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Despite possessing a local spin $2$ moment on the iron site and a Curie-Weisstemperature of $45K$, the A site spinel FeSc$_2$S$_4$ does not magneticallyorder down to 50mK. Previous theoretical work by Chen and Balents advanced anexplanation for this observation in the form of the "$J_2$-$\lambda$" modelwhich places FeSc$_2$S$_4$ close to a quantum critical point on the disorderedside of a quantum phase transition between a N\'{e}el ordered phase and a"Spin-Orbital Liquid" in which spins and orbitals are entangled, quenching themagnetization. We present new theoretical studies of the optical properties ofthe $J_2$-$\lambda$ model, including a computation of the dispersion relationfor the quasiparticle excitations and the form of the collective response toelectric field. We argue that the latter directly probes a low energyexcitation continuum characteristic of quantum criticality, and that ourresults reinforce the consistency of this model with experiment.

Theory of excitations and dielectric response at a spin-orbital quantum critical point