Statistics of irreversible displacements of domain walls in nanowires

The process of quasistatic displacement of domain walls is considered in a nanowire represented as a one-dimensional chain of ferromagnet crystallites. The domain wall pinning due to spatial fluctuations of the anisotropy axes is analyzed. Based on the theory of overshoots of random processes, we have calculated the distribution functions of the initial susceptibility and of the maximal force of interaction of the domain wall with inhomogeneities. These functions are found to be non-Gaussian. We have derived expressions for the magnetization curve and the coercive force, which depend on the length of the chain