We have studied the magnetic phase diagram for the bilayer compound Y1
-xCaxBa2Cu3O6 in the regime of low doping (hole concentration within a
CuO2 plane, p(sh) < 0.1). For p(sh) < 0.03, the data demonstrate the
freezing of the spin degrees of freedom associated with the doped hole
s into a spin-glass-like state which is superimposed on the preexistin
g long range order of the Cu2+ spins. Only a single spin-glass like tr
ansition at a temperature T-g is observed for samples in the hole conc
entration range 0.03 < p(sh) < 0.1. While the threshold for the occurr
ence of superconductivity is almost the same (p(sh) > 0.06) for the Y1
-xCaxBa2Cu3O6 and the La2-xSrxCuO4 systems, the magnetic correlations
that coexist with superconductivity are considerably stronger in the b
ilayer Y1-xCaxBa2Cu3O6 system as indicated by significantly increased
transition temperatures T-g.