Frenkel pair formation energy for cubic Fe₃O₄in DFT + U calculations

The cubic phase of magnetite is stabilized above the Verwey transition temperature of about 120 K via a complex electron-phonon interaction that is still not very well understood. In this work using the DFT + U method we describe our attempt to calculate point defect formation energies for this cubic phase in the static approximation. The electronic structure calculations and atomic relaxation peculiarities are discussed in this context. Only the cubic phase model with a small band gap and charge disproportionation (Fe²⁺/Fe³⁺) gives an adequate point defect formation energies, not the semi-metallic model. The relaxation of the local defect atomic structure and the relaxation of the surrounding crystal matrix are analyzed. Point defects cause only local perturbations of atomic positions and charge-orbital order. After analysis of the supercell size effects for up to 448 atoms, we justify the use of small supercells with 56 atoms to make calculations for the cubic phase. The extensive experimental results of Dieckmannet alon defects in magnetite at high temperature are deployed for comparison of our DFT + U results on Frenkel pair formation energies.