Relativistic Theory of Magnetic X-ray Scattering

We present a description of a first-principles formalism for the scattering of circularly polarised X-rays within the framework of relativistic density functional theory (DFT). The scattering amplitudes are calculated using standard time-dependent perturbation theory to second order in the electron-photon interaction vertex. An implementation of the theory based on relativistic spin-polarised multiple-scattering theory is discussed. This method is relatively easy to implement, but has a limited range of applicability. We suggest that an implementation using the self-interaction corrections to DFT may make the theory applicable to rare-earth materials where many of the key experiments have been performed. The theory is illustrated with appropriate examples.