Massive Monte Carlo simulations-guided interpretable learning of two-dimensional Curie temperature

Monte Carlo (MC) simulation of the classical Heisenberg model has become the de facto tool to estimate the Curie temperature (TC) of two-dimensional (2D) magnets. As an alternative, here we develop data-driven models for the five most common crystal types, considering the isotropic and anisotropic exchange of up to four nearest neighbors and the single-ion anisotropy. We sample the 20-dimensional Heisenberg spin Hamiltonian and conceive a bisection-based MC technique to simulate a quarter of a million materials for training deep neural networks, which yield testing R-2 scores of nearly 0.99. Since 2D magnetism has a natural tendency toward low T-C, learning-from-data is combined with data-from-learning to ensure a nearly uniform final data distribution over a wide range of T-C (10-1,000 K). Global and local analysis of the features confirms the models' interpretability. We also demonstrate that the TC can be accurately estimated by a purely first-principles-based approach, free from any empirical corrections.