Theoretical study of the structural dependence of nuclear quadrupole frequencies in high-Tcsuperconductors

The remarkable difference between the nuclear quadrupole frequencies ${\nu }_Q$ of Cu(1) and Cu(2) in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_6$ and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ is analyzed. We calculate the ionic contribution to the electric field gradients and estimate, by using experimental results for ${\mathrm{Cu}}_2$O and ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$, the contribution of the d valence electrons. Thus, we determine ${\nu }_{Q1}$, ${\nu }_{Q2}$, and the asymmetry parameter η for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_6$ and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. The number of holes in the Cu-O planes and chains is found to be important for the different behavior of ${\nu }_{Q1}$ and ${\nu }_{Q2}$.