Role of magnetic ions in the thermal Hall effect of the paramagnetic insulator <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>TmVO</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math>

In a growing number of materials, phonons have been found to generate a thermal Hall effect, but the underlying mechanism remains unclear. Inspired by previous studies that revealed the importance of ${\mathrm{Tb}}^{3+}$ ions in generating the thermal Hall effect in a family of pyrochlores, we investigated the role of ${\mathrm{Tm}}^{3+}$ ions in ${\mathrm{TmVO}}_{4}$, a paramagnetic insulator with a different crystal structure. We observe a negative thermal Hall conductivity in ${\mathrm{TmVO}}_{4}$ with a magnitude such that the Hall angle, $|{\ensuremath{\kappa}}_{xy}/{\ensuremath{\kappa}}_{xx}|$, is approximately $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ at $H$ = 15 T and $T$ = 20 K, typical for a phonon-generated thermal Hall effect. In contrast to the negligible ${\ensuremath{\kappa}}_{xy}$ found in the nonmagnetic pyrochlore analog (where the ${\mathrm{Tb}}^{3+}$ ions are replaced with ${\mathrm{Y}}^{3+}$), we observe a negative ${\ensuremath{\kappa}}_{xy}$ in ${\mathrm{YVO}}_{4}$ with a Hall angle of magnitude comparable to that of ${\mathrm{TmVO}}_{4}$. This shows that the ${\mathrm{Tm}}^{3+}$ ions are not essential for the thermal Hall effect in this family of materials. Interestingly, at an intermediate Y concentration of $x=0.3$ in ${\mathrm{Tm}}_{1\ensuremath{-}x}{\mathrm{Y}}_{x}{\mathrm{VO}}_{4}, {\ensuremath{\kappa}}_{xy}$ was found to have a positive sign, pointing to the importance of impurities in the thermal Hall effect of phonons.

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