Resonant x-ray Bragg diffraction from orbital moments in vanadium sesquioxide(V2O3) and haematite (α -Fe2O3)

Abstract

Resonant x-ray diffraction from V2O3 which has been observed at charge-forbidden reflections (h + k + l odd) is here attributed to orbital moments of the vanadium ion. Furthermore, it is argued that the contribution to intensity as a function of x-ray energy seen in the experiment on the low energy side of the electric dipole (E1) resonance is due to an electric quadrupole (E2) resonance. The absence of the E1 resonance for h odd, and appearance of the E2 resonance at h odd and h even is accounted for in the calculated structure factor. For h odd the structure factor is proportional to the octupole moment of the vanadium ion, which is estimated to have a magnitude similar to that of the orbital angular momentum. In the case of E2 resonant x-ray Bragg diffraction from haematite the calculated structure factor contains three orbital moments, two of odd rank and one of even rank. The calculated polarization dependence and azimuthal-angle scans are in complete accord with experimental findings. The contribution of even and odd rank moments is shown to make scattering depend on circular polarization.