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$_3$ 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. This hitherto unreported behavior is also visible in the case of La$_2$CuO$_4$ and $\alpha$-RuCl$_3$. 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.