Resonant Exchange Scattering: Polarization Dependence and Correlation Function

The cross section for X-ray resonant exchange scattering is reformulated in terms of linear polarization states perpendicular and parallel to the scattering plane, a basis particularly well suited to synchrotron X-ray diffraction experiments. The explicit polarization dependence of the terms is calculated for the electric dipole and quadrupole contributions. This expression, in turn, is rewritten in an orthonormal basis to highlight the dependence of the cross section on each component of the magnetic moment. This has the benefit of providing an empirically useful expression for the cross section. Diffraction patterns from a few simple magnetic structures are calculated. Finally, the correlation function measured at each resonant harmonic is derived.