The Drift of Magnetic Vortices in a Random Field of Anchoring Centers

This article theoretically solves the problem of the thermally activated motion of gas of non-interacting magnetic vortices/skyrmions in the field of defects located randomly, i.e., anchoring centers. The properties of the anchoring centers can also fluctuate. The factor that drives the gas of quasiparticles can be of any physical nature (fields, currents, gradients of the magnetic characteristics of the magnet, and so on). The process of vortices motion is described as a sequence of thermally activated separation of vortices from the attracting centers. The cases of some model distribution functions of the energy barriers are considered: 1) the barriers are of the same height; 2) the heights of the barriers are distributed evenly; and 3) the heights are distributed according to the normal law. Within these models, analytical expressions for the drift velocity and the diffusion gas coefficient of quasiparticles are obtained.