Dynamics of domain wall in thin film driven by spin current

The dynamics of magnetization under the applied spin current is modeled by the generalized Landau-Lifshitz-Gilbert equation with a spin transfer torque term. Using matched asymptotic expansion with the domain wall thickness epsilon as the small parameter, we derive analytically the dynamic law for the domain wall motion induced by the spin current. We show that the domain wall driven by adiabatic current spin-transfer torque moves with a decreasing velocity and eventually stops. With a pinning potential, the domain wall motion is a damped oscillation around the pinning site with an intrinsic frequency which is independent of the strength of the current. When the AC current is applied, the dynamic law shows that the frequency of the applied current can be turned to maximize the amplitude of the oscillation. The results obtained are consistent with the recent experimental and numerical results.