Abstract
The crystal structure of the mineral boleite contains clusters of 24 $S=1/2\phantom{\rule{4pt}{0ex}}{\mathrm{Cu}}^{2+}$ ions that have the shape of a truncated cube formed of eight trimers connected by edges. Susceptibility measurements and exact diagonalization calculations suggest that there are strong antiferromagnetic intratrimer interactions, such that effective $S=1/2$ degrees of freedom emerge on the trimers below $T\ensuremath{\lesssim}100$ K. Weaker intertrimer interactions lead to the formation of a singlet ground state for these effective spins at $T\ensuremath{\lesssim}5$ K. The clusters in boleite offer a situation similar to single molecule magnetism, accessible to both experiment and numerics, in which the interplay of quantum spins, geometric frustration, spin entanglement, and mesoscopic system size can be studied.
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