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Using neutron scattering we have determined the magnetic structure andfluctuations in the YBa2Cu3O6.35 superconductor (Tc=18 K). The long-rangeordered collinear spins of the insulating antiferromagnet are replaced by acommensurate central mode arising from slow, isotropically polarized,short-range spin correlations. The inelastic spectrum up to 30 meV is broad inwave vector and commensurate. In contrast to the the resonance peak of higherTc superconductors, the spins exhibit a single overdamped spectrum whose rateof relaxation decreases on cooling and saturates at 5 meV below 50 K. As therelaxation rate saturates the quasi-static spin correlations grow and becomeresolution limited in energy. The spin susceptibility at high temperaturesillustrates that the dominant energy scale is set by the temperature. At lowtemperatures, the scale length is geometric and not linked by velocity todynamic widths. There is no observable suppression of the spin fluctuations orcentral mode upon the onset of superconductivity. The spins respond not tocoherent charge pairs but to hole doping allowing coexistence of glassy shortrange spin order with superconductivity. Since the physics of the weaklysuperconducting system YBCO6.35 must connect continuously with that in morestrongly superconducting YBCO6.5, we find that neither incommensuratestripe-like spin modulations nor a well-defined neutron spin resonance areessential for the onset with doping of pairing in a high temperature cupratesuperconductor.

Spin dynamics near the critical doping in weakly-superconducting underdoped YBa2Cu3O6.35 (Tc=18K)