  We report measurements of the thermal Hall effect in single crystals of both
pristine and isotopically substituted strontium titanate. We discovered a two
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 ($|\kappa_{xy}/\kappa_{xx}|$) 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. 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.
