Spin Thermal Hall Conductivity of a Kagom\'e Antiferromagnet

A clear thermal Hall signal ($\kappa_{xy}$) was observed in the spin liquid phase of the $S=1/2$ kagom\'e antiferromagnet Ca kapellasite (CaCu$_3$(OH)$_6$Cl$_2\cdot 0.6$H$_2$O). We found that $\kappa_{xy}$ is well reproduced, both qualitatively and quantitatively, using the Schwinger-boson mean-field theory with the Dzyaloshinskii--Moriya interaction of $D/J \sim 0.1$. In particular, $\kappa_{xy}$ values of Ca kapellasite and those of another kagom\'e antiferromagnet, volborthite, converge to one single curve in simulations modeled using Schwinger bosons, indicating a common temperature dependence of $\kappa_{xy}$ for the spins of a kagom\'e antiferromagnet.