Theory of magnetic circular dichroism of nonresonant x-ray Raman scattering

We develop a theory of magnetic circular dichroism (MCD) of hard x-ray Raman scattering (XRS) to analyze the MCD signal at iron L edge from pure ferromagnetic iron. The obtained formula of scattering amplitude has terms corresponding to the charge (Thomson) scattering process, and the orbital and spin scattering processes in the elastic x-ray magnetic scattering. The total scattering intensity is almost independent of incident photon helicity since it is mainly produced by the charge scattering. The weak MCD signals are caused primarily by interference between the charge scattering amplitude and each of the orbital and spin scattering amplitudes. The shape of the MCD spectra depends on angle alpha(M) between the wave vector of the incident photon and the magnetization vector. At alpha(M) = 0 degrees, the spin scattering is suppressed so that the MCD spectrum becomes analogous to that observed in the x-ray absorption spectroscopy. At alpha(M) = 135 degrees, the orbital scattering is suppressed, and the spin scattering plays central roles in producing the MCD signal. The magnitude of the MCD signal turns out to be proportional to the spin density of states projected onto the 3d states in the unoccupied state. Consequently, the value of the integrated MCD signal is proportional to the spin moment in the 3d states at the scattering site. The calculated MCD spectra with the help of a band structure calculation well reproduce the observed spectra.