First-Principles Calculations of Magnetite (Fe 3 O 4 ) 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 Fe 3 O 4 above the Verwey temperature ( T v ). 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 Fe oct and Fe tet 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 Fe 3 O 4 compared to approximate DFT and DFT + U . In this context, DFT + U + V supports the half-metallic character of the bulk crystal Fe 3 O 4 above T v , since the Fermi level is found in the t 2g band with a Fe oct down-spin. Thus, the observations in the current study emphasize the significance of intersite interactions in the theoretical analysis of Fe 3 O 4 above the T v .