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In a growing number of materials, phonons have been found to generate athermal Hall effect, but the underlying mechanism remains unclear. Inspired byprevious studies that revealed the importance of Tb$^{3+}$ ions in generatingthe thermal Hall effect of Tb$_{2}$Ti$_{2}$O$_{7}$, we investigated the role ofTm$^{3+}$ ions in TmVO$_{4}$, a paramagnetic insulator with a different crystalstructure. We observe a negative thermal Hall conductivity in TmVO$_{4}$ with amagnitude such that the Hall angle, $|\kappa_{xy}$/$\kappa_{xx}|$, isapproximately 1 x 10$^{-3}$ at $H$ = 15 T and $T$ = 20 K, typical for aphonon-generated thermal Hall effect. In contrast to the negligible$\kappa_{xy}$ found in Y$_{2}$Ti$_{2}$O$_{7}$, we observe a negative$\kappa_{xy}$ in YVO$_{4}$ with a Hall angle of magnitude comparable to that ofTmVO$_{4}$. This shows that the Tm$^{3+}$ ions are not essential for thethermal Hall effect in this family of materials. Interestingly, at anintermediate Y concentration of 30 % in Tm$_{1-x}$Y$_{x}$VO$_{4}$,$\kappa_{xy}$ was found to have a positive sign, pointing to the possibleimportance of impurities in the thermal Hall effect of phonons.

Role of magnetic ions in the thermal Hall effect of the paramagnetic insulator TmVO$_{4}$