Current-spin coupling for ferromagnetic domain walls in fine wires
  The coupling between a current and a domain wall is examined. In the presence of a finite current and the absence of a potential which breaks the translational symmetry, there is a perfect transfer of angular momentum from the conduction electrons to the wall. As a result, the ground state is in uniform motion. This remains the case when relaxation is accounted for. This is described by, appropriately modified, Landau-Lifshitz-Gilbert equations. 
S. E. Barnes and S. Maekawa