Singlet-triplet excitations and long range entanglement in the spin-orbital liquid candidate FeSc$_2$S$_4$*

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. Using experimentally obtained parameters we compare to existing theoretical models to determine FeSc$_2$S$_4$'s proximity to the quantum critical point and establish FeSc$_2$S$_4$ as a SOL with long-range entanglement.