Thermal vector potential theory of magnon-driven magnetization dynamics

Thermal vector potential formulation is applied to study thermal dynamics of magnetic structures in insulating ferromagnets. By separating variables of the magnetic structure and magnons, the equation of motion for the structure including spin-transfer effect due to thermal magnons is derived in the case of a domain wall and a vortex. The magnon current is evaluated based on a linear response theory with respect to the thermal vector potential representing the temperature gradient. It is shown that the velocity of a domain wall when driven by thermal magnon has a strong temperature dependence unlike the case of an electrically-driven domain wall in metals.