The optical and magneto-optical spectra of charge-ordered magnetite $\left({\mathrm{Fe}}_3{\mathrm{O}}_4\right)$ below the Verwey transition and ${\mathrm{Mg}}^{2+}$- and ${\mathrm{Al}}^{3+}$-substituted ${\mathrm{Fe}}_3{\mathrm{O}}_4$ are investigated theoretically from first principles, using the fully relativistic Dirac linear muffin-tin orbital band structure method. The electronic structure is obtained with the local spin-density approximation (LSDA), as well as with the so-called $\mathrm{LSDA}+U$ approach for which the charge ordering is found to be a stable solution with an energy gap value of 0.19 eV (the experimental value is 0.14 eV) in contrast to a metallic state given by LSDA. The origin of the Kerr rotation realized in the compounds is examined.

• Received 7 October 1999

DOI:https://doi.org/10.1103/PhysRevB.64.134410