Scalar Spin Chirality Hall Effect

The scalar spin chirality, which characterizes the fundamental unit of noncoplanar spin structures, plays an important role in rich chiral physics of magnetic materials. In particular, the intensive research efforts over the past two decades have demonstrated that the scalar spin chirality is the source of various novel Hall transports in solid-state systems, offering a primary route to bring about chiral phenomena in condensed matter physics. However, in all of the previous studies, the scalar spin chirality has been given as a stationary background, serving only a passive role in the transport properties of materials. It remains an open question whether or not the scalar spin chirality itself can exhibit a Hall-type transport. In this work, we show that the answer is yes: The scalar spin chirality is Hall-transported in Kagome ferromagnets and antiferromagnets under an external bias, engendering a phenomenon which we dub the scalar spin chirality Hall effect. Notably, this effect is present even in the absence of any spin-orbit coupling. The analytical theory for the scalar spin chirality Hall effect is corroborated by atomistic spin simulations. Our findings call for the need to lift the conventional assumption that the scalar spin chirality is a passive background in order to discover the active roles of the scalar spin chirality in transport properties.