Role of entropy in domain wall motion in thermal gradients

Thermally driven domain wall (DW) motion caused solely by magnonic spin currents was forecast theoretically and has been measured recently in a magnetic insulator using magneto-optical Kerr effect microscopy. We present an analytical calculation of the DW velocity as well as the Walker breakdown within the framework of the Landau Lifshitz Bloch equation of motion. The temperature gradient leads to a torque term acting on the magnetization where the DW is mainly driven by the temperature dependence of the exchange stiffness, or--in a more general picture--by the maximization of entropy. The existence of this entropic torque term does not rest on the angular momentum transfer from the magnonic spin current. Hence, even DWs in antiferromagnets or compensated ferrimagnets should move accordingly. We further argue that the entropic torque exceeds that of the magnonic spin current.