Stochastic Dynamics of Domain Wall on a Racetrack: Impact of Line‐Edge Roughness

Abstract

We investigate the impact of line‐edge roughness on current‐driven domain wall dynamics in ferromagnetic racetracks. Modeling the edge disorder as a spatially correlated Ornstein–Uhlenbeck process, we demonstrate that even minimal experimentally relevant roughness induces pronounced stochastic pinning of domain walls. Notably, this stochasticity of the current‐driven motion arises purely from spatial disorder, even in the absence of thermal fluctuations. The racetrack‐to‐racetrack probability of a domain wall to reach a given position exhibits a robust sigmoidal dependence on the applied current, reflecting an effective distribution of depinning thresholds. At the same time, the underlying dynamics is highly nontrivial: The mean velocity shows a nonlinear dependence on both time and current, while the mean‐square displacement exhibits a ballistic regime at short times followed by saturation due to trapping at pinning sites. These results demonstrate that line‐edge roughness provides a controllable source of stochasticity in racetrack systems, establishing a physical mechanism for probabilistic domain‐wall dynamics with potential applications in racetrack‐based p‐bit concepts, event‐driven, and neuromorphic computing.