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Here we report the observation of Fermi surface (FS) pockets via theShubnikov de Haas effect in Na$_x$CoO$_2$ for $x = 0.71$ and 0.84,respectively. Our observations indicate that the FS expected for each compoundintersects their corresponding Brillouin zones, as defined by the previouslyreported superlattice structures, leading to small reconstructed FS pockets,but only if a precise number of holes per unit cell is \emph{localized}. For$0.71 \leq x < 0.75$ the coexistence of itinerant carriers and localized $S=1/2$ spins on a paramagnetic triangular superlattice leads at low temperaturesto the observation of a deviation from standard Fermi-liquid behavior in theelectrical transport and heat capacity properties, suggesting the formation ofsome kind of quantum spin-liquid ground state.

Local moment, itinerancy and deviation from Fermi liquid behavior in Na$_x$CoO$_2$ for $0.71 \leq x \leq 0.84$