Dynamics of domain walls in a cylindrical amorphous ferromagnetic microwire with magnetic inhomogeneities

We study the dynamics of a domain wall ($DW$) in the magnetic core of thin amorphous glass-coated bistable microwires with a circular cross section containing longitudinal inhomogeneities. We use a systematic analytic approach to the problem of finding particular solutions of the continuous Heisenberg model for which we use Landau–Lifshitz–Gilbert equations. We establish a relation between the structure of a material including defects and the DW mobility that explains some experimental data. For a given defect distribution in the longitudinal direction, we study the influence of defects on DW propagation in bistable glass-coated microwires. We obtain new key formulas for the DW velocity and acceleration based on taking the average defect distribution into account.