Numerical Study of Current-Induced Domain-Wall Dynamics: Crossover from   Spin Transfer to Momentum Transfer
  We study current-induced dynamics of a magnetic domain wall by solving a time-dependent Schr\"{o}dinger equation combined with Landau-Lifshitz-Gilbert equation in a one-dimensional electron system coupled to localized spins. Two types of domain-wall motions are observed depending on the hard-axis anisotropy, $K_{\perp}$, of the localized spin system. For small values of $K_{\perp}$, the magnetic domain wall shows a streaming motion driven by spin transfer. In contrast, for large values of $K_{\perp}$, a stick-slip motion driven by momentum transfer is obtained. We clarify the origin of these characters of domain-wall motions in terms of the dynamics of one-particle energy levels and distribution functions. 
Daisuke Matsubayashi, Masafumi Udagawa, Masao Ogata