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$^{115}$In Nuclear magnetic resonance data are presented for a series ofCe$_{1-x}$La$_x$CoIn$_5$ crystals with different La dilutions, $x$. MultipleIn(1) sites associated with different numbers of nearest-neighbor cerium atomsexhibit different Knight shifts and spin lattice relaxation rates. Analysis ofthe temperature dependence of these sites reveals both an evolution of theheavy electron coherence as a function of dilution, as well as spatialinhomogeneity associated with a complete suppression of antiferromagneticfluctuations in the vicinity of the La sites. Quantum critical fluctuationspersist within disconnected Ce clusters with dilution levels up to 75%, despitethe fact that specific heat shows Fermi liquid behavior in dilute samples.

Site Specific Knight Shift Measurements of the Dilute Kondo lattice System Ce$_{1-x}$La$_x$CoIn$_5$