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

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 $\xi /(\text{a}/2)\approx 8.2$ (where $\text{a}/2$ is the nearest neighbor lattice constant) which establishes FeSc${}_2$S${}_4$ as a SOL with long-range entanglement.

5 Pages, 4 Figures