Hall Effect of Spin Waves in Frustrated Magnets

We examine a possible spin Hall effect for localized spin systems with no charge degrees of freedom. In this scenario, a longitudinal magnetic field gradient induces a transverse spin current carried by spin wave excitations with an anomalous velocity which is associated with the Berry curvature raised by spin chirality, in analogy with anomalous Hall effects in itinerant electron systems. Our argument is based on a semiclassical equations of motion applicable to general spin systems. Also, a microscopic model of frustrated magnets which exhibits the anamalous spin Hall effect is presented.