Message-passing neural network for magnetic phase transition simulation

Predicting magnetic phase transitions traditionally relies on a Hamiltonian model to capture key magnetic interactions. Recent advances in machine learning enables the development of a unified approach that can handle diverse magnetic systems without designing new Hamiltonians for each case. To this end, we employ message-passing neural network (MPNN) potentials to investigate magnetic phase transitions of two-dimensional chromium trihalidesCrX3(X = I, Br, Cl) . We achieve this by introducing a specialized MPNN with the ability to incorporate the magnetic degrees of freedom. This magnetic MPNN incorporates atomic magnetic moments directly into the message-passing process, enabling accurate modeling of potential energy surfaces in magnetic materials. This approach improves on our previous work, which had the same aim but used Behler-Parrinello neural network that relies on hand-crafted descriptors as the underlying universal magnetic Hamiltonian. It also adds the capability to treat magnetic degrees of freedom and atom displacement in a unified way. Using two-dimensionalCrX3as examples and combining the MPNN with the Landau-Lifshitz-Gilbert equation, we simulate ferromagnetic and antiferromagnetic phase transitions as a function of temperature. These results highlight the potential of MPNNs for advancing research in magnetic materials.