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  • Open Access

Phonon-mediated spin-spin interactions

J. Fransson*

  • Department of Physics and Astronomy, Uppsala University, PO Box 524, 751 20 Uppsala, Sweden

  • *Contact author: Jonas.Fransson@physics.uu.se
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Phys. Rev. B 114, 204408 – Published 9 October, 2026

DOI: https://doi.org/10.1103/f5d2-9tq9

Abstract

Indirect long-range interactions between localized magnetic moments in metals are mediated by itinerant electrons. In insulators and semiconductors, such interactions cannot be mediated by itinerant electrons; however, delocalized electrons in the valence band may provide such a medium. Nevertheless, the existence of magnetically ordered insulators, for instance, metal oxides, is therefore an everlasting source for proposals of various mechanisms that may support the order. Here, phonon-mediated interactions between localized magnetic moments are considered as a mechanism that can provide quantifiable symmetric and antisymmetric anisotropic spin-spin interactions. It is demonstrated that while a symmetric anisotropic interaction exists for all types of phonons, the existence of antisymmetric anisotropic interactions requires broken inversion symmetry. The latter mechanism may explain the weak ferromagnetic order observed in chiral compounds, e.g., CuO and CoO. Furthermore, the interaction is nearly independent of temperature at low temperatures, while it approaches linear growth at high temperatures. Spatially, the interactions have an oscillatory power-law decay with the interatomic distance.

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Phys. Rev. B 114, 204408– Published 9 October, 2026
  • Received 16 April 2026
  • Revised 10 August 2026
  • Accepted 1 September 2026
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