Micromagnetic understanding of the skyrmion Hall angle current dependence in perpendicular magnetized ferromagnets

The understanding of the dynamical properties of skyrmions is a fundamental aspect for the realization of a competitive skyrmion based technology beyond complementary metal-oxide semiconductors. Most of the theoretical approaches are based on the approximation of a rigid skyrmion. However, thermal fluctuations can drive a continuous change of the skyrmion size via the excitation of thermal modes. Here, by taking advantage of the Hilbert-Huang transform, we demonstrate that at least two thermal modes can be excited which are nonstationary in time. In addition, one limit of the rigid skyrmion approximation is that this hypothesis does not allow for correctly describing the recent experimental evidence of skyrmion Hall angle dependence on the amplitude of the driving force, which is proportional to the injected current. In this paper, we show that, in an ideal sample, the combined effect of fieldlike and dampinglike torques on a breathing skyrmion can indeed give rise to such a current dependent skyrmion Hall angle. While here we design and control the breathing mode of the skyrmion, our results can be linked to the experiments by considering that the thermal fluctuations and/or disorder can excite the breathing mode. We also develop a generalized Thiele equation and propose an experiment to validate our findings.