Experimental Confirmation of the X-Ray Magnetic Circular Dichroism Sum Rules for Iron and Cobalt

High precision, $L$${}_{2,3}$-edge photoabsorption and magnetic circular dichroism spectra of iron and cobalt were measured in transmission with in situ grown thin films, eliminating experimental artifacts encountered by the indirect methods used in all previous measurements. The magnetic moments determined from the integrals of these spectra are found to be in excellent agreement (within 3%) for the orbital to spin moment ratios, and in good agreement (within 7%) for the individual moments, with those obtained from Einstein--de Haas gyromagnetic ratio measurements, demonstrating decisively the applicability of the individual orbital and spin sum rules.