  The understanding of the dynamical properties of skyrmion is a fundamental
aspect for the realization of a competitive skyrmion based technology beyond
CMOS. 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 non-stationary 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 work, we show that, in an ideal
sample, the combined effect of field-like and damping-like 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
propose an experiment to validate our findings.
