# Supervised learning magnetic skyrmion phases

## TL;DR

This paper introduces simple machine learning methods, including neural networks and minimum distance classification, to identify and distinguish complex magnetic phases like skyrmions in two-dimensional materials, aiding experimental and theoretical analysis.

## Contribution

It presents novel, easy-to-implement machine learning approaches for classifying magnetic phases, including transferability across different lattice models.

## Key findings

- Neural network accurately classifies magnetic phases from limited data.
- Minimum distance method provides fast, reliable phase assignment.
- Methods are applicable to experimental data analysis.

## Abstract

We propose and apply simple machine learning approaches for recognition and classification of complex non-collinear magnetic structures in two-dimensional materials. The first approach is based on the implementation of the single-hidden-layer neural network that only relies on the z projections of the spins. In this setup one needs a limited set of magnetic configurations to distinguish ferromag- netic, skyrmion and spin spiral phases, as well as their different combinations in transitional areas of the phase diagram. The network trained on the configurations for square-lattice Heisenberg model with Dzyaloshinskii-Moriya interaction can classify the magnetic structures obtained from Monte Carlo calculations for triangular lattice and vice versa. The second approach we apply, a minimum distance method performs a fast and cheap classification in cases when a particular configuration is to be assigned to only one magnetic phase. The methods we propose are also easy to use for analysis of the numerous experimental data collected with spin-polarized scanning tunneling microscopy and Lorentz transmission electron microscopy experiments.