Nonadiabatic Theory of Phonon Magnetic Moments in Insulators and Metals

TL;DR

This paper presents a nonadiabatic theoretical framework for phonon magnetic moments applicable to insulators and metals, incorporating Fermi-surface effects and resonant processes, and aligns with experimental data.

Contribution

It introduces a gauge-invariant, comprehensive nonadiabatic theory for phonon magnetic moments, extending previous adiabatic models to include Fermi-surface and interband effects.

Findings

Fermi-surface contributions significantly enhance phonon magnetic moments.

The theory reduces to adiabatic expressions in the low-frequency limit.

Application to Pb$_{1-x}$Sn$_x$Te matches experimental magnitudes.

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.