Thermodynamic Magnon Recoil for Domain Wall Motion

We predict a thermodynamic magnon recoil effect for domain wall motions in the presence of temperature gradients. All current thermodynamic theories assert that a magnetic domain wall must move toward the hotter side, based on equilibrium thermodynamic arguments. Microscopic calculations on the other hand show that a domain wall can move either along or against the direction of heat currents, depending on how strong the heat currents are reflected by the domain wall. We have resolved the inconsistency between these two approaches by augmenting the theory in the presence of thermal gradients by incorporating in the free energy of domain walls by a heat current term present in nonequilibrium steady states. The condition to observe a domain wall propagation toward the colder regime is derived analytically and can be tested by future experiments.