X-ray magnetic circular dichroism at rare-earth L(2,3) edges in RE-2Fe-14B compounds (RE = 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 ${R}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$ is studied experimentally and theoretically. By a quantitative comparison of the complicated MCD spectral shapes, we find that (i) the $4f\ensuremath{-}5d$ 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 $2p\ensuremath{-}5d$ 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.