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 $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.353}$ $({T}_{c}=18\phantom{\rule{0.3em}{0ex}}\mathrm{K})$, where the doping $\ensuremath{\sim}0.06$ 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 $\ensuremath{\simeq}2\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ relaxation rate and the other a central mode with a relaxation rate that slows to less than $0.08\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ below ${T}_{c}$. The spectrum mirrors that of a soft mode driving a central mode. Extremely short correlation lengths, $42\ifmmode\pm\else\textpm\fi{}5\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ in-plane and $8\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ 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 N\'eel 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.