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

Abstract

In this report, we have used the DFT + <i>U</i> + <i>V</i> approach, an extension of the DFT + <i>U</i> 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 (<i>T</i>_v). Moreover, we compared the simulated XAS spectra with experimental XAS data. We examined both orthogonalized and nonorthogonalized atomic orbital projectors and compared DFT + <i>U</i> + <i>V</i> to DFT, DFT + <i>U</i>, and HSE as a hybrid functional. It is noteworthy that, despite the widespread use of the same Hubbard <i>U</i> value for Fe_oct and Fe_tet at the DFT + <i>U</i> level in the literature, the HP code identified two distinct values for them using the Hubbard approaches (DFT + <i>U</i> and DFT + <i>U</i> + <i>V</i>). The resulting Hubbard <i>U</i> and <i>V</i> parameters are strongly dependent on the chosen orbital projectors. This study demonstrates how DFT + <i>U</i> + <i>V</i> can improve the structural, magnetic, and electronic properties of Fe₃O₄ compared to approximate DFT and DFT + <i>U</i>. In this context, DFT + <i>U</i> + <i>V</i> supports the half-metallic character of the bulk crystal Fe₃O₄ above <i>T</i>_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 <i>T</i>_v.