Electric field gradients from first-principles and point-ion calculations

Abstract

Point-ion models have been extensively used to determine ``hole numbers'' at copper and oxygen sites in high-temperature superconducting cuprate compounds from measured nuclear quadrupole frequencies. The present study assesses the reliability of point-ion models to predict electric field gradients accurately and also the implicit assumption that the values can be calculated from the ``holes'' and not the total electronic structure. First-principles cluster calculations using basis sets centered on the nuclei have enabled the determination of the charge- and spin-density distribution in the ${\mathrm{CuO}}_{2}$ plane. The contributions to the electric field gradients and the magnetic hyperfine couplings are analyzed in detail. In particular they are partitioned into regions in an attempt to find a correlation with the most commonly used point-ion model, the Sternheimer equation, which depends on the two parameters R and $\ensuremath{\gamma}.$ Our most optimistic objective was to find expressions for these parameters, which would improve our understanding of them, but although estimates of the R parameter were encouraging, the method used to obtain the $\ensuremath{\gamma}$ parameter indicated that the two parameters may not be independent. The problem seems to stem from the covalently bonded nature of the ${\mathrm{CuO}}_{2}$ planes in these structures which severely questions using the Sternheimer equation for such crystals, since its derivation is heavily reliant on the application of perturbation theory to predominantly ionic structures. Furthermore, it is shown that the complementary contributions of electrons and holes in an isolated ion cannot be applied to estimates of electric field gradients at copper and oxygen nuclei in cuprates.