Degeneracies and fluctuations of N\'e\`el skyrmions in confined geometries

TL;DR

This study uses Monte Carlo simulations to explore the stability, phase transitions, and fluctuation effects of Ne9e9l skyrmions in confined magnetic geometries with tunable Dzyaloshinskii-Moriya interactions, highlighting their robustness and detection methods.

Contribution

It provides new insights into how confinement and fluctuations influence skyrmion phases and degeneracies in layered magnetic materials with perpendicular anisotropy.

Findings

Skyrmions are stable over a large phase diagram region in confined geometries.

Confinement favors skyrmions over spiral phases compared to infinite systems.

States with more skyrmions are favored by fluctuations during phase transitions.

Abstract

The recent discovery of tunable Dzyaloshinskii-Moriya interactions in layered magnetic materials with perpendicular magnetic anisotropy makes them promising candidates for stabilization and manipulation of skyrmions at elevated temperatures. In this article, we use Monte Carlo simulations to investigate the robustness of skyrmions in these materials against thermal fluctuations and finite-size effects. We find that in confined geometries and at finite temperatures skyrmions are present in a large part of the phase diagram. Moreover, we find that the confined geometry favors the skyrmion over the spiral phase when compared to infinitely large systems. Upon tuning the magnetic field through the skyrmion phase, the system undergoes a cascade of transitions in the magnetic structure through states of different number of skyrmions, elongated and half-skyrmions, and spiral states. We consider how quantum and thermal fluctuations lift the degeneracies that occur at these transitions, and find that states with more skyrmions are typically favored by fluctuations over states with less skyrmions. Finally, we comment on electrical detection of the various phases through the topological and anomalous Hall effects.