X-ray resonant scattering of(004n+2)forbidden reflections in spinel ferrites

The origin of the x-ray resonant scattering of (002) and (006) forbidden reflections in the spinel ferrites has been investigated. Resonant features were previously observed in ${\mathrm{Fe}}_3{\mathrm{O}}_4$ at the pre-edge and main-edge energies of the $\mathrm{Fe}K$-absorption edge. They were ascribed to dipole–quadrupole and dipole transitions at the tetrahedral and pseudo-octahedral Fe ions, respectively. To corroborate this origin and to differentiate between effects at the different metal sites, we have studied the energy and azimuthal dependencies of these reflections at the Fe, Co, and $\mathrm{Mn}K$ edges in $\mathrm{Mn}{\mathrm{Fe}}_2{\mathrm{O}}_4$ and $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$ spinels. ${\mathrm{Mn}}^{2+}$ mainly replaces Fe in the tetrahedral site whereas ${\mathrm{Co}}^{2+}$ occupies the octahedral site. No pre-edge peak is observed either at the $\mathrm{Fe}K$-edge in $\mathrm{Mn}{\mathrm{Fe}}_2{\mathrm{O}}_4$ or at the $\mathrm{Co}K$ edge in $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$. On the other hand, the peak at the absorption edge and the oscillations at energies beyond the edge are observed at the $\mathrm{Fe}K$ edge in $\mathrm{Mn}{\mathrm{Fe}}_2{\mathrm{O}}_4$ and $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$ and at the $\mathrm{Co}K$ edge in $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$. Therefore, the pre-edge peak comes from the metal ions at the tetrahedral site while the main-edge peak arises from the metal ions at the pseudo-octahedral site of the spinel structure. The azimuthal dependence and the energy line shape confirm the dipole–quadrupole and dipole characters of these pre-edge and main-edge resonances, respectively. The energy-dependence spectra of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ above and below the Néel temperature are alike, discarding any magnetic effect on the resonant spectra. Finally, the fine structure at energies beyond the absorption edge has been theoretically simulated considering only the local anisotropy of the dipolar atomic scattering factor of the pseudo-octahedral metal atom. These results demonstrate that $(004n+2)$ resonant reflections arise from the anisotropy of the local structure around the transition-metal atom without contributions of charge or $d$-orbital ordering.