- 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

Finite-temperature enhancement of magnetic interactions from first principles

Ravi Kaushik1, Ryota Ono2, and Sergey Artyukhin

PDF

Phys. Rev. B 114, 165143 – Published 30 September, 2026

DOI: https://doi.org/10.1103/fh3c-61jn

Abstract

Density functional theory has demonstrated remarkable predictive power in calculating magnetic properties at zero temperature. At finite temperatures, thermally excited phonons affect magnetism. Efficient ab initio methods for calculating the temperature dependence of magnetic exchange interactions are still lacking despite the importance of room temperature magnetism for applications. Here we present a method to calculate the exchange interactions at finite temperatures from first principles using only two supercell calculations per temperature. Focusing on magnetic insulators, we find that magnetic exchange interactions decrease with temperature in NiO, while in Cr2O3 a substantial temperature-induced enhancement of 10% at T=300K is uncovered. The exchange constant is governed by an interplay between metal-ligand hybridization, Hubbard repulsion, and the band gap. They all depend on equilibrium interatomic distances and bond angles, themselves modified by thermal phonons.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (35)

  1. S. Mankovsky, S. Polesya, and H. Ebert, Exchange coupling constants at finite temperature, Phys. Rev. B 102, 134434 (2020).
  2. I. P. Miranda, M. Pankratova, M. Weißenhofer, A. B. Klautau, D. Thonig, M. Pereiro, E. Sjöqvist, A. Delin, M. I. Katsnelson, O. Eriksson, and A. Bergman, Spin-lattice couplings in 3d ferromagnets: Analysis from first principles, Phys. Rev. Mater. 9, 024409 (2025).
  3. D. I. Badrtdinov, M. I. Katsnelson, and A. N. Rudenko, Phonon-induced renormalization of exchange interactions in metallic two-dimensional magnets, Phys. Rev. B 110, L060409 (2024).
  4. S. T. Bramwell, Temperature dependence of the isotropic exchange constant, J. Phys.: Condens. Matter 2, 7527 (1990).
  5. P. R. Baral, O. I. Utesov, C. Luo, F. Radu, A. Magrez, J. S. White, and V. Ukleev, Direct observation of exchange anisotropy in the helimagnetic insulator Cu2OSeO3, Phys. Rev. Res. 5, L032019 (2023).
  6. A. M. Glazer, The classification of tilted octahedra in perovskites, Acta Crystallogr. B: Struct. Sci. Cryst. Eng. Mater. 28, 3384 (1972).
  7. M. Klanjšek, D. Arčon, A. Sans, P. Adler, M. Jansen, and C. Felser, Phonon-modulated magnetic interactions and spin Tomonaga-Luttinger liquid in the p-orbital antiferromagnet CsO2, Phys. Rev. Lett. 115, 057205 (2015).
  8. M. E. Lines and M. A. Bösch, Magnetogyration, Phys. Rev. B 23, 263 (1981).
  9. M. Rinaldi, M. Mrovec, A. Bochkarev, Y. Lysogorskiy, and R. Drautz, Non-collinear magnetic atomic cluster expansion for iron, npj Comput. Mater. 10, 12 (2024).
  10. M. Zacharias and F. Giustino, Theory of the special displacement method for electronic structure calculations at finite temperature, Phys. Rev. Res. 2, 013357 (2020).
  11. M. Zacharias and F. Giustino, One-shot calculation of temperature-dependent optical spectra and phonon-induced band-gap renormalization, Phys. Rev. B 94, 075125 (2016).
  12. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, New York, 1996).
  13. B. Monserrat, Vibrational averages along thermal lines, Phys. Rev. B 93, 014302 (2016).
  14. A. Liechtenstein, M. Katsnelson, V. Antropov, and V. Gubanov, Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys, J. Magn. Magn. Mater. 67, 65 (1987).
  15. M. I. Katsnelson and A. I. Lichtenstein, First-principles calculations of magnetic interactions in correlated systems, Phys. Rev. B 61, 8906 (2000).
  16. A. A. Mostofi, J. R. Yates, G. Pizzi, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, An updated version of Wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 185, 2309 (2014).
  17. G. Pizzi et al., Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32, 165902 (2020).
  18. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  19. P. Giannozzi et al., QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
  20. P. Giannozzi et al., Advanced capabilities for materials modelling with QUANTUM ESPRESSO, J. Phys.: Condens. Matter 29, 465901 (2017).
  21. P. Giannozzi, O. Baseggio, P. Bonfà, D. Brunato, R. Car, I. Carnimeo, C. Cavazzoni, S. de Gironcoli, P. Delugas, F. Ferrari Ruffino, A. Ferretti, N. Marzari, I. Timrov, A. Urru, and S. Baroni, QUANTUM ESPRESSO toward the exascale, J. Chem. Phys. 152, 154105 (2020).
  22. D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013).
  23. M. Schlipf and F. Gygi, Optimization algorithm for the generation of ONCV pseudopotentials, Comput. Phys. Commun. 196, 36 (2015).
  24. 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).
  25. I. Timrov, N. Marzari, and M. Cococcioni, Hp – a code for the calculation of hubbard parameters using density-functional perturbation theory, Comput. Phys. Commun. 279, 108455 (2022).
  26. B. Himmetoglu, R. M. Wentzcovitch, and M. Cococcioni, First-principles study of electronic and structural properties of CuO, Phys. Rev. B 84, 115108 (2011).
  27. S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73, 515 (2001).
  28. See Supplemental Material at http://link.aps.org/supplemental/10.1103/fh3c-61jn for the derivation of temperature-dependent exchange from superexchange theory, computational workflow, and additional computational details.
  29. S. Shi, A. L. Wysocki, and K. D. Belashchenko, Magnetism of chromia from first-principles calculations, Phys. Rev. B 79, 104404 (2009).
  30. D. M. Korotin, V. V. Mazurenko, V. I. Anisimov, and S. V. Streltsov, Calculation of exchange constants of the Heisenberg model in plane-wave-based methods using the Green's function approach, Phys. Rev. B 91, 224405 (2015).
  31. Peng Chen et al., LInvariant second principles suite, 2020, https://github.com/PaulChern/LINVARIANT.
  32. P. Souvatzis, O. Eriksson, M. I. Katsnelson, and S. P. Rudin, Entropy driven stabilization of energetically unstable crystal structures explained from first principles theory, Phys. Rev. Lett. 100, 095901 (2008).
  33. J. R. Tomlinson, L. Domash, R. G. Hay, and C. W. Montgomery, The high temperature heat content of nickel oxide, J. Am. Chem. Soc. 77, 909 (1955).
  34. M. T. Hutchings and E. J. Samuelsen, Measurement of spin-wave dispersion in NiO by inelastic neutron scattering and its relation to magnetic properties, Phys. Rev. B 6, 3447 (1972).
  35. G. Fischer, M. Däne, A. Ernst, P. Bruno, M. Lüders, Z. Szotek, W. Temmerman, and W. Hergert, Exchange coupling in transition metal monoxides: Electronic structure calculations, Phys. Rev. B 80, 014408 (2009).

Outline

Information

Phys. Rev. B 114, 165143– Published 30 September, 2026
  • Received 30 May 2024
  • Revised 17 August 2026
  • Accepted 27 August 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