Microscopic Connection between Phonon Hall Viscosity and Acoustic Faraday Effect in Spin-Orbit-Coupled Magnets

Abstract

The acoustic Faraday effect probes phonon Hall viscosity through the rotation of transverse acoustic polarization, conventionally interpreted in terms of circular birefringence. We show that magnetic order breaking rotational symmetry generates anisotropic phonon responses and elliptically polarized eigenmodes, so that Faraday rotation cannot be attributed to Hall viscosity alone. To elucidate their microscopic origin and consequences, we derive spin-strain couplings from a generic spin-orbit-coupled exchange model. We identify transverse strain couplings for propagation along the c-axis arising linearly from the changes in the bond-dependent interactions, along with strain-induced g-tensor contributions. Applying our theory to $\alpha$-RuCl${}_3$, we find that static strain responses modify the extraction of Hall viscosity from Faraday rotation, yielding a value significantly different from that inferred assuming rotational symmetry. Our results establish a microscopic connection between magnetic interaction, lattice dynamics, and phonon Hall viscosity in spin-orbit-coupled magnets.

arXiv comment6 pages, 3 figures