  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.
