Pseudo-chiral phonon splitting from octupolar magnetic order

TL;DR

This paper investigates how octupolar magnetic order in multipolar magnets can induce pseudo-chiral phonon modes with energy splitting, extending the concept of chiral phonons to new magnetic systems.

Contribution

It introduces a theoretical framework showing that octupolar and quadrupolar orders cause degeneracy breaking of Raman-active phonons, revealing pseudo-chiral phonon modes.

Findings

Octupolar order favors pseudo-chiral phonon eigenmodes.

Degeneracy of $E_g$ phonon doublet is broken by multipolar order.

Raman spectroscopy can probe hidden octupolar order in materials.

Abstract

Motivated by the recent discovery of anomalously large magnetic response of chiral phonons in dipolar magnets, we explore an extension to study Einstein quantum phonon modes coupled to multipolar moments. We consider the case of non-Kramers $\Gamma_3$ doublets which encapsulate quadrupolar and Ising octupolar degrees of freedom, and which feature a symmetry-allowed linear coupling between local quadrupolar moments and Raman active $E_g$ phonon modes $(d_{x^2-y^2},d_{3z^2-r^2})$. We show that either octupolar or quadrupolar ordering leads to degeneracy breaking of the $E_g$ phonon doublet, with ferro-octupolar order favoring pseudo-chiral phonon eigenmodes with a detectable energy splitting. We describe this physics using a path integral approach in the limit where `fast' phonon modes sense the `slow' pseudospins as a static background which we average over using Monte Carlo simulations. We discuss implications for materials such as Ba$_2$CaOsO$_6$ and PrV$_2$Al$_{20}$ where Raman spectroscopy of phonons could be used as a potential probe of hidden octupolar order. Our work extends the important concept of chiral phonons to a large class of multipolar magnets.