Determination of the sequence and magnitude of charge order in LuFe2O4 by resonant x-ray scattering

We have investigated the low-temperature phases of LuFe2O4 by resonant x-ray scattering (RXS) at the Fe K edge to determine both the ordering sequence and magnitude of charge segregation. Two successive charge ordering (CO) phases have been detected. Resonant superlattice (1/3,1/3,l/2) reflections appear below the so-called CO phase at TCO ¿ 320 K. Additionally, resonant superlattice (1/3,1/3,l) reflections are observed below 240 K concurrent with the onset of the magnetic ordering. The ¿-¿¿ polarization dependence for all the measured superlattice reflections indicates the absence of local anisotropy of the electronic density at the Fe atom. The energy dependence of the resonant intensity for these reflections has been quantitatively analyzed following the monoclinic C2/m structure in the CO phase between 320 and 240 K and the triclinic P1¯ structure below 240 K. We find a four-modal charge segregation among the Fe atoms in the C2/m phase with formal valences Fe2.77+,Fe2.63+,Fe2.36+, and Fe2.22+ whereas the simplest charge distribution that explains successfully all the RXS data in the P1¯ phase is the trimodal Fe2.8+,Fe2.5+, and Fe2.2+. Both ordering models imply the lack of charge segregation along the c axis discarding a polar configuration and thus the occurrence of ferroelectricity.