Singlet-Triplet Excitations and Long-Range Entanglement in the Spin-Orbital Liquid Candidate FeSc2S4

Theoretical models of the spin-orbital liquid (SOL) FeSc2S4 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 FeSc2S4 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 threefold splitting of this excitation is observed as a function of applied magnetic field. As singlet-triplet excitations are typically not allowed in pure spin systems, our results demonstrate the entangled spin and orbital character of singlet ground and triplet excited states. Using experimentally obtained parameters we compare to existing theoretical models to determine FeSc2S4's proximity to the quantum critical point. In the context of these models, we estimate the characteristic length of the singlet correlations to be ξ/(a/2)≈8.2 (where a/2 is the nearest neighbor lattice constant), which establishes FeSc2S4 as a SOL with long-range entanglement.