Deterministic approach to skyrmionic dynamics at nonzero temperatures: Pinning sites and racetracks

The discovery of room-temperature skyrmions in some magnetic materials has boosted the investigation of their dynamics in view of future applications. We study the dynamics of skyrmions in the presence of defects or borders using a deterministic (finding and solving a deterministic Fokker-Planck differential equation) while probabilistic (the solution is the probability density for the presence of a skyrmion) approach. The probability that a skyrmion becomes trapped in a pinning center or the probability of the survival of a skyrmion along a racetrack are obtained as a function of temperature. The present work can be relevant in the design of skyrmionic devices where the probability of finding skyrmions at a given position and time is crucial for their feasibility.