In thin magnetic layers with structural inversion asymmetry and spin-orbit coupling, a Dzyaloshinskii-Moriya interaction arises at the interface. When a spin wave current ${bf j}_m$ flows in a system with a homogeneous magnetization {bf m}, this interaction produces an effective field-like torque on the form ${bf T}_{rm FL}propto{bf m}times({bf z}times{bf j}_m)$ as well as a damping-like torque, ${bf T}_{rm DL}propto{bf m}times[({bf z}times{bf j}_m)times{bf m}]$ in the presence of spin-wave relaxation (${bf z}$ is normal to the interface). These torques mediated by the magnon flow can reorient the time-averaged magnetization direction and display a number of similarities with the torques arising from the electron flow in a magnetic two dimensional electron gas with Rashba spin-orbit coupling. This magnon-mediated spin-orbit torque can be efficient in the case of magnons driven by a thermal gradient.
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