Sum Rules in X-Ray Resonant Raman Scattering: Recovering the Co Ground State Information inCoFe2O4as a Test Case

We present an approach to x-ray resonant Raman scattering suitable for sum-rule analysis. In magnetic systems it gives ground state information as represented by an expansion in coupled multipoles of orbital and spin moments. The experiment is based on the angular dependence of the integrated peak intensities. In $3d$ transition elements one obtains information up to order $4$ from the channel $2p^{6}3d^n\to 2p^{5}3d^{n+1}\to 2p^{6}3s^{1}3d^{n+1}$. By combining these results with $L_{2,3}$ absorption dichroism, we show quantitatively the atomiclike properties of cobalt in ${\mathrm{C}\mathrm{o}\mathrm{F}\mathrm{e}}_2{\mathrm{O}}_4$ up to high-order multipoles.