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Field-concentration phase diagram of a quantum spin liquid with bond defects

The magnetic susceptibility of the gapped quantum spin liquid compound (C$_4$H$_{12}$N$_2$)Cu$_2$Cl$_6$ and its chemically disordered derivatives (C$_4$H$_{12}$N$_2$)Cu$_2$(Cl$_{1-x}$Br$_{x}$)$_6$ are systematically studied in magnetic fields of up to 45 T, as a function of Br concentration. The corresponding field-temperature and field-concentration phase diagrams are determined. Measurements on the disorder-free parent compound are not fully consistent with previously published results by other authors [PRL{\bf 96}, 257203 (2006)]. The effect of Br/Cl substitution on the magnetic properties is superficially similar to that of finite temperature. However, important differences are identified and discussed with reference to the previously studied magnetic excitation spectra.