Novel Quantum Spin Liquid States in the $S=\frac{1}{2}$ Three-Dimensional Compound Y${}_3$Cu${}_2$Sb${}_3$O${}_{14}$

The three-dimensional $S=\frac{1}{2}$ system Y${}_3$Cu${}_2$Sb${}_3$O${}_{14}$ consists of two inequivalent Cu${}^{2+}$ sites, each forming an edge shared triangular lattice. Our magnetic susceptibility $\chi (T)$, specific heat $C_p(T)$, ${}^{89}$Y nuclear magnetic resonance (NMR), muon spin relaxation ($\text{upmu}\mathrm{S}\mathrm{R}$), 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 ${}^{89}$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 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-neighbour interactions between the Cu ions are also found to be antiferromagnetic and are thought to drive the frustration.