Magnetic circular dichroism in hard x-ray Raman scattering as a probe of local spin polarization

We argue that the magnetic circular dichroism (MCD) of the hard x-ray Raman scattering (XRS) could be used as an element selective probe of local spin polarization. The magnitude of the XRS-MCD signal is directly proportional to the local spin polarization when the angle between the incident wavevector and the magnetization vector is $135^{\circ}$ or $-45^{\circ}$. By comparing the experimental observation and the configuration interaction calculation at the $L_{2,3}$ and $M_{2,3}$ edges of ferromagnetic iron, we suggest that the integrated MCD signal in terms of the transferred energy could be used to estimate the local spin moment even in the case where the application of the spin sum-rule in X-ray absorption is questionable. We also point out that XRS-MCD signal could be observed at the $M_{1}$ edge with a magnitude comparable to that at the $M_{2,3}$ edge, although the spin-orbit coupling is absent in the core orbital. By combining the XRS-MCD at various edges, spin polarization distribution depending on the orbital magnetic quantum number would be determined.