi.org/10.18154/RWTH-2023-02316.
  39. R. I. Bewley, R. S. Eccleston, K. A. McEwen, S. M. Hayden, M. T. Dove, S. M. Bennington, J. R. Treadgold, and R. L. S. Coleman, MERLIN, a new high count rate spectrometer at ISIS, Physica B 385-386, 1029 (2006).
  40. Mantid 6.13.0: Manipulation and analysis toolkit for instrument data; Mantid project, http://dx.doi.org/10.5286/SOFTWARE/MANTID6.13.
  41. O. Arnold, J. Bilheux, J. Borreguero, A. Buts, S. Campbell, L. Chapon, M. Doucet, N. Draper, R. F. Leal, M. Gigg, V. Lynch, A. Markvardsen, D. Mikkelson, R. Mikkelson, R. Miller, K. Palmen, P. Parker, G. Passos, T. Perring, P. Peterson, et al., Mantid—data analysis and visualization package for neutron scattering and μSR experiments, Nucl. Instrum. Methods Phys. Res. Sect. A 764, 156 (2014).
  42. R. Ewings, A. Buts, M. Le, J. van Duijn, I. Bustinduy, and T. Perring, Horace: Software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments, Nucl. Instrum. Methods Phys. Res. Sect. A 834, 132 (2016).
  43. ISIS data analysis as a service, https://isis.analysis.stfc.ac.uk, accessed: 2025-11-11.
  44. S. Toth and B. Lake, Linear spin wave theory for single-Q incommensurate magnetic structures, J. Phys.: Condens. Matter 27, 166002 (2015).
  45. M. Stekiel, Implementation of SpinW in Python, Github, 2025, https://github.com/mstekiel/spinwaves, accessed: 2025-11-11.
  46. D. Dahlbom, H. Zhang, C. Miles, S. Quinn, A. Niraula, B. Thipe, M. Wilson, S. Matin, H. Mankad, S. Hahn, D. Pajerowski, S. Johnston, Z. Wang, H. Lane, Y. W. Li, X. Bai, M. Mourigal, C. D. Batista, and K. Barros, Sunny.jl: A Julia package for spin dynamics, J. Open Source Software 10, 8138 (2025).
  47. A. Scheie, PyCrystalField: Software for calculation, analysis and fitting of crystal electric field Hamiltonians, J. Appl. Crystallogr. 54, 356 (2021).
  48. K. Momma and F. Izumi, VESTA: A three-dimensional visualization system for electronic and structural analysis, J. Appl. Crystallogr. 41, 653 (2008).
  49. K. Park, H. Sim, J. C. Leiner, Y. Yoshida, J. Jeong, S.-i. Yano, J. Gardner, P. Bourges, M. Klicpera, V. Sechovský, M. Boehm, and J.-G. Park, Low-energy spin dynamics of orthoferrites AFeO3 (A = Y, La, Bi), J. Phys.: Condens. Matter 30, 235802 (2018).
  50. A. Gukasov, U. Steigenberger, S. Barilo, and S. Guretskii, Neutron scattering study of spin waves in TbFeO3, Physica B 234-236, 760 (1997).
  51. R. M. White, R. J. Nemanich, and C. Herring, Light scattering from magnetic excitations in orthoferrites, Phys. Rev. B 25, 1822 (1982).
  52. K. W. H. Stevens, Matrix elements and operator equivalents connected with the magnetic properties of rare earth ions, Proc. Phys. Soc. A 65, 209 (1952).
  53. From the symmetry point of view, the coexistence of Fe3+ (Γ2, Pbn′m′) and Er3+ (Γ1, Pbnm.1) magnetic orderings below TNEr leads to the monoclinic P21/b.1 1 1 (nonstandard setting of P21/c.1 magnetic space group) symmetry [15] with 1 (trivial) site-symmetry point group, which in-principle lifts all restrictions on CEF Blm parameters. However, as magnetocrystalline coupling is weak and does not lead to the observable shifts of atomic positions, the approximation of the Pbnm space group with the ..m site-symmetry point group of Er3+ is justified below TNEr.
  54. M. T. Hutchings, in Point-Charge Calculations of Energy Levels of Magnetic Ions in Crystalline Electric Fields, edited by F. Seitz and D. Turnbull, Solid State Physics Vol. 16 (Academic Press, 1964), pp. 227–273.
  55. The B20O20+B21O21 anisotropy is equivalent to B20(3Jz2−1)+12B21(JxJz+JzJx). For Bnm values from Table  1 this gives tilted anisotropy ellipsoid, with the main (easy) axis vector tilted 30 degrees away from the z axis toward the x axis.
  56. The dipolar interactions involve all ions and take magnetic moments as parameters, that is 5μB for iron and 9μB for erbium.
  57. R. M. Bozorth, V. Kramer, and J. P. Remeika, Magnetization in single crystals of some rare-earth orthoferrites, Phys. Rev. Lett. 1, 3 (1958).
  58. Y. B. Bazaliy, L. T. Tsymbal, G. N. Kakazei, A. I. Izotov, and P. E. Wigen, Spin-reorientation in ErFeO3: Zero-field transitions, three-dimensional phase diagram, and anisotropy of erbium magnetism, Phys. Rev. B 69, 104429 (2004).
  59. R. L. White, Review of recent work on the magnetic and spectroscopic properties of the rare‐earth orthoferrites, J. Appl. Phys. 40, 1061 (1969).
  60. D. R. Bhosale, P. Fabrykiewicz, M. Meven, A. Schneidewind, A. Devashi, and M. Stekiel, High-energy spin dynamics in multiferroic ErFeO3 for magnon transport application, STFC ISIS Neutron and Muon Source, 2025, https://doi.org/10.5286/ISIS.E.RB2510189.
  61. E. F. Bertaut, Representation analysis of magnetic structures, Acta Cryst. A 24, 217 (1968).

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Phys. Rev. B 114, 094403– Published 3 August, 2026
  • Received 22 April 2026
  • Revised 25 June 2026
  • Accepted 9 July 2026
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