Charge disproportion at octahedral Fe sites in magnetite was observed at low temperature using two inversion-symmetry related three-wave resonant x-ray diffraction, 022-311 and $002\mathrm{\text{−}}\overline{3}\overline{1}1$, near the iron $K$ edge. Both of the three-wave cases involve the (002) forbidden-weak reflection. The self-normalized three-wave to two-wave (002) diffraction intensity ratio automatically cancels the self-absorption effect and leads to direct determination of charge disproportion for magnetite below 120 K. This approach provides a more direct and effective way for extracting charge-ordering information.

• Received 12 May 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.146404