First-Principles Calculations of Magnetite (Fe3O4) above the Verwey Temperature by Using Self-Consistent DFT + U + V

In this report, we have used the DFT + U + V approach, an extension of the DFT + U approach that takes into account both on-site and intersite interactions, to simulate structural, magnetic, and electronic properties together with the Fe and O K-edge XAS spectra of Fe3O4 above the Verwey temperature (Tv). Moreover, we compared the simulated XAS spectra with experimental XAS data. We examined both orthogonalized and nonorthogonalized atomic orbital projectors and compared DFT + U + V to DFT, DFT + U, and HSE as a hybrid functional. It is noteworthy that, despite the widespread use of the same Hubbard U value for Feoct and Fetet at the DFT + U level in the literature, the HP code identified two distinct values for them using the Hubbard approaches (DFT + U and DFT + U + V). The resulting Hubbard U and V parameters are strongly dependent on the chosen orbital projectors. This study demonstrates how DFT + U + V can improve the structural, magnetic, and electronic properties of Fe3O4 compared to approximate DFT and DFT + U. In this context, DFT + U + V supports the half-metallic character of the bulk crystal Fe3O4 above Tv, since the Fermi level is found in the t2g band with a Feoct down-spin. Thus, the observations in the current study emphasize the significance of intersite interactions in the theoretical analysis of Fe3O4 above the Tv.