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 (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 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 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 Fe₃O₄ above the T_v.