Dynamics and distribution of doped holes in the CuO$_2$ plane of slightly doped antiferromagnetic YBa$_2$(Cu$_{1-z}$Li$_z)_3$O$_{6+x}$ $(x<0.1)$ studied by Cu(1) NQR

Incidence of doped holes in the CuO$_2$ plane on the AF state was studied by Cu(1) nuclear quadrupole resonance (NQR) in slightly doped YBa$_2$(Cu$_{1-z}$Li$_z$)$_3$O$_{6+x}$ compounds. Inhomogeneous distribution of doped holes in the plane was detected in the low temperature measurements of transverse ($1/T_2$) and longitudinal ($1/T_1$) relaxation rates. We establish that at lower $T$ the holes motion slows down and we estimate that the holes localize finally in restricted regions ($\sim3$ lattice constants) in the Coulomb potential of the Li$^+$ ions. Also we compared the hole behavior in slightly doped YBa$_2$(Cu$_{1-z}$Li$_z$)$_3$O$_{6+x}$ samples with that in slightly doped Y$_{1-y}$Ca$_y$Ba$_2$Cu$_3$O$_6$. A stronger trapping potential of the in-plane Li$^+$ impurities was concluded as compared to slightly doped Y$_{1-y}$Ca$_y$Ba$_2$Cu$_3$O$_6$ compound with out-of-plane Ca$^{2+}$ impurities.