Final-state effects in the $3d$ photoelectron spectrum of ${\mathrm{Fe}}_3$${\mathrm{O}}_4$ and comparison with ${\mathrm{Fe}}_x\mathrm{O}$

Photoelectron-spin-polarization measurements with photon energies up to 11 eV on ${\mathrm{Fe}}_3$ ${\mathrm{O}}_4$ and energy distribution curves in the photon energy range $5<h\nu <90\mathrm{}$ eV on magnetite ${\mathrm{Fe}}_3$ ${\mathrm{O}}_4$ and wustite (FeO) are interpreted in terms of the atomic theory of the single-ion-in-a-crystal-field model. The combination of the two different experiments yields the shapes and positions of the filled oxygen $2p$ bands and the $3d^{n-1\mathrm{}}$ final states of Fe ions with a reliability previously not attained. The $3d^{n-1\mathrm{}}$-multiplet structure of ${\mathrm{Fe}}_3$ ${\mathrm{O}}_4$ can be explained with the following set of parameters: $10Dq=1.75\mathrm{}$ eV and the Racah parameter $B=645\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ for ${\mathrm{Fe}}^{3+}$ left behind in $B$ lattice sites; $10Dq=1.55\mathrm{}$ eV for ${\mathrm{Fe}}^{4+}$ in $A$ sites. The difference in threshold for photoionization of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ in $B$ sites is 1.0 eV. The oxygen $2p$ emission is found to be centered at 7.3 eV below the Fermi level with a full width of 3 eV at half-maximum. The $3d$-multiplet structure of ${\mathrm{Fe}}_x\mathrm{O}$ can be explained with $10Dq=1.7\mathrm{}\pm 0.1$ eV and $B=800\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$.