Vibronic and Magnetic Excitations in the Spin-Orbital Liquid State of ${\mathrm{FeSc}}_2{\mathrm{S}}_4$

Inelastic neutron scattering results on the spin-orbital liquid in ${\mathrm{FeSc}}_2{\mathrm{S}}_4$ are presented. This sulfospinel reveals strong geometric frustration in the spin and in the orbital sector. In the present experiments the orbital liquid is evidenced by a clear spectroscopic signature of a dynamic Jahn-Teller effect with a vibronic splitting $3\Gamma \approx 2\mathrm{meV}$ in agreement with theoretical estimates. The excitations of the spin liquid reveal strong dispersion and can be characterized as cooperative spin excitations in a supercooled paramagnet with a spin gap of $\Delta \approx 0.2\mathrm{meV}$.

Figure 1

Coordination polyhedra of the spinel structure of ${\mathrm{FeSc}}_2{\mathrm{S}}_4$. $A$-site Fe (red) is embedded in a tetrahedral environment of sulfur (yellow), while $B$-site Sc has octahedral environment (left part). The $A$-site exchange is mediated via three different Fe-S-Sc-S-Fe interaction paths. A plaquette containing nearest, next nearest, and next-next nearest neighbors of the $A$-site sublattice with corresponding exchange constants $J$, $J^{\prime }$, and $J^{\prime \prime }$ is shown at the right.

Figure 2

Contour plot $S(Q,\omega )$ of ${\mathrm{FeSc}}_2{\mathrm{S}}_4$ obtained by inelastic neutron scattering with an incident neutron energy of 17 meV at $T=1.6\mathrm{K}$.

Figure 3

$S(Q,\omega )$ of ${\mathrm{FeSc}}_2{\mathrm{S}}_4$ at constant $Q=1.1{\AA }^{-1}$ at $T=80\mathrm{K}$ (blue triangles) and at $T=1.6\mathrm{K}$ (red circles) as derived from Fig. 2. The full black line is a fit to the data employing an elastic Gaussian and a single inelastic Lorentzian line, multiplied by the detailed balance factor and convoluted with the instrumental resolution. Inset: the dynamic Jahn-Teller effect is illustrated by the vibronic splitting $3\Gamma$ of electronic configuration in addition to the conventional crystal-field splitting.

Figure 4

Contour plot of $S(Q,\omega )$ of ${\mathrm{FeSc}}_2{\mathrm{S}}_4$ in the low-$Q$ and low-energy region at $T=80\mathrm{K}$ (upper panel) and $T=1.6\mathrm{K}$ (lower panel). The full lines indicate a constant-$Q$ scan at $0.6{\AA }^{-1}$ and a constant-energy scan at $\hslash \omega =1.6\mathrm{meV}$, respectively, shown in Fig. 5.

Figure 5

Constant-energy scan at $\hslash \omega =1.6\mathrm{meV}$ and $T=1.6\mathrm{K}$ (upper panel) and constant-$Q$ scans at $0.6{\AA }^{-1}$ for various temperatures (lower panel), respectively.