Structural implications of nuclear electric quadrupole splittings in high-Tcsuperconductors

The electric field gradients and nuclear quadrupole coupling constants are calculated for La in ${\mathrm{La}}_2$Cu${\mathrm{O}}_4$, Eu in Eu${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, and Cu and Fe (as a replacement for Cu) in Y${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. We use an ionic model which regards the high-$T_c$ superconductors as primarily ionic crystals modified by the introduction of a relatively small number of charge carriers via doping in ${\mathrm{La}}_2$Cu${\mathrm{O}}_4$ and non-stoichiometry in $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ for $\delta <0.5\mathrm{}$. Good agreement between theory and experiment is obtained for the spherically symmetric free-ion species ${\mathrm{La}}^{3+}$ and ${\mathrm{Eu}}^{3+}$ with distortion of the partially filled ${\mathrm{Eu}}^{3+}$ ${}_{}{}^4{}_{}{}^{}F_0^{}{}_{}{}^{}$ state by the ionic crystal field playing an important role. Comparison of theory and experiment for the Cu and Fe cases suggests Cu is present largely as ${\mathrm{Cu}}^{2+}$ and supports the assignment of the low- and high-frequency nuclear quadrupole resonance lines to the chain and plane sites of Y${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, respectively, while Fe is present as a mixture of ${\mathrm{Fe}}^{2+}$ (ca. 25% to 50%) and ${\mathrm{Fe}}^{3+}$.