We show by inelastic neutron scattering that dynamic spin correlations coexist with superconductivity in YBa2Cu3O6+x (x=0.4,0.45,0.5). For the x=0.5, Tc=50 K sample, the inelastic magnetic intensity at E=6 meV does not show any change near Tc and is approximately constant from 250 to 10 K, in contrast to earlier data on superconducting La1.85Sr0.15CuO4 (Tc=35 K) which showed a decrease of the integrated intensity at a temperature well above Tc. The inelastic magnetic cross section observed here can be consistently modeled as two-dimensional spin waves overdamped by short correlation lengths. The correlation length in the x=0.5 sample is an order of magnitude smaller than in the x=0.40 and x=0.45 samples, indicating a drastic disruption of planar copper spin-spin correlation upon hole doping. The present results are compared with recent NMR studies of Tc=60 K material.
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