Sizeable Suppression of Thermal Hall Effect upon Isotopic Substitution in SrTiO$_3$

We report measurements of the thermal Hall effect in single crystals of both pristine and isotopically substituted strontium titanate. We discovered a 2 orders of magnitude difference in the thermal Hall conductivity between SrTi$^{16}$O$_3$ and $^{18}$O-enriched SrTi$^{18}$O$_3$ samples. In most temperature ranges, the magnitude of thermal Hall conductivity ($\kappa_{xy}$) in SrTi$^{18}$O$_3$ is proportional to the magnitude of the longitudinal thermal conductivity ($\kappa_{xx}$), which suggests a phonon-mediated thermal Hall effect. However, they deviate in the temperature of their maxima, and the thermal Hall angle ratio ($\left\vert\kappa_{xy}/\kappa_{xx}\right\vert$) shows anomalously decreasing behavior below the ferroelectric Curie temperature T$_c$ ~25 K. This observation suggests a new underlying mechanism, as the conventional scenario cannot explain such differences within the slight change in phonon spectrum[1,2]. Notably, the difference in magnitude of thermal Hall conductivity and rapidly decreasing thermal Hall angle ratio in SrTi$^{18}$O$_3$ is correlated with the strength of quantum critical fluctuations in this displacive ferroelectric. This relation points to a link between the quantum critical physics of strontium titanate and its thermal Hall effect, a possible clue to explain this example of an exotic phenomenon in non-magnetic insulating systems.