Starting from the stochastic Landau-Lifschitz-Gilbert equation, we derive Langevin equations that describe the nonzero-temperature dynamics of a rigid domain wall. We derive an expression for the average drift velocity of the domain wall as a function of the applied current, and find qualitative agreement with recent magnetic semiconductor experiments. Our model implies that at any nonzero temperature the average domain-wall velocity initially varies linearly with current, even in the absence of non-adiabatic spin torques.
@article{arxiv.cond-mat/0607663,
title = {Thermally-Assisted Current-Driven Domain Wall Motion},
author = {R. A. Duine and A. S. Nunez and A. H. MacDonald},
journal= {arXiv preprint arXiv:cond-mat/0607663},
year = {2009}
}