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-perpendicular to/V-parallel to of the skyrmion velocity perpendicular (V-perpendicular to) and parallel (V-parallel to) 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. We show that the changes in the skyrmion Hall effect correlate with changes in the power spectrum of the skyrmion velocity noise fluctuations. The plastic flow regime is associated with 1 / f noise, while in the regime in which R has saturated, the noise is white with a weak narrow band signal, and the noise power drops by several orders of magnitude. At low drives, the velocity noise in the perpendicular and parallel directions is of the same order of magnitude, while at intermediate drives the perpendicular noise fluctuations are much larger.