Magnetic phase transition of monolayer chromium trihalides investigated with machine learning: toward a universal magnetic Hamiltonian.

The prediction of magnetic phase transitions often requires model Hamiltonians to describe the necessary magnetic interactions. The advance of machine learning provides an opportunity to build a unified approach that can treat various magnetic systems without proposing new model Hamiltonians. Here, we develop such an approach by proposing a novel set of descriptors that describes the magnetic interactions and training the artificial neural network (ANN) that plays the role of a universal magnetic Hamiltonian. We then employ this approach and Monte Carlo simulation to investigate the magnetic phase transition of two-dimensional monolayer chromium trihalides using the trained ANNs as energy calculator. We show that the machine-learning-based approach shows advantages over traditional methods in the investigation of ferromagnetic and antiferromagnetic phase transitions, demonstrating its potential for other magnetic systems.