Orbital, spin, charge and geometric ordering as seen by resonant x-ray scattering spectroscopy

Yves Joly

Laboratoire de Cristallographie, CNRS, BP 166, 38042 Grenoble Cedex 9, France

The interplay among spin, charge, orbital and lattice degrees of freedom in transition-metal oxides has attracted considerable attention from condensed-matter physicists. In that context, the crystal and electronic structure of different prototypical compounds as LaMnO3, Fe3O4, V2O3 or NaV2O5 has been the subject of intensive theoretical and experimental studies over the last years. These compounds undergoe phase transitions at low temperature with important modifications of their magneto-electric properties. Among the different techniques applied to investigate these phenomena, resonant X-ray scattering (RXS) is supposed to be a powerful tool for extracting direct informations on magnetic, orbital and charge ordering. Nevertheless the ability of such a technique to separate the different contributions and thus to evaluate them quantitatively is subject of an intense debate. Indeed, the orbital ordering which is certainly present and at the basis of the interpretation of many properties of the transition metal oxides is associated with a Jahn-Teller distortion and in some cases also with a spin ordering. All these distortions have the same symmetry and thus induce the same kind of tensorial, or anisotropic, scattering factor. Only a quantitative analysis can separate the different phenomena. We demonstrate that for V2O3 the signal is essentially due to the magnetic ordering and not to the orbital ordering. For NaV2O5 and Fe3O4 we show that RXS is able to evaluate with a good precision the integrated charge ordering. For this purpose realistic calculations using the relativistic multiple scattering theory and the finite difference method with a tensorial approach of the structure factors are necessary.