On the Simulation of the Brownian Motion of a Domain Wall in Nanowires

A method has been proposed for computer simulation of thermal fluctuation motion of domain walls in polycrystalline ferromagnetic nanowires with allowance for their interaction with a field of magnetic inhomogeneities. The algorithm includes the stochastic Langevin function and takes into account the term describing the random force relief of the pinning of a domain wall at magnetic inhomogeneities. The proposed algorithm has been used to obtain different statistical characteristics of the process of displacement of the domain walls: distributions of magnetization jumps, activation energies, depinning waiting times, and jump times. It has been shown that the Einstein-Smoluchowski relation is not applicable to the description of thermal fluctuation motion of a particle in a random force relief.