Spin-Orbital Singlet and Quantum Critical Point on the Diamond Lattice:FeSc2S4

We present a theory of spin and orbital physics in the $A$-site spinel compound ${\mathrm{FeSc}}_2{\mathrm{S}}_4$, which experimentally exhibits a broad “spin-orbital liquid” regime. A spin-orbital Hamiltonian is derived from a combination of microscopic consideration and symmetry analysis. We demonstrate a keen competition between spin-orbit interactions, which favor formation of a local “spin-orbital singlet,” and exchange, which favors magnetic and orbital ordering. Separating the spin-orbital singlet from the ordered state is a quantum critical point. We argue that ${\mathrm{FeSc}}_2{\mathrm{S}}_4$ is close to this quantum critical point on the spin-orbital singlet side. The full phase diagram includes a commensurate-incommensurate transition within the ordered phase. A variety of comparisons to and suggestions for experiments are discussed.