Full phase diagram of isolated skyrmions in a ferromagnet

TL;DR

This paper develops a comprehensive theoretical framework for understanding isolated skyrmions in ferromagnets, accurately matching experimental data and revealing new phases like bi-stability, thus advancing skyrmion research and engineering.

Contribution

It introduces a novel, precise model for skyrmion energy that applies to various materials and sizes, enabling complete phase diagram mapping and inverse material design.

Findings

No topological protection of skyrmions is proven.

Discovery of bi-stability phase in skyrmions.

Complete phase diagram of static skyrmions obtained.

Abstract

Magnetic skyrmions are topological quasi particles of great interest for data storage applications because of their small size, high stability, and ease of manipulation via electric current. Theoretically, however, skyrmions are poorly understood since existing theories are not applicable to small skyrmion sizes and finite material thicknesses. Here, we present a complete theoretical framework to determine the energy of any skyrmion in any material, assuming only a circular symmetric 360$^\circ$ domain wall profile and a homogeneous magnetization profile in the out-of-plane direction. Our model precisely agrees with existing experimental data and micromagnetic simulations. Surprisingly, we can prove that there is no topological protection of skyrmions. We discover and confirm new phases, such as bi-stability, a phenomenon unknown in magnetism so far. The outstanding computational performance and precision of our model allow us to obtain the complete phase diagram of static skyrmions and to tackle the inverse problem of finding materials corresponding to given skyrmion properties, a milestone of skyrmion engineering.