Classical and quantum depinning of a domain wall with a spin-polarized current

We study in detail the classical and quantum depinning of a domain wall (DW) induced by a fast-varying spin-polarized current. By confirming the adiabatic condition for calculating the spin-torque in fast-varying current case, we show that the time-dependent spin current has two critical values that determine the classical depinning of DW. This discovery successfully explains the recent experiments. Furthermore, a feasible way is proposed to lower the threshold of spin currents and control the direction of DW's motion. Finally, the quantum properties for the depinning of DW are also investigated in this paper.