Field-Driven Brownian Motion of Magnetic Domain Walls

The dynamics of a magnetic domain wall (DW) in a wire is studied. The DW is modeled as a Brownian particle subjected to thermal fluctuations and is characterized by the mass, position and velocity. Its motion is damped by friction, pinned by the irregularities in the material and driven by a constant force due to the external magnetic field. We have obtained the corresponding Langevin equation that contains a white-noise force. The use of an effective method taken from the statistical physics allowed us to convert this stochastic equation into an ordinary differential equation. From its solution the mean square displacement of the DW with other relevant time correlation functions and their spectral densities have been found. The electric current induced by the moving DW is also calculated.