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

• Received 7 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.064405