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 (Tc=18 K) where the doping ~0.06 is near the critical value (pc=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 ~2 meV relaxation rate and the other a central mode with a relaxation rate that slows to less than 0.08 meV below Tc. The spectrum mirrors that of a soft mode driving a central mode. Extremely short correlation lengths, 42+-5 Angstrom in-plane and 8+-2 Angstrom 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. 
C. Stock, W. J. L. Buyers, Z. Yamani, C. Broholm, J.-H. Chung, Z. Tun,   R. Liang, D. Peets, D. Bonn, W. N. Hardy, R. J. Bir...