Polaronic transport and thermoelectricity in ${\mathbf{Fe}}_{1-x}{\mathbf{Co}}_x{\mathbf{Sb}}_2{\mathbf{S}}_4$ ($x=0$, 0.1, and 0.2)

We report a study of Co-doped berthierite ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{\mathrm{Sb}}_2{\mathrm{S}}_4$ ($x=0$, 0.1, and 0.2). The alloy series of ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{\mathrm{Sb}}_2{\mathrm{S}}_4$ crystallize in an orthorhombic structure with the Pnma space group, similar to ${\mathrm{FeSb}}_2$, and show semiconducting behavior. The large discrepancy between activation energy for conductivity, $E_{\rho }$ (146 $\sim 270\mathrm{meV}$), and thermopower, $E_S$ (47 $\sim 108\mathrm{meV}$), indicates the polaronic transport mechanism. Bulk magnetization and heat-capacity measurements of pure ${\mathrm{FeSb}}_2{\mathrm{S}}_4$ ($x=0$) exhibit a broad antiferromagnetic transition ($T_N=46\mathrm{K}$) followed by an additional weak transition ($T^{*}=50\mathrm{K}$). Transition temperatures ($T_N$ and $T^{*}$) slightly decrease with increasing Co content $x$. This is also reflected in the thermal conductivity measurement, indicating strong spin-lattice coupling. ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{\mathrm{Sb}}_2{\mathrm{S}}_4$ shows relatively high value of thermopower (up to $\sim 624\mu \mathrm{V}{\mathrm{K}}^{-1}$ at 300 K) and thermal conductivity much lower when compared to ${\mathrm{FeSb}}_2$, a feature desired for potential applications based on ${\mathrm{FeSb}}_2$ materials.

Figure 1

(a) Crystal structure. (b) Fourier-transform magnitudes of the extended x-ray absorption fine structure (EXAFS) data of ${\mathrm{FeSb}}_2{\mathrm{S}}_4$ measured at room temperature. The experimental data are shown as blue symbols alongside the model fit plotted as a red line. Inset in (b) shows the corresponding EXAFS oscillation with the model fit.

Figure 2

(a) Powder x-ray diffraction (XRD) patterns for ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{\mathrm{Sb}}_2{\mathrm{S}}_4$ ($x=0$, 0.1, and 0.2). Impurity peak of CoSbS is labeled by an asterisk. (b) The evolution of lattice parameters $a, b$, and $c$.

Figure 3

(a) Temperature-dependent electrical resistivity $\rho \left(T\right)$ of ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{\mathrm{Sb}}_2{\mathrm{S}}_4$ ($x=0$, 0.1, and 0.2). (b) $\ln (\rho /T$) vs $1000/T$ curves fitted by the adiabatic small polaron hopping model, $\rho \left(T\right)=AT\text{exp}(E_{\rho }/k_{B}T)$, where $E_{\rho }$ is activation energy and $k_B$ is Boltzmann constant. Inset: The evolution of $E_{\rho }$. (c) Temperature-dependent thermopower $S\left(T\right)$ of ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{\mathrm{Sb}}_2{\mathrm{S}}_4$ ($x=0$, 0.1, and 0.2). Inset: the values of thermopower at room temperature. (d) $S\left(T\right)$ vs $1000/T$ curves fitted using $S\left(T\right)=(k_B/e)(\alpha +E_S/k_{B}T)$, where $E_S$ is activation energy. Inset: The evolution of $E_S$.

Figure 4

(a) Temperature-dependent magnetic susceptibility obtained at $H=5\mathrm{T}$ with zero-field cooling (ZFC) and field cooling (FC) modes. (b) $1/\chi$ vs $T$ fitted by the modified Curie-Weiss law $\chi ={\chi }_0+\frac{C}{T-\theta }$, where ${\chi }_0$ is the temperature-independent susceptibility, $C$ is the Curie-Weiss constant, and $\theta$ is the Weiss temperature. (c) $d\left(\chi T\right)/dT$ vs $T$ curves. The solid and dashed lines are guides to the eye. (d) The hysteresis loops taken at $T=2\mathrm{K}$ of ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{\mathrm{Sb}}_2{\mathrm{S}}_4$ ($x=0$, 0.1, and 0.2). Inset: The magnification in the low field region and the evolution of coercive field $H_c$.

Figure 5

Temperature-dependent thermal conductivity $\kappa \left(T\right)$ of ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{\mathrm{Sb}}_2{\mathrm{S}}_4$ ($x=0$, 0.1, and 0.2). Inset: $d\left(\kappa T\right)/dT$ vs $T$ curves. The solid line is guide to the eye.

Figure 6

Temperature-dependent heat capacity of ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{\mathrm{Sb}}_2{\mathrm{S}}_4$ ($x=0$, 0.1, and 0.2). Insets: The enlargement of the specific-heat anomaly between 36 K and 60 K, and the evolution of transition temperatures ($T_N$ and $T^{*}$) and Debye temperature (${\mathrm{\Theta }}_D$) as a function of Co content $x$.

Figure 7

Density of states and band structure of ${\mathrm{FeSb}}_2{\mathrm{S}}_4$ using experimental values (a), (b) and DFT-relaxed lattice parameters (c), (d). The states with Fe $d$, S $p$, and Sb $p$ character are denoted by thick red, medium blue, and thin green lines, respectively. Inset in (a) shows the sketch of the ${\mathrm{FeSb}}_2{\mathrm{S}}_4$ Brillouin zone.