High-topological-number magnetic skyrmions and topologically protected dissipative structure

TL;DR

This paper demonstrates the creation and stabilization of magnetic skyrmions with topological number two ($Q=2$) as nonequilibrium, topologically protected dissipative structures driven by spin-polarized current, expanding understanding of complex magnetic topologies.

Contribution

It introduces the concept of $Q=2$ skyrmions as dynamic, topologically protected structures stabilized by current-induced energy balance, not static configurations.

Findings

$Q=2$ skyrmions can be created and stabilized by current.

They are topologically protected against fluctuations.

The nucleation and destruction mechanisms are elucidated.

Abstract

The magnetic skyrmion with the topological number of unity ($Q=1$) is a well-known nanometric swirling spin structure in the nonlinear $\sigma$ model with the Dzyaloshinskii-Moriya interaction. Here, we show that magnetic skyrmion with the topological number of two ($Q=2$) can be created and stabilized by applying vertical spin-polarized current though it cannot exist as a static stable excitation. Magnetic skyrmion with $Q=2$ is a nonequilibrium dynamic object, subsisting on a balance between the energy injection from the current and the energy dissipation by the Gilbert damping. Once it is created, it becomes a topologically protected object against fluctuations of various variables including the injected current itself. Hence, we may call it a topologically protected dissipative structure. We also elucidate the nucleation and destruction mechanisms of the magnetic skyrmion with $Q=2$ by studying the evolutions of the magnetization distribution, the topological charge density as well as the energy density. Our results will be useful for the study of the nontrivial topology of magnetic skyrmions with higher topological numbers.