Quantum Magnetism in the Paratacamite Family: Towards an Ideal Kagomé Lattice

We report muon spin rotation measurements on the $S=1/2$ (${\mathrm{Cu}}^{2+}$) paratacamite ${\mathrm{Zn}}_x{\mathrm{Cu}}_{4-x}(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ family. Despite a Weiss temperature of $\sim -300\mathrm{K}$, the $x=1$ compound is found to have no transition to a magnetic frozen state down to 50 mK as theoretically expected for the kagomé Heisenberg antiferromagnet. We find that the limit between a dynamical and a partly frozen ground state occurs around $x=0.5$. For $x=1$, we discuss the relevance to a singlet picture.

Figure 1

${\mu }^{+}$ polarization in $x=1$ compound, either in zero field (H and D samples) and under an applied field (H sample). No static internal field other than of nuclear origin is detected and a weak dynamical relaxation is observed.

Figure 2

Left panel: time evolution of the polarization for the $x=1$ D sample in ZF and LF. The slowing down observed below 1 K is more pronounced for $x=0.66$ than for $x=1$ (right panel).

Figure 3

${\mu }^{+}$ polarization [23] plotted versus time for $x=0$, 0.15, 0.33, 0.5, 0.66, 1.0. Lines are for fits described in the text. The data for $x=0$ are from 19.

Figure 4

$T$ variation of the frozen fraction for all $x$ where a magnetic transition is observed. Inset: low-$T$ fraction versus $x$. Symbols used here are the same as in Fig. 3. Lines are guides to the eyes.