Quantum Criticality in FeSc$_2$S$_4$

Despite possessing a local spin $2$ moment on the iron site and a Curie-Weiss temperature of $45K$, the A site spinel FeSc$_2$S$_4$ does not magnetically order down to 50mK. Previous theoretical work by Chen and Balents advanced an explanation for this observation in the form of the ``$J_2$-$\lambda$'' model which places FeSc$_2$S$_4$ close to a quantum critical point on the disordered side 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 the magnetization. We present new theoretical studies of the optical properties of the $J_2$-$\lambda$ model, including a computation of the dispersion relation for the quasiparticle excitations and the form of the collective response to electric field. We argue that the latter directly probes a low energy excitation continuum characteristic of quantum criticality, and that our results reinforce the consistency of this model with experiment.