We report detailed systematic measurements of the spatial variation in electronic states in the high T{ c} superconductor La{ 2-x}Sr{ x}CuO{ 4} (0.04<= x <= 0.16) using { 63}Cu NQR for { 63}Cu isotope enriched poly-crystalline samples. We demonstrate that the spatial variation in local hole concentration { 63}x{ local} given by { 63}x{ local} = x +/- { 63}Dx{ local}, where x is the nominal hole concentration and { 63}Dx{ local} is defined as the amplitude (or extent) of the spatial variation, is reflected in the frequency dependence of the spin-lattice relaxation rate { 63}1/T{ 1} across the inhomogeneous linebroadening of the { 63}Cu NQR spectrum. By using high precision measurements of the temperature dependence of { 63}1/T_{ 1} at various positions across the { 63}Cu NQR lineshape, we demonstrate that { 63}Dx{ local} increases below 500 - 600 K and reaches values as large as { 63}Dx{ local} / x ~ 0.5 in the temperature region > 150 K. By incorporating the random positioning of { +2}Sr donor ions in the lattice in a novel approach, a lower bound to the length scale of the spatial variation { 63}R{ patch} is deduced by fitting the entire { 63}Cu NQR spectrum (including the ``B'' -line) using a patch-by-patch distribution of the spatial variation { 63}x{ local} with the patch radius { 63}R_{ patch} > 3.0 nm as the only free parameter. A corresponding upper bound to the amplitude of the spatial variation { 63}Dx{ patch} (~ 1/{ 63}R_{ patch}) is deduced within the model, and consistent results are found with { 63}Dx{ local} . We also deduce the onset temperature T{ Q} (> 400 K) for local orthorhombic lattice distortions which, in the region x > 0.04, is found to be larger than the onset temperature of long range structural order.
Categories: cond-mat.str-el cond-mat.supr-con