Topological quantization of the flow of magnetic skyrmions driven by a ratchet-like potential under thermal fluctuations

TL;DR

This paper demonstrates that magnetic skyrmion flow driven by a periodic, asymmetric current under thermal fluctuations exhibits topological quantization, linked to the Chern number, offering a robust method for skyrmion manipulation.

Contribution

It introduces a topological quantization framework for skyrmion flow under thermal fluctuations and asymmetric driving, supported by analytical and numerical evidence.

Findings

Skyrmion flow is quantized as an integer multiple of the ratio of space and time periods.

Quantization is associated with the Chern number, a topological invariant.

Thermal fluctuations below a threshold do not disrupt the quantized flow.

Abstract

We consider a magnetic skyrmion adiabatically driven by a spin-polarized electrical current periodic in both space and time and asymmetric in space, and also subject to a random magnetic field representing the thermal fluctuations. We show that when the random magnetic field is low enough, while the time variation of the driving current is slow enough, the skyrmion flow is an integer multiply of the ratio between the space and time periods, the integer being a topological invariant called Chern number. This result is also demonstrated by numerically solving the stochastic Landau-Lifshitz-Gilbert (sLLG) and Langevin equations. Our work suggests a novel method of manipulating skyrmions with topological stability.