Neutron scattering from high-quality YBa2Cu3O6.33 (YBCO6.33) single crystals with a Tc of 8.4 K shows no evidence of a coexistence of superconductivity with long-range antiferromagnetic order at this very low, near-critical doping of p~0.055. However, we find short-range three dimensional spin correlations that develop at temperatures much higher than Tc. Their intensity increases smoothly on cooling and shows no anomaly that might signify a Neel transition. The system remains subcritical with spins correlated over only one and a half unit cells normal to the planes. At low energies the short-range spin response is static on the microvolt scale. The excitations out of this ground state give rise to an overdamped spectrum with a relaxation rate of 3 meV. The transition to the superconducting state below Tc has no effect on the spin correlations. The elastic interplanar spin response extends over a length that grows weakly but fails to diverge as doping is moved towards the superconducting critical point. Any antiferromagnetic critical point likely lies outside the superconducting dome. The observations suggest that conversion from Neel long-range order to a spin glass texture is a prerequisite to formation of paired superconducting charges. We show that while pc =0.052 is a critical doping for superconducting pairing, it is not for spin order.
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