Machine learning–enabled identification of material phase transitions based on experimental data: Exploring collective dynamics in ferroelectric relaxors

Exploration of phase transitions and construction of associated phase diagrams are of fundamental importance for condensed matter physics and materials science alike, and remain the focus of extensive research for both theoretical and experimental studies. For the latter, comprehensive studies involving scattering, thermodynamics, and modeling are typically required. We present a new approach to data mining multiple realizations of collective dynamics, measured through piezoelectric relaxation studies, to identify the onset of a structural phase transition in nanometer-scale volumes, that is, the probed volume of an atomic force microscope tip. Machine learning is used to analyze the multidimensional data sets describing relaxation to voltage and thermal stimuli, producing the temperature-bias phase diagram for a relaxor crystal without the need to measure (or know) the order parameter. The suitability of the approach to determine the phase diagram is shown with simulations based on a two-dimensional Ising model. These results indicate that machine learning approaches can be used to determine phase transitions in ferroelectrics, providing a general, statistically significant, and robust approach toward determining the presence of critical regimes and phase boundaries.