Topological Thermal Hall Effect in Frustrated Kagom\'e Antiferromagnets

In frustrated magnets the Dzyaloshinsky-Moriya interaction arising from spin-orbit coupling can induce a magnetic long-range order. Here, we report a theoretical prediction of thermal Hall effect in frustrated kagom'e magnets such as KCr${}_3$(OH)${}_6$(SO4)${}_2$ and KFe${}_3$(OH)${}_6$(SO${}_4$)${}_2$. The thermal Hall effects in these materials are induced by scalar spin chirality as opposed to DMI in previous studies. The scalar spin chirality originates from magnetic-field-induced chiral spin configuration due to non-coplanar spin textures, but in general it can be spontaneously developed as a macroscopic order parameter in chiral quantum spin liquids. Therefore, we infer that there is a possibility of thermal Hall effect in frustrated kagom'e magnets such as herbertsmithite ZnCu${}_3$(OH)${}_6$Cl${}_2$ and the chromium compound Ca${}_{10}$Cr${}_7$O${}_{28}$, although they also show evidence of magnetic order in the presence of a magnetic field or pressure.