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

Quadrupole-coupling constants were obtained from measurements on La¹⁴⁰, Eu¹⁵⁴, Gd¹⁵⁹, and Lu¹⁷⁷ 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 Y₂⁰ in the crystal-field potential, i.e., (1-γ_∞) A₂⁰. This term increases fairly slowly throughout the rare earths, with an average value of approximately (3×10⁴ cm^-1)a₀^-2. These values were compared with theoretical estimates of -80 for γ_∞ to yield the quantities A₂⁰. Comparison of the A₂⁰'s with the corresponding V₂⁰'s taken from optical spectroscopy, using Hartree-Fock radial moments 〈r²〉 for the $4f$ electrons, together with some extrapolation, gives a complete set of shielding factors (1-σ₂) for the crystal-field component V₂⁰. These factors vary from 0.6 in Lu³⁺ to 0.4 in Eu³⁺ and drop to -0.2 in La³⁺. Thus not only is there substantial shielding of V₂⁰, but this shielding seems to vary considerably in the $4f$ series. The σ₂'s are typically larger by about 50% than theoretical estimates.