Abstract
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 finite resistivity at zero temperature. The value of the staggered magnetization at zero temperature is $\ensuremath{\approx}$$0.6\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}$, the maximum value allowed by spin quantum fluctuations. The staggered magnetization is almost independent of doping. On the other hand, the N\'eel temperature decays very quickly, from ${T}_{N}=420\phantom{\rule{0.28em}{0ex}}\text{K}$ at $x=0$ to practically zero at $x\ensuremath{\approx}6%$. 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 $x<6%$.
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