  We study the spin fluctuations of pure and Zn-substituted high temperature
superconductors (HTS) using the muon spin relaxation (muSR) technique.
Superconductivity is found to coexist with low frequency spin fluctuations over
a large region of the superconducting phase diagram. The characteristic
temperature of spin fluctuations detected by muSR decreases with increasing
doping and vanishes above a critical doping pc=0.19 where the normal state
pseudogap vanishes. Furthermore, it is at pc that our penetration depth studies
show an abrupt change in the doping dependence of the superfluid density. For
p>pc the absolute value of the superfluid density is large and nearly
independent of carrier concentration whereas for p<pc it drops rapidly,
signalling a crossover to weak superconductivity. These results are discussed
in terms of a quantum transition involving fluctuating short-range magnetic
order that separates the superconducting phase diagram of HTS into two distinct
ground states.
