Evidence for spin liquid behavior in the frustrated three-dimensional $S = 1/2$ Heisenberg garnet NaCa$_{2}$Cu$_{2}$(VO$_{4}$)$_{3}$

TL;DR

This study provides evidence for a three-dimensional quantum spin liquid state in a garnet material, showing persistent magnetic correlations and unusual excitations at very low temperatures, challenging the notion that such states are rare in high-dimensional systems.

Contribution

The paper demonstrates the existence of spin liquid behavior in a 3D garnet, supported by neutron and muon spectroscopy, and introduces the role of frustration and Jahn-Teller effects in stabilizing this state.

Findings

Persistent short-range magnetic correlations down to 50 mK.

Observation of dual response with dispersive and quasi-elastic excitations.

Frustrated exchange interactions and Jahn-Teller effects likely drive the spin liquid behavior.

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.