O17NMR study of the inhomogeneous electronic state inLa2−xSrxCuO4crystals

Abstract

We report measurements on the inhomogeneous line broadening of the $^{17}\mathrm{O}$ NMR spectrum in the high ${T}_{c}$ superconductor ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ for single crystals with nominal hole concentrations $x=0.035$, 0.05, 0.07, 0.115, and 0.15. A substantial overlap between the $^{17}\mathrm{O}$ NMR spectrum of different crystals is reported, and the extent of the overlap is shown to increase with decreasing temperature. The spin-lattice relaxation rate divided by temperature, $1∕^{17}T_{1}T$, is found to vary linearly with frequency (or Knight shift $^{17}K_{\mathit{\text{spin}}}$, equivalently) across the $^{17}\mathrm{O}$ NMR spectrum of each crystal, with the same scaling form given by $1∕^{17}T_{1}T=\ensuremath{\beta}^{17}K_{\mathit{\text{spin}}}$, where $\ensuremath{\beta}=2.4(2)\phantom{\rule{0.3em}{0ex}}{(\mathrm{sK}%)}^{\ensuremath{-}1}$. We therefore argue that the overlap between the $^{17}\mathrm{O}$ NMR spectrum of different crystals $x$ is a result of an inherent spatial variation in hole concentration within each crystal, and that the extent of the line broadening, $^{17}\ensuremath{\Delta}{K}_{\mathit{\text{spin}}}$, is a measure of the extent $^{17}\ensuremath{\Delta}{x}_{\mathit{\text{local}}}$ (or amplitude) of the spatial variation in local hole concentration, $^{17}x_{\mathit{\text{local}}}=x\ifmmode\pm\else\textpm\fi{}^{17}\ensuremath{\Delta}{x}_{\mathit{\text{local}}}$. We successfully fit the $^{17}\mathrm{O}$ NMR line shapes with a simple numerical model that determines the random distribution in local hole concentration $^{17}x_{\mathit{\text{local}}}$ as a result of the random spatial distribution in ${\mathrm{Sr}}^{2+}$ hole donors within a patch radius $^{17}R_{\mathit{\text{patch}}}$. We find that $^{17}R_{\mathit{\text{patch}}}=2--5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ best fits the data, implying a short length scale for the inhomogeneous electronic state. In this report we present the first systematic study of the spatial distribution in the local static spin susceptibility in the high ${T}_{c}$ cuprates.