Depinning of domain walls with an internal degree of freedom

Taking into account the coupling between the position of the wall and an internal degree of freedom, namely, its phase phi, we examine, in the rigid-wall approximation, the dynamics of a magnetic domain wall subject to a weak pinning potential. We determine the corresponding force-velocity characteristics, which display several unusual features when compared to the standard depinning behavior. At zero temperature, there exists a bistable regime for low forces, with a logarithmic behavior close to the transition. For weak pinning, there occurs a succession of bistable transitions corresponding to different topological modes of the phase evolution. At finite temperature, the force-velocity characteristics become nonmonotonous. We compare our results to recent experiments on permalloy nanowires.