Unsupervised machine learning for the detection of exotic phases in skyrmion phase diagrams
arxiv(2024)
摘要
Undoubtedly, machine learning techniques are being increasingly applied to a
wide range of situations in the field of condensed matter. Amongst these
techniques, unsupervised techniques are especially attractive, 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 and Convolutional
Autoencoder (CAE). First, we train these algorithms with an artificial dataset
of skyrmion lattices constructed from an analytical parametrization, for
different 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 with in-plane
Dzyaloshinskii-Moriya (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 between the input and
output snapshots as a function of the external magnetic field and temperature.
We find that the RMSE 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 orderings of a skyrmion phase diagram
(helical, skyrmions and ferromagnetic). 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. Despite the predictably larger RMSE, we find that, even in these cases,
RMSE is also an indicator of different orderings and the emergence of
particular features, such as the well-known pseudo-plateau in the pure exchange
case.
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