Shielding and distortion of rare-earth crystal-field spectra

The electronic spectra of rare-earth ions in crystalline fields are generally analyzed in terms of a static crystalline field, Vc=n,mAnmrnYnm(θ,), which acts on the open shell of 4f electrons. In this paper, the contributions of the closed atomic shells to this electrostatic interaction are examined and are found to be significant in several respects: First, the magnitude of the crystal-field splittings are reduced from the values obtained by considering just the 4f shell alone; this result supports the familiar assertion that the 4f electrons are shielded from the external crystalline field. Secondly, and quite striking, is the result that the ordering and relative spacing of the crystal-field levels are not necessarily those implied by the 4f crystal-field matrix elements alone. It is shown that in some cases the distortion of the ion's charge distribution produces severe deviations from the 4f crystal-field level scheme predicted by Vc directly. When such "nonlinear" deviations occur, they make questionable the standard crystal field parametrization schemes used for fitting observed rare-earth spectra. In addition, we also investigate the role played by the crystal field in producing by means of the distortion of the closed and 4f shells, and the interaction of these distortions with the open 4f shell, contributions to the magnetic (and electric) hyperfine interactions.