Doping induced magnetic clusters and Co spin state transition in Na_xCoO_2 with 0.78

By muon spin rotation we investigated the magnetic properties of a series of highly Na doped NaxCoO2 single crystals with 0.78(1)<x<0.97(1). Our data provide evidence for an intrinsically inhomogeneous magnetic state which can be described in tems of hole doping (Na vacancy) induced magnetic clusters that percolate at 1-x>0.04 until they yield a bulk magnetic state near x=0.78. Evidence for a strong (likely geometrical) frustration of the magnetic order is obtained from the anomalous doping dependence of the spin fluctuation rate (above the ordering temperature) which is strongly enhanced at x=0.78 as compared to x=0.97.