  Using neutron scattering we have determined the magnetic structure and
fluctuations in the YBa2Cu3O6.35 superconductor (Tc=18 K). The long-range
ordered collinear spins of the insulating antiferromagnet are replaced by a
commensurate central mode arising from slow, isotropically polarized,
short-range spin correlations. The inelastic spectrum up to 30 meV is broad in
wave vector and commensurate. In contrast to the the resonance peak of higher
Tc superconductors, the spins exhibit a single overdamped spectrum whose rate
of relaxation decreases on cooling and saturates at 5 meV below 50 K. As the
relaxation rate saturates the quasi-static spin correlations grow and become
resolution limited in energy. The spin susceptibility at high temperatures
illustrates that the dominant energy scale is set by the temperature. At low
temperatures, the scale length is geometric and not linked by velocity to
dynamic widths. There is no observable suppression of the spin fluctuations or
central mode upon the onset of superconductivity. The spins respond not to
coherent charge pairs but to hole doping allowing coexistence of glassy short
range spin order with superconductivity. Since the physics of the weakly
superconducting system YBCO6.35 must connect continuously with that in more
strongly superconducting YBCO6.5, we find that neither incommensurate
stripe-like spin modulations nor a well-defined neutron spin resonance are
essential for the onset with doping of pairing in a high temperature cuprate
superconductor.
