Effect of Coulomb interaction on the X-ray magnetic circular dichroism spin sum rule in 3d transition elements

A deviation from the X-ray magnetic circular dichroism (MCD) spin sum rule, which is derived assuming well separated core spin-orbit multiplets in the final state of X-ray absorption, is calculated for the L(2,3) edge in the magnetized Ni, Co, Fe and Mn ions on the basis of an atomic model including the full multiplet and the crystal field with O-h symmetry. Due to the Coulomb interaction between electrons, which mixes the so-called L(3) and L(2) regions with each other, it is found that the deviation can be similar to 10 percent for the former three ions, while for Mn2+ it amounts to more than 30 percent. A list of the deviations for various ionic states for the above elements is presented, which may serve as a correction factor in the estimation of expectation values of magnetic quantities from MCD data.