Spin and Orbital Frustration in ${\mathrm{MnSc}}_2{\mathrm{S}}_4$ and ${\mathrm{FeSc}}_2{\mathrm{S}}_4$

Crystal structure, magnetic susceptibility, and specific heat were measured in the normal cubic spinel compounds ${\mathrm{MnSc}}_2{\mathrm{S}}_4$ and ${\mathrm{FeSc}}_2{\mathrm{S}}_4$. Down to the lowest temperatures, both compounds remain cubic and reveal strong magnetic frustration. Specifically the Fe compound is characterized by a Curie-Weiss (CW) temperature ${\Theta }_{\mathrm{CW}}=-45\mathrm{K}$ and does not show any indications of order down to 50 mK. In addition, the Jahn-Teller ion ${\mathrm{Fe}}^{2+}$ is orbitally frustrated. Hence, ${\mathrm{FeSc}}_2{\mathrm{S}}_4$ belongs to the rare class of spin-orbital liquids. ${\mathrm{MnSc}}_2{\mathrm{S}}_4$ is a spin liquid for temperatures $T>T_N\approx 2\mathrm{K}$.

Figure 1

Diffraction pattern of ${\mathrm{MnSc}}_2{\mathrm{S}}_4$ (upper frame) and ${\mathrm{FeSc}}_2{\mathrm{S}}_4$ (lower frame). The solid lines represent fits of a Rietveld analysis. The difference spectra shown below the data demonstrate the absence of any impurity phases. Inset: [333] reflection at 100 and 200 K, respectively.

Figure 2

Inverse susceptibility $1/\chi (T)$ of ${\mathrm{MnSc}}_2{\mathrm{S}}_4$ (triangles up) and ${\mathrm{FeSc}}_2{\mathrm{S}}_4$ (triangles down). The solid lines are linear fits with a Curie-Weiss law $\chi =C/(T-{\Theta }_{\mathrm{CW}})$. Upper inset: FC and ZFC susceptibility loop measured in ${\mathrm{FeSc}}_2{\mathrm{S}}_4$ at 10 Oe. Lower inset: susceptibility $\chi (T)$ vs $T$ at low temperatures.

Figure 3

Specific heat $C(T)/T$ for ${\mathrm{MnSc}}_2{\mathrm{S}}_4$ (triangles up), ${\mathrm{FeSc}}_2{\mathrm{S}}_4$ (triangles down), and ${\mathrm{CdIn}}_2{\mathrm{S}}_4$ (circles). The solid line represents the calculated specific heat of the nonmagnetic reference compound ${\mathrm{CdIn}}_2{\mathrm{S}}_4$. The dashed line gives the estimated phonon contribution for $A{\mathrm{Sc}}_2{\mathrm{S}}_4$ ($A=\mathrm{Mn},\mathrm{Fe}$).

Figure 4

(a) Magnetic contribution of the specific heat $C_m/T$ vs $T$ for ${\mathrm{MnSc}}_2{\mathrm{S}}_4$ and ${\mathrm{FeSc}}_2{\mathrm{S}}_4$. (b) Magnetic entropy of ${\mathrm{MnSc}}_2{\mathrm{S}}_4$ and ${\mathrm{FeSc}}_2{\mathrm{S}}_4$. The horizontal lines give the magnetic entropy $S_{\mathrm{m}}$ which is theoretically expected for the spin and orbital degrees of freedom (see text).