Landau-Lifshitz theory of the thermomagnonic torque

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We derive the thermomagnonic torque associated with smooth magnetic textures subjected to a temperature gradient, in the framework of the stochastic Landau-Lifshitz-Gilbert equation. Our approach captures on equal footing two distinct contributions: (1) A local entropic torque that is caused by a temperature dependence of the effective exchange field, the existence of which had been previously suggested based on numerics and (2) the well-known spin-transfer torque induced by thermally-induced magnon flow. The dissipative components of two torques have the same structure, following a common phenomenology, but opposite signs, with the twice larger entropic torque leading to a domain-wall motion toward the hotter region. We compare the efficiency of the torque-driven domain-wall motion with the recently proposed Brownian thermophoresis.