Magnetic circular dichroism in Fe2presonant photoemission of magnetite

Measurements of magnetic circular dichroism in Fe $2p$ resonant photoemission and calculations based on a full-multiplet cluster model reveal the parameters of the electronic structure of ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}.$ We obtained on-site Coulomb energy ${U}_{\mathrm{dd}}$ of $3d$ electrons, charge-transfer energy $\ensuremath{\Delta}$ which is defined as the energy required to transfer an electron from O $2p$ to Fe $3d,$ and the hybridization strength between Fe $3d$ and O $2p$ at different Fe ion sites of ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ by analyzing the data of magnetic circular dichroism. The charge-transfer energy of ${\mathrm{Fe}}^{3+}$ ions was found to be significantly smaller than that of ${\mathrm{Fe}}^{2+}$ ions. We determined the energy positions of the low-lying multiplets of each Fe ion site. These energy positions for ${\mathrm{Fe}}^{3+}$ ion sites are 1.5\char21{}2.5 eV higher than those obtained from band-structure calculations. Our calculations also show that the photoemission spectral weight in binding energy bigger than 10 eV is substantial, in contrast to the results of band-structure calculations. Our findings conclude that ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ is a system with strong electron-electron interactions.