Supervised learning approach for recognizing magnetic skyrmion phases

Abstract

We propose and apply simple machine learning approaches for recognition and classification of complex noncollinear 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 ferromagnetic, 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 the square-lattice Heisenberg model with Dzyaloshinskii-Moriya interaction can classify the magnetic structures obtained from Monte Carlo calculations for a 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. © 2018 American Physical Society.