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

TL;DR

This paper studies how line-edge roughness affects the stochastic behavior of domain walls in ferromagnetic racetracks, revealing that even minimal roughness causes significant pinning and complex dynamics without thermal effects.

Contribution

It models edge disorder as a correlated process and uncovers how roughness induces stochastic pinning and nonlinear domain wall dynamics, informing probabilistic computing applications.

Findings

Minimal roughness causes pronounced stochastic pinning.

Domain wall velocity shows nonlinear dependence on time and current.

Displacement exhibits ballistic regime followed by saturation due to pinning.

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.