Resonant x-ray diffraction: multipole interpretation

The aim of this work is to provide a critical review of the multipole interpretation of resonant x-ray diffraction. After a brief historical introduction, we focus on the general formalism of electromagnetic multipole expansion in condensed matter. We then introduce the anomalous scattering amplitude from perturbation theory in the low-energy limit of the Dirac Hamiltonian. Finally, we merge the two previous sections by showing how the anomalous scattering amplitude can be interpreted in terms of electric and magnetic multipoles. Some examples are then discussed, concerning the electric quadrupole in manganites, 'exotic' polar and axial toroidal multipoles in transition-metal oxides and polarization analysis allowing the disentanglement of nearby-lying multipoles in the energy spectrum.