  The present work addresses YBa$_{2}$Cu$_{3}$O$_{y}$ at doping below x=6%
where the compound is a collinear antiferromagnet. In this region
YBa$_{2}$Cu$_{3}$O$_{y}$ is a normal conductor with a finite resistivity at
zero temperature. The value of the staggered magnetization at zero temperature
is 0.6\mu_B, the maximum value allowed by spin quantum fluctuations. The
staggered magnetization is almost independent of doping. On the other hand, the
Neel temperature decays very quickly from T_N=420K at x=0 to practically zero
at x = 0.06. The present paper explains these remarkable properties and
demonstrates that the properties result from the physics of a lightly doped
Mott insulator with small hole pockets. Nuclear quadrupole resonance data are
also discussed. The data shed light on mechanisms of stability of the
antiferromagnetic order at x < 6%.
