The effective spin sum rule is widely used in the quantitative analysis of x-ray magnetic circular dichroism spectra. Here, this important, though imperfect, sum rule is reviewed with a detailed analysis of the various sources for errors and deviations. The simulations confirm that the final state effects of the core level spin-orbit coupling and the core-valence exchange interactions (multiplet effects) are linearly related with the effective spin sum-rule error. Within the charge transfer multiplet approach, we have analyzed these effects, in combination with the interactions affecting the magnetic ground state, including the crystal field strength, the charge transfer effects, the exchange (magnetic) field, and the $3d$ spin-orbit coupling. We find that for the late transition-metal systems, the error in the effective spin moment is between 5% and 10%, implying that for covalent and/or metallic systems the effective spin sum rule is precise to within 5–10 %. The error for $3d^5$ systems is $\sim 30\%$ and for $3d^4$ systems, the error is very large, implying that, without further information, the derived effective spin sum-rule values for $3d^4$ systems have no meaning.

• Received 6 August 2009

DOI:https://doi.org/10.1103/PhysRevB.80.184410