Abstract
The orbitally degenerate $A$-site spinel compound ${\text{FeSc}}_{2}{\text{S}}_{4}$ has been experimentally identified as a ``spin-orbital liquid,'' with strong fluctuations of both spins and orbitals. Assuming that the second-neighbor spin-exchange ${J}_{2}$ is the dominant one, we argued in a recent theoretical study [G. Chen et al., Phys. Rev. Lett. 102, 096406 (2009)] that ${\text{FeSc}}_{2}{\text{S}}_{4}$ is in a local ``spin-orbital singlet'' state driven by spin-orbit coupling, close to a quantum critical point, which separates the spin-orbital singlet phase from a magnetically and orbitally ordered phase. In this paper, we refine further and develop this theory of ${\text{FeSc}}_{2}{\text{S}}_{4}$. First, we show that inclusion of a small first-neighbor exchange ${J}_{1}$ induces a narrow region of incommensurate phase near the quantum critical point. Next, we derive the phase diagram in the presence of an external magnetic field $B$, and show that the latter suppresses the ordered phase. Lastly, we compute the field-dependent dynamical magnetic susceptibility $\ensuremath{\chi}(\mathbf{k},\ensuremath{\omega};B)$, from which we extract a variety of physical quantities. Comparison with and suggestions for experiment are discussed.
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