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

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°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., $(1-{\gamma }_{\infty }) {A_2}^0$. This term increases fairly slowly throughout the rare earths, with an average value of approximately $(3\mathrm{}\times {10}^4 {\mathrm{cm}}^{-1\mathrm{}}){a_0}^{-2\mathrm{}}$. These values were compared with theoretical estimates of -80 for ${\gamma }_{\infty }$ 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 ($1-{\sigma }_2$) 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 ${\sigma }_2$'s are typically larger by about 50% than theoretical estimates.