Triple helix vs. skyrmion lattice in two-dimensional non-centrosymmetric magnets

TL;DR

This paper compares two theoretical models for describing skyrmion lattices in two-dimensional non-centrosymmetric magnets, finding that the stereographic projection approach is more accurate at high magnetic fields, especially near phase transitions.

Contribution

It introduces and compares a Belavin-Polyakov-like skyrmion lattice model with a deformed triple helix model, highlighting the conditions where each is more effective.

Findings

Models are nearly identical at zero temperature and intermediate fields.

Stereographic projection better describes disordered skyrmion phases at high fields.

Secondary Bragg peak intensities are estimated to be a few percent of the main peak.

Abstract

It is commonly assumed that a lattice of skyrmions, emerging in two-dimensional non-centrosymmetric magnets in external magnetic fields, can be represented as a sum of three magnetic helices. In order to test this assumption we compare two approaches to a description of regular skyrmion structure. We construct (i) a lattice of Belavin-Polyakov-like skyrmions within the stereographic projection method, and (ii) a deformed triple helix defined with the use of elliptic functions. The estimates for the energy density and magnetic profiles show that these two ansatzes are nearly identical at zero temperature for intermediate magnetic fields. However at higher magnetic fields, near the transition to topologically trivial uniform phase, the stereographic projection method is preferable, particularly, for the description of disordered skyrmion liquid phase. We suggest to explore the intensities of the secondary Bragg peaks to obtain the additional information about the magnetic profile of individual skyrmions. We estimate these intensities to be several percents of the main Bragg peak at high magnetic fields.