Abstract
We report experimental and theoretical results on the Fe K edge x-ray absorption spectrum and $1s2p$ resonant inelastic x-ray scattering (RIXS) spectra in $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}.$ The results are interpreted using an ${\mathrm{FeO}}_{6}^{9\ensuremath{-}}$ cluster model with intra-atomic multiplet coupling and interatomic covalency hybridization. The $1s2p$ RIXS is treated as a coherent second-order optical process. It is shown that the double-peak structure in the pre-edge region of Fe K absorption spectrum is due to the cubic crystal-field splitting, and that the intensity of the ${e}_{g} {(t}_{2g})$ component in the $1s2p$ resonant inelastic spectrum is enhanced by tuning the incident photon energy to the ${e}_{g} {(t}_{2g})$ component in the absorption spectrum.
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