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 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 exhibits 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 and enables p-bit-like functionality in racetrack systems, offering a pathway toward hardware implementations of probabilistic and neuromorphic computing.