Direct observation of charge order and an orbital glass state in multiferroic LuFe₂O₄

Abstract

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.