Phonon Magnetic Moment from Electronic Topological Magnetization

TL;DR

This paper explores the electronic topological origins of phonon magnetic moments, revealing that they can be significantly larger and more complex than traditional models suggest, especially in topological materials with band inversions.

Contribution

It introduces a refined theory incorporating a $m{k}$ resolved Born effective charge and topological effects, providing new insights into phonon magnetization in topological materials.

Findings

Electronic orbital magnetization described by a second Chern form.

Large magnetic moments observed in optical phonons of topological materials.

Magnetic moments change sign during band inversion.

Abstract

The traditional theory of magnetic moments for chiral phonons is based on the picture of the circular motion of the Born effective charge, typically yielding a small fractional value of the nuclear magneton. Here we investigate the adiabatic evolution of electronic states induced by lattice vibration of a chiral phonon and obtain an electronic orbital magnetization in the form of a topological second Chern form. We find that the traditional theory needs to be refined by introducing a $\bm{k}$ resolved Born effective charge, and identify another contribution from the phonon-modified electronic energy together with the momentum-space Berry curvature. The second Chern form can diverge when there is a Yang's monopole near the parameter space of interest as illustrated by considering a phonon at the Brillouin zone corner in a gaped graphene model. We also find large magnetic moments for the optical phonon in bulk topological materials where non-topological contribution is also important. The magnetic moment experiences a sign change when the band inversion happens.