Antisite disorder and the magnetic groundstate of an experimental $S=1/2$ kagomé antiferromagnet

We carried out neutron powder-diffraction measurements, and studied the heat capacity in fields between 0 and 9 T of zinc paratacamite Zn$_x$Cu$_{4-x}$(OH)$_6$Cl$_2$ with $x=1$ and $0.5 \leq x \leq 1$ respectively. The $x=1$ phase has recently been shown to be an outstanding realisation of the $S=1/2$ kagom\'{e} antiferromagnet, in which no symmetry-breaking transition is observed down to 50 mK. We show that due to the presence of antisite disorder between the Cu and the Zn sites, systems with $0.8\leq x \leq 1$ model the kagom\'{e} antiferromagnet equally well. Within this range of Zn stoichiometries $x$ the system gradually develops a magnetic hysteresis and no quantum-critical phase transition is found. By correcting for the contributions of the antisite spins, we obtain for the first time estimates for the heat capacity and non-zero magnetic susceptibility of an experimental $S=1/2$ kagom\'{e} antiferromagnet.