X-ray magnetic circular dichroism at rare-earth L_2,3 edges in R₂Fe₁₄B compounds (R=La, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu)

Magnetic circular dichroism (MCD) in the x-ray-absorption spectroscopy at the L_2,3 edges for almost the entire series of rare-earth (RE) elements in R₂Fe₁₄B is studied experimentally and theoretically. By a quantitative comparison of the complicated MCD spectral shapes, we find that (i) the 4f-5d intra-atomic exchange interaction not only induces the spin and orbital polarization of the 5d states, but also it accompanies a contraction of the radial part of the 5d wave function depending on its spin and orbital states, which results in the enhancement of the 2p-5d dipole matrix element, (ii) there are cases where the spin polarization of the 5d states due to the hybridization with the spin polarized 3d states of surrounding irons plays important roles, and (iii) the electric quadrupole transition from the 2p core states to the 4f states is appreciable at the pre-edge region of the 2p to 5d 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 L_2.3 edges.