Central mode and spin confinement near the boundary of the superconducting phase in YBa2Cu3O6.353 (Tc=18 K)

We have mapped the neutron scattering spin spectrum at low energies in YBa2Cu3O6.353 (T-c=18 K), where the doping similar to 0.06 is near the critical value (p(c)=0.055) for superconductivity. No coexistence with long-range-ordered antiferromagnetism is found. The spins fluctuate on two energy scales: one a damped spin response with a similar or equal to 2 meV relaxation rate and the other a central mode with a relaxation rate that slows to less than 0.08 meV below T-c. The spectrum mirrors that of a soft mode driving a central mode. Extremely short correlation lengths, 42 +/- 5 A in-plane and 8 +/- 2 A along the c direction, and isotropic spin orientations for the central mode indicate that the correlations are subcritical with respect to any second-order transition to Neel order. The dynamics follows a model where damped spin fluctuations are coupled to the slow fluctuations of regions with correlations shortened by the hole doping.