Experimental and theoretical investigations of strongly correlated ${\mathrm{FeSb}}_{2-x}{\mathrm{Sn}}_x$

Thermopower, resistivity, and heat capacity have been measured on eight Sn-substituted ${\mathrm{FeSb}}_{2-x}{\mathrm{Sn}}_x$ samples with $x=0–0.15$. A giant peak in the low temperature thermopower of ${\mathrm{FeSb}}_2$ is observed and is similar to what is found in the Kondo insulator $\mathrm{FeSi}$. The ab initio calculated band structure of ${\mathrm{FeSb}}_2$ shows striking similarities to that of $\mathrm{FeSi}$. For the samples with Sn substitution the data indicate that as the Sn content increases ${\mathrm{FeSb}}_{2-x}{\mathrm{Sn}}_x$ evolves from a Kondo insulator into a heavy fermion metal similar to what is observed for ${\mathrm{FeSi}}_{1-x}{\mathrm{Al}}_x$.

Figure 1

(Color online) Structure of ${\mathrm{FeSb}}_2$. Red (dark) atoms are Fe and white atoms are Sb. The unit cell is orthorhombic with $a=5.83\mathrm{\AA }$, $b=6.54\mathrm{\AA }$, and $c=3.20\mathrm{\AA }$ and the structure belongs to space group No. 58 (Pnnm). The Sb atoms are tetrahedrally coordinated by three Fe atoms and one Sb atom. The Fe atoms are octahedrally coordinated by six Sb atoms. The $\mathrm{Fe}\text{−}\mathrm{Sb}$ and $\mathrm{Sb}\text{−}\mathrm{Sb}$ dimer (dark, blue) bonds are $2.58\mathrm{\AA }$, $2.60\mathrm{\AA }$, and $2.88\mathrm{\AA }$, respectively. There are no direct $\mathrm{Fe}\text{−}\mathrm{Fe}$ bonds and the shortest $\mathrm{Fe}\text{−}\mathrm{Fe}$ distance is $3.20\mathrm{\AA }$. The unit cell contains two formula units.

Figure 2

(Color online) X-ray powder diffraction patterns of ${\mathrm{FeSb}}_{2-x}{\mathrm{Sn}}_x$ with $x=0$ (black), 0.03 (red), and 0.12 (blue). Vertical bars indicate the position and magnitude of the theoretical peaks for ${\mathrm{FeSb}}_2$. Arrows indicate the position of the two strongest diffraction peaks of the $\mathrm{SbSn}$ alloy.

Figure 3

Lattice parameters and unit cell volume for ${\mathrm{FeSb}}_{2-x}{\mathrm{Sn}}_x$ as function of $x$ (the nominal stoichiometry).

Figure 4

(Color online) The main panel shows the density of states $\left(g\right)$ of ${\mathrm{FeSb}}_2$ as a function of electron energy $\left(\epsilon \right)$. The straight dotted line represents the Fermi level $\left({\epsilon }_{\mathrm{F}}\right)$. Inset is a replot of the same data in the vicinity of the Fermi level, a nonzero $g\left({\epsilon }_{\mathrm{F}}\right)$ is observed. The unit cell contain two ${\mathrm{FeSb}}_2$ formula units.

Figure 5

(Color online) Projected density of states with respect to a coordinate system with the $z$ axis parallel to the short $\mathrm{Fe}\text{−}\mathrm{Sb}$ bond and the $x$ axis parallel to the long $\mathrm{Fe}\text{−}\mathrm{Sb}$ bond (the “chemical axes” in Table ). The straight dotted line represents the Fermi level.

Figure 6

Resistivity $\left(\rho \right)$ as function of temperature $\left(T\right)$ for the ${\mathrm{FeSb}}_{2-x}{\mathrm{Sn}}_x$ samples. Inset shows ${\rho }_{3K}∕{\rho }_{300\mathrm{K}}$ as a function of $x$. The solid line is a guide to the eye. The second inset is an Arrhenius plot of $\rho \left(T\right)$ for the $x=0$ sample. The solid line is a linear fit to data above $50\mathrm{K}$ with an activation energy of $265\mathrm{K}$.

Figure 7

Thermopower $\left(S\right)$ as function of temperature $\left(T\right)$ for the ${\mathrm{FeSb}}_{2-x}{\mathrm{Sn}}_x$ samples. Upper inset is a replot of the same data with a much reduced $y$ scale. Lower inset shows $S$ as a function of $x$ at $50\mathrm{K}$ and $200\mathrm{K}$ (note the broken $y$ axis).

Figure 8

Sommerfeld coefficient $\left(\gamma \right)$ of ${\mathrm{FeSb}}_{2-x}{\mathrm{Sn}}_x$ as a function of $x$. Dotted curve is a guide to the eye. Inset shows the specific heat divided by temperature $(C_p∕T)$ as a function of $T^2$ at lowest temperatures. Linear fits (not shown) to the curves are used to extract $\gamma$ with the relation $C_p∕T=\gamma +\beta T^2$.

Figure 9

Specific heat $\left(C_p\right)$ per mole ${\mathrm{FeSb}}_{2-x}{\mathrm{Sn}}_x$ as function of temperature $\left(T\right)$ for $x=0$ and $x=0.15$. The dotted line is the classical Dulong Petit value $3NR=74.8\mathrm{J}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$. Inset shows the same data in the high temperature region. The solid curve is a Debye model calculation with three atoms per unit cell and a Debye temperature of $340\mathrm{K}$. The dashed curve is a sum between the Debye model and the contribution from two narrow bands where the total density per band is 2.96 states per unit cell (1.48 per formula unit), the band gap is $862\mathrm{K}$, and the band width is $295\mathrm{K}$, see Ref. 27.