The three-dimensional $S=\frac{1}{2}$ system ${\mathrm{Y}}_3{\mathrm{Cu}}_2{\mathrm{Sb}}_3{\mathrm{O}}_{14}$ consists of two inequivalent ${\mathrm{Cu}}^{2+}$ sites, each forming an edge shared triangular lattice. Our magnetic susceptibility $\chi (T)$, specific heat $C_p(T)$, ${}^{89}\mathrm{Y}$ nuclear magnetic resonance (NMR), muon spin relaxation ($\mathrm{\mu }\mathrm{SR}$), and electron spin resonance (ESR) measurements on this system confirm the absence of any long-range magnetic ordering and the persistence of spin dynamics down to 0.077 K. In ${}^{89}\mathrm{Y}$ NMR, we find an anomaly at about 120 K, which we suggest arises from a fraction of the spins condensing into a singlet (a valence bond solid, or VBS) state. A plateau in the muon relaxation rate is observed between 60 K and 10 K (signifying the VBS state from a fraction of the spins) followed by an increase and another plateau below about 1 K (presumably signifying the quantum spin liquid state from all the spins). Our density functional theory calculations find a dominant antiferromagnetic interaction along the body diagonal with inequivalent Cu(1) and Cu(2) ions alternately occupying the corners of the cube. All other near-neighbor interactions between the Cu ions are also found to be antiferromagnetic and are thought to drive the frustration.

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• Quantum spin liquid
• Valence bond solid
• Density functional theory
• Muon spin relaxation & rotation
• Nuclear magnetic resonance
• Specific heat measurements
• Susceptibility measurements