Approximate analytic expression for the Skyrmions crystal

TL;DR

This paper develops an approximate analytical model for two-dimensional magnetic Skyrmion lattices in the non-linear sigma model with Dzyaloshinskii-Moriya interaction, matching known numerical and experimental phenomenology.

Contribution

It introduces a novel analytic construction for Skyrmion solutions, bridging different spatial regions, and reproduces the phase behavior observed in simulations and experiments.

Findings

Reproduces Skyrmion lattice phenomenology

Identifies phase transitions between spiral, Skyrmion, and ferromagnetic states

Provides an analytic approximation consistent with numerical results

Abstract

We find approximate solutions for the two-dimensional non-linear {\Sigma}-model with Dzyalioshinkii-Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and ferromagnetic phases for low and high magnetic field respectively.