Spin-dependent optical charge transfer in magnetite from transmitting optical magnetic circular dichroism

In this study, we demonstrate that optical magnetic circular dichroism (OMCD) in Faraday geometry can serve as an effective means of characterizing the valence electronic structure of magnetic oxide systems. Molecular-beam-epitaxy-grown magnetite thin film single crystals served as the test sample. The dominant spin channels of optical charge transfer were resolved from transmitting OMCD spectra, which can only be interpreted by considering electron correlation effects and including polarized $2p$ oxygen. First-principles calculations based on density-functional theory with Hubbard-$U$ correction ($\mathrm{DFT}+U$) were performed on cubic inverse spinel ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ ($\mathrm{F}d\overline{3}m$). We determined that the main features of optical conductivity [S. K. Park et al., Phys. Rev. B 58, 3717 (1998)] were similar to those of a Mott-Hubbard insulator. According to the extent of $2p$ character in the mixed $\mathrm{Fe}(3d)\ensuremath{-}\mathrm{O}(2p$) valence that engendered the relaxation of Laporte selection, we classified dominant optical charge transfer into three categories: (1) intervalence spin-minority $d\ensuremath{-}d$ charge transfer relax from lattice distortion; (2) intersublattice $d\ensuremath{-}d$ charge transfer across the valence gap of spin majority; and (3) ligand-to-metal $p\ensuremath{-}d$ charge transfer across the valence gap of spin minority. We conclude that the transmitting OMCD spectrum can generally reflect the competition between optical transitions from the $B$-site $\mathrm{Fe}(3d$) spin majority and the $\mathrm{O}(2p$) spin minority. Finally, we found the OMCD signal of magnetite exhibited similar trend to the valence band spin polarization deduced from Mott spin polarimetry. Excitation spectrum that access the direct information about the ``bare'' electronic states from soft x-ray spin-resolved photoemission were also revisited.