Unsupervised machine learning for the detection of exotic phases in skyrmion phase diagrams

Undoubtedly, machine learning (ML) techniques are being increasingly applied to a wide range of situations in the field of condensed matter. Amongst these techniques, unsupervised techniques are especially atractive, since they imply the possibility of extracting information from the data without previous labeling. In this work, we resort to the technique known as “anomaly detection” to explore potential exotic phases in skyrmion phase diagrams, using two different algorithms: Principal Component Analysis (PCA) and a Convolutional Autoencoder (CAE). First, we train these algorithms with an artificial dataset of skyrmion lattices constructed from an analytical parametrization, fordifferent magnetizations, skyrmion lattice orientations, and skyrmion radii. We apply the trained algorithms to a set of snapshots obtained from Monte Carlo simulations for three ferromagnetic skyrmion models: two including in-plane Dzyaloshinskii-Moriya interaction (DMI) in the triangular and kagome lattices, and one with an additional out-of-plane DMI in the kagome lattice. Then, we compare the root mean square error (RMSE) and the binary cross entropy (BCE) between the input and output snapshots as a function of the external magnetic field and temperature. We find that the RMSE error and its variance in the CAE case may be useful to not only detect exotic low temperature phases, but also to differentiate between the characteristic low temperature orderingsof a skyrmion phase diagram (helical, skyrmions and ferromagetic order). Moreover, we apply the skyrmion trained CAE to two antiferromagnetic models in the triangular lattice, one that gives rise to antiferromagnetic skyrmions, and the pure exchange antiferromagnetic case, finding that thebehaviour of the RMSE is still an indicator of different ordering. Finally, we explore the portability of the technique with the same CAE applying it to a ferromagnetic skyrmion model in the square lattice.