Fluctuations of current-driven domain walls in the non-adiabatic regime

We outline a general framework to determine the effect of non-equilibrium fluctuations on driven collective coordinates, and apply it to a current-driven domain wall in a nanocontact. In this case the collective coordinates are the domain-wall position and its chirality, that give rise to momentum transfer and spin transfer, respectively. We determine the current-induced fluctuations corresponding to these processes and show that at small frequencies they can be incorporated by two separate effective temperatures. As an application, the average time to depin the domain wall is calculated and found to be lowered by current-induced fluctuations. It is shown that current-induced fluctuations play an important role for narrow domain walls, especially at low temperatures.