Evidence for spin liquid behavior in the frustrated three-dimensional $S=1/2$ Heisenberg garnet NaCa${}_2$Cu${}_2$(VO${}_4$)${}_3$

Abstract

Three-dimensional quantum spin liquids have remained elusive, hindered by reduced quantum fluctuations from larger lattice connectivity inherent to high-dimensional systems. Here, we investigate the remarkable persistence of dynamical short-range magnetic correlations in the nearly body-centered cubic garnet NaCa${}_2$Cu${}_2$(VO${}_4$)${}_3$ down to $T=50$ mK, two orders of magnitude below its Curie-Weiss temperature. Using a combination of neutron and muon spectroscopies plus numerical simulations, we demonstrate that a dynamical regime emerges, characterized by a dual response in the inelastic spectrum composed of short-live dispersive excitations and a quasi-elastic component. Strongly frustrated exchange interactions combined with subtle temperature-dependent Jahn-Teller spin-lattice effects are a plausible mechanism to explain the origin of this spin-liquid behavior.

10 pages, 4 figures. Supplemental Material: 5 pages, 6 figures