Phonon Thermal Hall Effect in Strontium Titanate

It has been known for more than a decade that phonons can produce an off-diagonal thermal conductivity in presence of magnetic field. Recent studies of thermal Hall conductivity, $\kappa_{xy}$, in a variety of contexts, however, have assumed a negligibly small phonon contribution. We present a study of $\kappa_{xy}$ in quantum paraelectric SrTiO$_3$, which is a non-magnetic insulator and find that its peak value exceeds what has been reported in any other insulator, including those in which the signal has been qualified as 'giant'. Remarkably, $\kappa_{xy}(T)$ and $\kappa(T)$ peak at the same temperature and the former decreases faster than the latter at both sides of the peak. Interestingly, in the case of La$_2$CuO$_4$ and $\alpha$-RuCl$_3$, $\kappa_{xy}(T)$ and $\kappa(T)$ peak also at the same temperature. We also studied KTaO$_3$ and found a small signal, indicating that a sizable $\kappa_{xy}(T)$ is not a generic feature of quantum paraelectrics. Combined to other observations, this points to a crucial role played by antiferrodistortive domains in generating $\kappa_{xy}$ of this solid.