Electronic structure of charge-orderedFe3O4from calculated optical, magneto-optical Kerr effect, and OK-edge x-ray absorption spectra

The electronic structure of the low-temperature (LT) monoclinic magnetite ${\mathrm{Fe}}_3{\mathrm{O}}_4$ is investigated using the local spin density approximation (LSDA) and the $\mathrm{LSDA}+U$ method. The self-consistent charge-ordered $\mathrm{LSDA}+U$ solution has a pronounced [001] charge density wave character. In addition, a minor $\left[00\frac{1}{2}\right]$ modulation in the phase of the charge order (CO) also occurs. While the existence of CO is evidenced by the large difference between the occupancies of the minority spin $t_{2g}$ states of “$2+$” and “$3+$” ${\mathrm{Fe}}_B$ cations, the total $3d$ charge disproportion is small, in accord with the valence-bond-sum analysis of structural data. Weak Fe orbital moments of $\sim 0.07{\mu }_{\mathrm{B}}$ are obtained from relativistic calculations for the CO phase which is in good agreement with recent x-ray magnetic circular dichroism measurements. Optical, magneto-optical Kerr effect, and O $K$-edge x-ray absorption spectra calculated for the charge-ordered $\mathrm{LSDA}+U$ solution are compared to corresponding LSDA spectra and to available experimental data. The reasonably good agreement between the theoretical and experimental spectra supports the relevance of the CO solution obtained for the monoclinic LT phase. The results of calculations of effective exchange coupling constants between Fe spin magnetic moments are also presented.