Origin of electric-field gradients in high-temperature superconductors: ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

The origin of the electric-field gradients (EFG) at nuclear sites in the high-${\mathit{T}}_{\mathit{c}}$ superconductor ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ is investigated theoretically by means of highly precise local-density full-potential linearized-augmented-plane-wave calculations. In all cases considered (i.e., at Cu, O, Ba, and Y nuclei), the theoretical predictions for the principal axis ${\mathit{V}}_{\mathit{z}\mathit{z}}$ and the anisotropy parameter η of the EFG tensor agree well with available experiments and the results of Ambrosch-Draxl et al. The principal axis at O sites are found to lie in the direction of the Cu-O dpσ bonding axis, and the oxygen η values are largely determined by the internal anisotropy inside the oxygen spheres. This is consistent with the finding that the main contribution to the EFG at the Cu sites comes from the intrinsic quadrupole field provided by the nonspherical (internal) charge distributions surrounding each Cu atom arising from the strong anisotropic hybridization between Cu d and O p electrons. Surprisingly, the (Sternheimer antishielding) contribution from the core electrons–mainly from the Cu 3p ‘‘semicore’’ electrons–is found to be very small. Overall, the agreement of the oxygen EFG components themselves with experiment is good. The calculated ${\mathit{V}}_{\mathit{z}\mathit{z}}$ values are within 20% of the experiment, except for Cu(2), which is only half of the observed value and results in a reversal of the relative magnitude of the EFG at Cu(1) and Cu(2) sites. This error may result from the inexact treatment of the 3p semicore states when they are allowed to relax and are described as band states. This is seen from the extreme sensitivity of the EFG to the calculated anisotropic charge distributions of the core electrons. Thus, a transfer of only 0.0014 electrons from Cu(2) 3${\mathit{p}}_{\mathit{x}}$ and 3${\mathit{p}}_{\mathit{y}}$ to 3${\mathit{p}}_{\mathit{z}}$ would enhance the EFG value and produce perfect agreement with experiment.