The coupling between a current and a domain wall is examined. In the presence of a finite current and in 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 and this remains the case even when relaxation is included. This is described by, appropriately modified, Landau-Lifshitz-Gilbert equations. The results for a simple pinning model are compared with experiment.
Barnes, S. E. and Maekawa, S., "Current-Spin Coupling for Ferromagnetic Domain Walls in Fine Wires" (2005). Physics Articles and Papers. 79.