Magnetic circular dichroism in x-ray resonant Raman scattering in perpendicular geometry from ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ and Co metal:  A comparison of valence and inner-shell channels

We present results on resonant Raman scattering (RRS) in perpendicular geometry excited with circularly polarized x rays at the Co $L_{3,2}$ edges in ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ (Co ferrite) and Co metal. In this geometry the incident x-ray beam is perpendicular to the magnetization and the magnetic dichroism is only present in the RRS and not in the absorption. We compare the $3s-\mathrm{R}\mathrm{R}\mathrm{S}$ channel terminating in an inner shell $3s$ hole and extra $3d$ electron ${(2p}^6{3d}^n\to {2p}^5{3d}^{n+1\mathrm{}}\to {2p}^6{3s}^1{3d}^{n+1\mathrm{}})$ and the $3d-\mathrm{R}\mathrm{R}\mathrm{S}$ channel ending in a $3d$ electron-hole pair ${(2p}^6{3d}^n\to {2p}^5{3d}^{n+1\mathrm{}}\to {2p}^6{3d}^n).\mathrm{}$ The work is based on the measurement of the spectra vs the incident photon energy and integrated over the scattered photon energy. In both samples the dichroism of the inner-shell channel is about an order of magnitude larger than that of the valence channel. The result is explained by a theory based on the fast-collision approximation. We show that this theory provides a general way to choose the optimum scattering channel in the study of magnetic dichroism in perpendicular geometry. The impact of the results is briefly discussed.