Simulation of the Brownian motion of the domain wall in a nonlinear force field of nanowires

The paper proposes a computer simulation method of the thermo-fluctuational motion of domain walls in ferromagnetic polycrystalline nanowires, taking into account a non-linear force field of magnetic inhomogeneities. The method makes use of stochastic Langevin function. Into the Langevin equation we added a member describing random force pattern of domain wall fixation on magnetic inhomogeneities. A variety of statistic characteristics of domain wall propagation process have been obtained: magnetization jumps distribution, activation energies distribution, distribution of magnetization switch waiting times and distribution of magnetization jump times. Paper shows that it is incorrect to apply Einstein-Smoluchowski equation for particle’s thermo-fluctuational motion in non-linear force field pattern