Emergence of Lissajous trajectories in skyrmion oscillator

TL;DR

This study demonstrates that skyrmions driven by AC currents in a thin film can form Lissajous trajectories, behaving like forced oscillators, with their paths affected by temperature-induced fluctuations.

Contribution

It reveals the emergence of Lissajous trajectories in skyrmion motion under AC currents and analyzes temperature effects on their dynamics.

Findings

Skyrmions follow sinusoidal current pulses as forced oscillators.

Lissajous figures form in the x-y plane under combined AC currents.

Temperature causes deviations and deformations in skyrmion trajectories.

Abstract

Understanding the dynamics of current-driven skyrmion is essential for their practical applications. In this study, we apply an AC current pulse (a) in x-- direction, and (b) in both x-- and y-- directions through the free layer of a Co/Pt thin film and investigate the motion of the skyrmion. We show that the skyrmion follows the sinusoidal current pulse and behaves like a forced oscillator in the range of current amplitude 1 $\times$ 10$^{11}$ A/m$^2$ to 1 $\times$ 10$^{12}$ A/m$^2$ and frequency 5 $\times$ 10$^{8}$ Hz to 1 $\times$ 10$^{10}$ Hz. For current pulse of (A$_1$sin$\omega_1$t, A$_2$sin($\omega_2$t+$\phi$), 0), the skyrmion forms Lissajous figures in the x-y plane, same as observed in classical mechanics. The results are compared at T = 0 K and T $>$ 0 K to analyze the effect of temperature. As the skyrmion Hall angle ($\theta_{SkH}$) and stochastic thermal fluctuation ($\textbf{F}^{Th}$) are functions of temperature, the skyrmion starts deviating from its path at T = 0 K with increasing temperature and eventually generates somewhat deformed Lissajous figures from ideal.