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

TL;DR

This paper investigates how thermal fluctuations and torques influence the skyrmion Hall angle in perpendicular ferromagnets, revealing a current-dependent behavior linked to skyrmion breathing modes, challenging the rigid skyrmion approximation.

Contribution

It demonstrates that thermal modes and combined torques can explain the current dependence of the skyrmion Hall angle, extending understanding beyond rigid skyrmion models.

Findings

Thermal modes can be excited, affecting skyrmion dynamics.

Combined field-like and damping-like torques induce current-dependent Hall angles.

Proposes an experiment to validate the thermal mode influence.

Abstract

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.