X-ray scattering by rare-earth multipoles in multiaxial structures

The Thompson scattering of x-rays is a direct probe for the electronic charge distribution of atoms. It should then be useful for determining types of ordering which involve a periodical asphericity of the atoms inside a crystal. We focus on die case of the periodical multiaxial orientation of the 4f shells in a rare-earth compound. Using the Stevens equivalent-operator method, the formalism of the multipolar scattering is hem developed within the ground-state multiplet of the rare-earth ion. It allows one to consider proper 4f wave functions, accounting for the various interactions present in the system, and to calculate the quadrupolar, octupolar and dodecapolar contributions to the scattering. In order to validate this x-ray technique, we propose its application to compounds presenting magnetic orderings which coincide with multiaxial orbital arrangements.