Systematic Variation of Quadrupole Crystal-Field Shielding in Rare-Earth Ethyl Sulfates

Abstract

Quadrupole-coupling constants were obtained from measurements on ${\mathrm{La}}^{140}$, ${\mathrm{Eu}}^{154}$, ${\mathrm{Gd}}^{159}$, and ${\mathrm{Lu}}^{177}$ nuclei oriented in neodymium ethyl sulfate at temperatures down to 0.01\ifmmode^\circ\else\textdegree\fi{}K. These results are combined with the other available quadrupole-coupling data on La, Dy, Tm, and Lu in ethyl sulfate lattices to determine the quadrupole-antishielded term transforming as ${{Y}_{2}}^{0}$ in the crystal-field potential, i.e., $(1\ensuremath{-}{\ensuremath{\gamma}}_{\ensuremath{\infty}}) {{A}_{2}}^{0}$. This term increases fairly slowly throughout the rare earths, with an average value of approximately $(3\ifmmode\times\else\texttimes\fi{}{10}^{4} {\mathrm{cm}}^{\ensuremath{-}1}){{a}_{0}}^{\ensuremath{-}2}$. These values were compared with theoretical estimates of -80 for ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$ to yield the quantities ${{A}_{2}}^{0}$. Comparison of the ${{A}_{2}}^{0}$'s with the corresponding ${{V}_{2}}^{0}$'s taken from optical spectroscopy, using Hartree-Fock radial moments $〈{r}^{2}〉$ for the $4f$ electrons, together with some extrapolation, gives a complete set of shielding factors ($1\ensuremath{-}{\ensuremath{\sigma}}_{2}$) for the crystal-field component ${{V}_{2}}^{0}$. These factors vary from 0.6 in ${\mathrm{Lu}}^{3+}$ to 0.4 in ${\mathrm{Eu}}^{3+}$ and drop to -0.2 in ${\mathrm{La}}^{3+}$. Thus not only is there substantial shielding of ${{V}_{2}}^{0}$, but this shielding seems to vary considerably in the $4f$ series. The ${\ensuremath{\sigma}}_{2}$'s are typically larger by about 50% than theoretical estimates.