Limitation of the Magnetic-Circular-Dichroism Spin Sum Rule for Transition Metals and Importance of the Magnetic Dipole Term

Magnetic-circular-dichroism (MCD) spectra and the spin magnetic dipole term (〈Tz〉) for bulk $3d$ transition metals and their surfaces were calculated from full potential linearized augmented plane wave electronic band structure results. The recently proposed MCD spin sum rule is found to result in a much larger error [of up to 50% for the Ni(001) surface] than does its orbital counterpart. In support of recent experiments for bulk, we find that by combining the MCD orbital and spin sum rules the ratio of spin and orbital moments can be determined from the MCD spectra even for low dimension systems with an error of 10% when the 〈Tz〉 contribution is included.