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 • or −45 • . 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.1 arXiv:1909.13490v1 [cond-mat.mtrl-sci] 30 Sep 2019 X-ray magnetic circular dichroism (MCD) has been one of the powerful tools to investigate the electronic structure in magnetic materials. Particularly, owing to the orbital and spin sum-rules, 1,2 the MCD in the soft x-ray absorption spectroscopy (XAS) has been playing crucial roles for elucidating the electronic structure at and around the absorption site. 3 The MCD measurements in x-ray emission and resonant inelastic scattering are also important tools to clarify the electronic excitations in magnetic materials. 4Recently, the MCD in the hard x-ray Raman scattering (XRS) at the Fe L 2,3 -edges in the ferromagnetic iron has been investigated. 5,6 The XRS is a kind of non-resonant inelasticx-ray scattering. 7 In the process of photon scattering, where an incident photon of energy ω i is absorbed and a photon of energy ω f is emitted, the electron system in the initial ground state of the energy E i is excited to the final state of the energyThe final state of the XRS is essentially the same with that of XAS: A core hole is left behind at the scattering site and an electron is added to the valence or conduction state.Therefore, the XRS intensity as a function of transferred energy is similar to the soft xray absorption coefficient as a function of the incident photon energy. Contrasting to the XAS, the hard-in-hard-out feature of the XRS is preferable for bulk sensitive measurements or the measurements under extreme conditions. In addition, the XRS can access the final states that are inaccessible by the dipole transition, because the non-dipole transition matrix elements become significant for shallow core excitation. By virtue of these features, the innercore-exciting XRS has been demonstrating its usefulness particularly to unveil the electronic state of materials under extreme conditions. 8 Recently, the electronic state of Fe in Fe 2 SiO 4 , Fe 2 O 3 and FeS under high pressure is discussed by analyzing the XRS spectra at the F...