Ground State of the Kagomé-Like $S=1/2$ Antiferromagnet Volborthite ${\mathrm{Cu}}_3{\mathrm{V}}_2{\mathrm{O}}_7(\mathrm{OH}{)}_2·2{\mathrm{H}}_2\mathrm{O}$

The volborthite compound is one of the very few realizations of $S=1/2$ quantum spins on a highly frustrated kagomé-like lattice. Low-$T$ SQUID measurements reveal a broad magnetic transition below 2 K which is further confirmed by a peak in the ${}^{51}\mathrm{V}$ nuclear spin relaxation rate ($1/T_1$) at $1.4\mathrm{K}\pm 0.2\mathrm{K}$. Through ${}^{51}\mathrm{V}$ NMR, the ground state (GS) appears to be a mixture of different spin configurations, among which 20% corresponds to a well defined short-range order, possibly of the $\sqrt{3}\times \sqrt{3}$ type. While the freezing involves all the ${\mathrm{Cu}}^{2+}$ spins, only 40% of the copper moment is actually frozen which suggests that quantum fluctuations strongly renormalize the GS.