Effect of Coulomb interaction on the X-ray magnetic circular dichroism spin sum rule in rare earths

A deviation from the spin sum rule, which relates the integrated intensity of the X-ray magnetic circular dichroism (MCD) signal to the expectation value of the spin operator S-z ((S-z)), is numerically calculated in the case of the 3d --> 4f absorption for rare earths from the trivalent Ce to Tm. The calculation on the basis of an atomic model including the full multiplet shows that the deviation increases from similar to 60. To for Ce with increasing 4f electron number, reaches at similar to 230% for Sm and drops to less than similar to 10% for Gd and heavier rue earths An interplay of the 3d-4f exchange interaction. the 3d core spin-orbit interaction and the 4f electron configuration in the initial ground state Is shown to cause the chemical trend of the deviation from the sum rule