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Frustrated magnetism on the kagome lattice has been a fertile ground for richand fascinating physics, ranging from experimental evidence of a spin liquid totheoretical predictions of exotic superconductivity. Among experimentallyrealized spin-$\frac{1}{2}$ kagome magnets, herbertsmithite, kapellasite, andhaydeeite [(Zn,Mg)Cu$_{3}$(OH)$_{6}$Cl$_{2}$] are all well described by athree-parameter Heisenberg model, but they exhibit distinctly differentphysics. We address the problem using a pseudofermion functionalrenormalization-group approach and analyze the low-energy physics in theexperimentally accessible parameter range. Our analysis places kapellasite andhaydeeite near the boundaries between magnetically ordered and disorderedphases, implying that slight modifications could dramatically affect theirmagnetic properties. Inspired by this, we perform \textit{ab initio} densityfunctional theory calculations of (Zn,Mg,Cd)Cu$_{3}$ (OH)$_{6}$Cl$_{2}$ atvarious pressures. Our results suggest that by varying pressure and compositionone can traverse a paramagnetic regime between different magnetically orderedphases.

Paramagnetism in the kagome compounds (Zn,Mg,Cd)Cu$_{3}$(OH)$_{6}$Cl$_{2}$