Direct Observation of Charge Order and an Orbital Glass State in Multiferroic LuFe2O4

Geometrical frustration of the Fe ions in LuFe2O4 leads to intricate charge and magnetic order and a strong magnetoelectric coupling. Using resonant x-ray diffraction at the Fe K edge, the anomalous scattering factors of both Fe sites are deduced from the (h/3 k/3 l/2) reflections. The chemical shift between the two types of Fe ions equals 4.0(1) eV corresponding to full charge separation into Fe2+ and Fe3+. The polarization and azimuthal angle dependence of the superlattice reflections demonstrate the absence of differences in anisotropic scattering revealing random orientations of the Fe2+ orbitals characteristic of an orbital glass state.