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arXiv · 2605.06983

Nonadiabatic Theory of Phonon Magnetic Moments in Insulators and Metals

Haoran Chen·Wenqin Chen·Kaijie Yang·Ting Cao·Di Xiao
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Abstract

We develop a nonadiabatic theory of phonon magnetic moments applicable to both insulators and metals. By relating the phonon magnetic moment to the force-velocity response of ions in a magnetic field, we derive a gauge-invariant expression using a gauge-covariant Wigner expansion. The formalism naturally separates Fermi-sea and Fermi-surface contributions and captures the full dependence on phonon frequency. In gapped systems, our theory reduces to previous adiabatic expressions in the low-frequency limit. Beyond this limit, it reveals additional contributions arising from resonant interband processes and the Fermi surface. Applying our theory to Pb$_{1-x}$Sn$_x$Te, we find that the Fermi-surface contribution substantially enhances the phonon magnetic moment, reproducing the same order of magnitude as the experimental observation. Our results provide a unified framework for describing phonon magnetic moments beyond the adiabatic regime.

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Haoran Chen, Wenqin Chen, Kaijie Yang, Ting Cao, Di Xiao. 2026-05-07. Nonadiabatic Theory of Phonon Magnetic Moments in Insulators and Metals. https://arxiv.org/abs/2605.06983

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