Constrained DFT-based magnetic machine-learning potentials for magnetic alloys: a case study of Fe–Al

Abstract

We propose a machine-learning interatomic potential for multi-component magnetic materials. In this potential we consider magnetic moments as degrees of freedom (features) along with atomic positions, atomic types, and lattice vectors. We create a training set with constrained DFT (cDFT) that allows us to calculate energies of confgurations with non-equilibrium (excited) magnetic moments and, thus, it is possible to construct the training set in a wide confguration space with great variety of non-equilibrium atomic positions, magnetic moments, and lattice vectors. Such a training set makes possible to ft reliable potentials that will allow us to predict properties of confgurations in the excited states (including the ones with non-equilibrium magnetic moments). We verify the trained potentials on the system of bcc Fe–Al with diferent concentrations of Al and Fe and diferent ways Al and Fe atoms occupy the supercell sites. Here, we show that the formation energies, the equilibrium lattice parameters, and the total magnetic moments of the unit cell for diferent Fe–Al structures calculated with machine-learning potentials are in good correspondence with the ones obtained with DFT. We also demonstrate that the theoretical calculations conducted in this study qualitatively reproduce the experimentally-observed anomalous volume-composition dependence in the Fe–Al system.