The magnetic groundstate of an experimental $S=1/2$ kagom\'{e} antiferromagnet

We have carried out neutron powder-diffraction measurements on zinc paratacamite Zn$_x$Cu$_{4-x}$(OH)$_6$Cl$_2$ with $x=1$, and studied the heat capacity in fields of up to 9 T for $0.5 \leq x \leq 1$. The $x=1$ phase has recently been shown to be an outstanding realisation of the $S=1/2$ kagom\'{e} antiferromagnet. A weak mixing of Cu$^{2+}$/Zn$^{2+}$ between the Cu and the Zn sites, corresponding to $\sim 9$% of all Cu$^{2+}$ for $x=1$, is observed using neutron diffraction. This ``antisite disorder'' provides a consistent explanation of the field dependence of the heat capacity for $0.8 \leq x \leq 1$. From comparison of the derived Cu$^{2+}$ occupancy of the Zn sites for $x = 0.8... 1$ with the magnetic susceptibility, we argue that for $x = 0.8... 1$ zinc paratacamite is a spin liquid without a spin gap. The presence of unpaired but nevertheless strongly interacting spins gives rise to a macroscopically degenerate ground state manifold, with increasingly glassy dynamics as $x$ is lowered.