Singlet-triplet excitations and long range entanglement in the spin-orbital liquid candidate FeSc2S4

TL;DR

This study investigates the magnetic excitations of FeSc2S4, revealing singlet-triplet excitations and long-range entanglement indicative of a spin-orbital liquid near a quantum critical point.

Contribution

It provides experimental evidence of singlet-triplet excitations and long-range entanglement in FeSc2S4, supporting its classification as a spin-orbital liquid close to quantum criticality.

Findings

Observation of a singlet-triplet excitation with three-fold splitting under magnetic field.

Demonstration of non-trivial entangled spin-orbital ground state.

Estimation of long-range singlet correlations with a length scale of approximately 8.2 lattice units.

Abstract

Theoretical models of the spin-orbital liquid (SOL) FeSc$_2$S$_4$ have predicted it to be in close proximity to a quantum critical point separating a spin-orbital liquid phase from a long-range ordered magnetic phase. Here, we examine the magnetic excitations of FeSc$_2$S$_4$ through time-domain terahertz spectroscopy under an applied magnetic field. At low temperatures an excitation emerges that we attribute to a singlet-triplet excitation from the SOL ground state. A three-fold splitting of this excitation is observed as a function of applied magnetic field. As singlet-triplet excitations are forbidden in inversion symmetric pure spin systems, our results demonstrate the non-trivial character of the entangled spin-orbital singlet ground state. Using experimentally obtained parameters we compare to existing theoretical models to determine FeSc$_2$S$_4$'s proximity to the quantum critical point. In the context of these models, we estimate that the characteristic length of the singlet correlations to be $\xi/ (\textbf{a}/2) \approx 8.2$ (where $\textbf{a}/2$ is the nearest neighbor lattice constant) which establishes FeSc$_2$S$_4$ as a SOL with long-range entanglement.