A theory of skyrmion crystal formation

TL;DR

This paper develops a comprehensive theoretical framework for skyrmion crystal formation in chiral magnetic films, explaining various metastable states, thermodynamic behaviors, and the influence of parameters like Dzyaloshinskii-Moriya interaction strength.

Contribution

It introduces a generic theory that predicts multiple metastable states and explains skyrmion crystal formation and stability in relation to key parameters and external magnetic fields.

Findings

Multiple metastable states depend on skyrmion density and DMI strength.

Skyrmion crystals form around an optimal magnetic field when DMI is sufficiently strong.

Temperature-dependent DMI strength influences skyrmion metastability.

Abstract

A generic theory about skyrmion crystal (SkX) formation in chiral magnetic thin films and its fascinating thermodynamic behaviours is presented. A chiral magnetic film can have many metastable states with an arbitrary skyrmion density up to a maximal value when a parameter $\kappa$, which measures the relative Dzyaloshinskii-Moriya interaction (DMI) strength, is large enough. The lowest energy state of an infinite film is a long zig-zagged ramified stripe skyrmion occupied the whole film in the absence of a magnetic field. Under an intermediate field perpendicular to the film, the lowest energy state has a finite skyrmion density. This is why a chiral magnetic film is often in a stripy state at a low field and a SkX only around an optimal field when $\kappa$ is above a critical value. The lowest energy state is still a stripy helical state no matter with or without a field when $\kappa$ is below the critical value. The multi-metastable states explains the thermodynamic path dependences of various metastable states of a film. Decrease of $\kappa$ value with the temperature explains why SkXs become metastable at low temperature in many skyrmion systems. These findings open a new avenue for SkX manipulation and skyrmion-based applications.