${}^{63}\mathrm{Cu}$ NQR Evidence for Spatial Variation of Hole Concentration in ${\mathrm{La}}_{2-\mathit{x}}{\mathrm{Sr}}_{\mathit{x}}{\mathrm{CuO}}_4$

We report experimental evidence for the spatial variation of hole concentration $x_{\mathrm{hole}}$ in the high $T_c$ superconductor ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ ( $0.04\le x\le 0.16$) via ${}^{63}\mathrm{Cu}$ NQR using ${}^{63}\mathrm{Cu}$ isotope enriched samples. We demonstrate that the extent of the spatial variation of the local hole concentration $\Delta x_{\mathrm{hole}}$ is reflected on ${}_{}{}^{63}{}_{}{}^{}1{/T}_1$ and deduce the temperature dependence. $\Delta x_{\mathrm{hole}}$ increases below 500–600 K, and reaches values as large as $\Delta x_{\mathrm{hole}}/x\sim 0.5$ below $\sim 150\mathrm{K}$. We estimate the length scale of the spatial variation in $x_{\mathrm{hole}}$ to be $R_{\mathrm{hole}}\gtrsim 3\mathrm{nm}$ from an analysis of the NQR spectrum.