Parameterization of dilute Ising model for iron-containing lanthanum gallate and aluminate solid solutions based on first-principles calculations

Abstract

Calculations of the cubic models of two solid solutions LaGa0.5Fe0.5O3 and LaAl0.5Fe0.5O3 have been performed within the hybrid density functional theory. Multiple configurations have been considered for the solid solutions resulting from a different distribution of Fe atoms over the p-metal (Ga or Al) positions accounting for different spin orientation for Fe atoms themselves. It was demonstrated that 27 structures for both LaGa0.5Fe0.5O3 and LaAl0.5Fe0.5O3 should be treated to account for all the possible configurations in case of cubic 2 × 2 × 2 supercell. Optimized geometry, energy, and electron properties were calculated for all the obtained configurations. Statistical weights and probabilities were estimated for each symmetry non-equivalent configuration of the solid solutions within the canonical ensemble. A new parameterization for the dilute Ising model has been proposed. In this model, we account for non-magnetic contributions, which are absent in the simple Ising model, using the lattice approach based on the concept of interchange energy. Two model parameters (the magnetic coupling constant and interchange energy) were fitted to the calculated total energies of all considered configurations of both solid solutions. The dilute Ising model confirmed the benefit of Fe-clustering in doped lanthanum gallate against aluminate. Different signs of the estimated interchange energy enable us to explain the reasons for such differences.