Origin of the Phonon Hall Effect in Rare-Earth Garnets

TL;DR

This paper explains the phonon Hall effect in rare-earth garnets as arising from resonant skew scattering of phonons by crystal field states of Tb3+ ions, linking microscopic interactions to observed temperature gradients.

Contribution

It identifies the microscopic mechanism behind the phonon Hall effect in Tb3Gd5O12, highlighting the role of crystal field states and strain coupling in phonon skew scattering.

Findings

The effect is due to resonant skew scattering from Tb3+ crystal field states.

The estimated magnitude matches experimental data at 5 K.

The effect can be enhanced at higher temperatures.

Abstract

The phonon Hall effect has been observed in the paramagnetic insulator, Tb3Gd5O12. A magnetic field applied perpendicularly to a heat current induces a temperature gradient that is perpendicular to both the field and the current. We show that this effect is due to resonant skew scattering of phonons from the crystal field states of superstoichiometric Tb^3+ ions. This scattering originates from the coupling between the quadrupole moment of Tb^3+ ions and the lattice strain. The estimated magnitude of the effect is consistent with experimental observations at T=5 K, and can be significantly enhanced by increasing temperature.