Charged Defects and Phonon Hall Effects in Ionic Crystals

It has been known for decades that a magnetic field can deflect phonons as they flow in response to a thermal gradient, producing a thermal Hall effect. Several recent experiments have revealed ratios of the phonon Hall conductivity to the phonon longitudinal conductivity in oxide dielectrics that are larger than ${10}^{-3}$ when phonon mean-free-paths exceed phonon wavelengths. At the same time ${\kappa }_H\mathrm{/}{\kappa }_L$ is not strongly temperature dependent. We argue that these two properties together imply a mechanism related to phonon scattering from defects that break time-reversal symmetry, and we show that Lorentz forces acting on charged defects produce substantial skew-scattering amplitudes, and related thermal Hall effects that are consistent with recent observations.