Topological Spin-Orbit Torque in Ferrimagnetic Weyl Semimetal

The spin-orbit torque (SOT) in a compensated ferrimagnetic Weyl semimetal, ${\rm Ti}_{2}{\rm MnAl}$, is studied by the linear response theory. We elucidate that the SOT driven by all the occupied electronic states is present in magnetic Weyl semimetal, unlike in conventional metallic magnets. Around the energy of the Weyl points, we find that such an SOT is dominant and almost independent of the disorder. The emergence of the SOT in ${\rm Ti}_{2}{\rm MnAl}$ can be understood from the structure of the mixed Berry curvature around the Weyl points, which is similar to that of the ordinary Berry curvature.