Magnetic phase transition in a machine trained spin model: A study of hexagonal CrN monolayer

By employing the combination of non-collinear density functional theory, artificial neural network, and classical Monte Carlo simulation we study the ferromagnetic phase transition in CrN monolayers. The artificial neural network is successfully trained from different spin alignments to reproduce interaction energy at the DFT level in two dimensions. The training is performed solely based on spin spatial angles and second-order interactions energy without any speculation for the shape of spin Hamiltonian. The neural network model predicts the angle-dependent spin energy and mimics the magnetic anisotropy energy. The neural network is then validated for a larger supercell size against density functional theory results. Finally, the trained neural network spin model is used to study the finite temperature magnetization and phase transition in the two-dimensional CrN monolayer. The Curie temperature of the CrN monolayer is estimated equal to 600 K from the temperature-dependent magnetization and specific heat.