A thermodynamic theory for thermal-gradient-driven domain wall motion

Spin waves (or magnons) interact with magnetic domain walls (DWs) in a complicated way that a DW can propagate either along or against magnon flow. However, thermally activated magnons always drive a DW to the hotter region of a nanowire of magnetic insulators under a temperature gradient. We theoretically illustrate why it is surely so by showing that DW entropy is always larger than that of a domain as long as material parameters do not depend on spin textures. Equivalently, the total free energy of the wire can be lowered when the DW moves to the hotter region. The larger DW entropy is related to the increase of magnon density of states at low energy originated from the gapless magnon bound states

Thermal gradient driven domain wall dynamics

The issue of whether a thermal gradient acts like a magnetic field or an electric current in the domain wall (DW) dynamics is investigated. Broadly speaking, magnetization control knobs can be classified as energy-driving or angular-momentum driving forces. DW propagation driven by a static magnetic field is the best-known example of the former in which the DW speed is proportional to the energy dissipation rate, and the current-driven DW motion is an example of the latter. Here we show that DW propagation speed driven by a thermal gradient can be fully explained as the angular momentum transfer between thermally generated spin current and DW. We found DW-plane rotation speed increases as DW width decreases. Both DW propagation speed along the wire and DW-plane rotation speed around the wire decrease with the Gilbert damping. These facts are consistent with the angular momentum transfer mechanism, but are distinct from the energy dissipation mechanism. We further show that magnonic spin-transfer torque (STT) generated by a thermal gradient has both damping-like and field-like components. By analyzing DW propagation speed and DW-plane rotation speed, the coefficient ( \b{eta}) of the field-like STT arising from the non-adiabatic process, is obtained. It is found that \b{eta} does not depend on the thermal gradient; increases with uniaxial anisotropy K_(||) (thinner DW); and decreases with the damping, in agreement with the physical picture that a larger damping or a thicker DW leads to a better alignment between the spin-current polarization and the local magnetization, or a better adiabaticity