For some time now, there has been considerable experimental and theoretical
effort to understand the role of the normal-state "pseudogap" phase in und
erdoped high-temperature cuprate superconductors. Recent debate has centere
d on the question of whether the pseudogap is independent of superconductiv
ity. We provide evidence from zero-field muon spin relaxation measurements
in YBa2Cu3O6+x for the presence of small spontaneous static magnetic fields
of electronic origin intimately related to the pseudogap transition. Our m
ost significant finding is that, for optimal doping, these weak static magn
etic fields appear well below the superconducting transition temperature. T
he two compositions measured suggest the existence of a quantum critical po
int somewhat above optimal doping.