X-ray magnetic circular dichroism at rare-earth (formula presented) edges in (formula presented) compounds (formula presented) Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu)

Magnetic circular dichroism (MCD) in the x-ray-absorption spectroscopy at the (formula presented) edges for almost the entire series of rare-earth (RE) elements in (formula presented) is studied experimentally and theoretically. By a quantitative comparison of the complicated MCD spectral shapes, we find that (i) the (formula presented) intra-atomic exchange interaction not only induces the spin and orbital polarization of the (formula presented) states, but also it accompanies a contraction of the radial part of the (formula presented) wave function depending on its spin and orbital states, which results in the enhancement of the (formula presented) dipole matrix element, (ii) there are cases where the spin polarization of the (formula presented) states due to the hybridization with the spin polarized (formula presented) states of surrounding irons plays important roles, and (iii) the electric quadrupole transition from the (formula presented) core states to the (formula presented) states is appreciable at the pre-edge region of the (formula presented) to (formula presented) dipole spectrum. Especially, our results evidence that it is important to include the enhancement effect of the dipole matrix element in the correct interpretation of the MCD spectra at the RE (formula presented) edges.