From classical to quantum Kagomé antiferromagnet in a magnetic field

We study the magnetic properties of the Kagomé antiferromagnet going from the classical limit to the deep quantum regime of spin $1/2$ systems. In all the cases there are special values for the magnetization, $1/3$ in particular, in which a singular behavior is observed to occur in both the classical and quantum cases. We show clear evidence for a magnetization plateau for all S, in a wide range of $\mathrm{XXZ}$ anisotropies and for the occurrence of quantum order by disorder effects.