Noise fluctuations and drive dependence of the skyrmion Hall effect in disordered systems

Using a particle-based simulation model, we show that quenched disorder creates a drive-dependent skyrmion Hall effect as measured by the change in the ratio $R=V_{\perp}/V_{||}$ of the skyrmion velocity perpendicular ($V_{\perp}$) and parallel ($V_{||}$) to an external drive. $R$ is zero at depinning and increases linearly with increasing drive, in agreement with recent experimental observations. At sufficiently high drives where the skyrmions enter a free flow regime, $R$ saturates to the disorder-free limit. This behavior is robust for a wide range of disorder strengths and intrinsic Hall angle values, and occurs whenever plastic flow is present. For systems with small intrinsic Hall angles, we find that the Hall angle increases linearly with external drive, as also observed in experiment. In the weak pinning regime where the skyrmion lattice depins elastically, $R$ is nonlinear and the net direction of the skyrmion lattice motion can rotate as a function of external drive.