Machine learning techniques to construct detailed phase diagrams for skyrmion systems

Recently, there has been an increased interest in the application of machine learning (ML) techniques to a variety of problems in condensed-matter physics. In this regard, of particular significance is the characterization of simple and complex phases of matter. Here, we use a ML approach to construct the full phase diagram of a well-known spin model combining ferromagnetic exchange and Dzyaloshinskii-Moriya (DM) interactions where topological phases emerge. At low temperatures, the system is tuned from a spiral phase to a skyrmion crystal by a magnetic field. However, thermal fluctuations induce two types of intermediate phases, bimerons and skyrmion gas, which are not as easily determined as spirals or skyrmion crystals. We resort to large-scale Monte Carlo simulations to obtain low-temperature spin configurations and train a convolutional neural network (CNN), taking only snapshots at specific values of the DM couplings, to classify between the different phases, focusing on the intermediate and intricate topological textures. We then apply the CNN to higher-temperature configurations and to other DM values to construct a detailed magnetic-field--temperature phase diagram, achieving outstanding results. We discuss the importance of including the disordered paramagnetic phases in order to get the phase boundaries, and, finally, we compare our approach with other ML algorithms.