Lattice dynamics in the FeSb${}_3$ skutterudite

Thin films of FeSb${}_3$ were characterized by electronic transport, magnetometry, x-ray diffraction, ${}^{57}$Fe and ${}^{121}$Sb nuclear inelastic scattering, and ${}^{57}$Fe Mössbauer spectroscopy. Resistivity and magnetometry measurements reveal semiconducting behavior with a 16.3(4) meV band gap and an effective paramagnetic moment of 0.57(6) ${\mu }_{\mathrm{B}}$, respectively. A systematic comparison of the lattice dynamics with CoSb${}_3$ and EuFe${}_4$Sb${}_{12}$ reveals that the Fe${}_4$Sb${}_{12}$ framework is softer than the Co${}_4$Sb${}_{12}$ framework, and that the observed softening and the associated lowering of the lattice thermal conductivity in the $R$Fe${}_4$Sb${}_{12}$ filled skutterudites are not only related to the filler but also to the Fe${}_4$Sb${}_{12}$ framework.

Figure 1

Electrical resistivity ${\rho }_{\mathit{el}}$ of FeSb${}_3$ obtained between 10 and 300 K on a crack-free sample; the errors are the size of the data points. The inset shows the fit between 220 and 300 K that yields an energy gap of 16.3(4) meV; see text.

Figure 2

The molar magnetic susceptibility and the inverse susceptibility obtained at 0.25 T between 10 and 300 K for FeSb${}_3$ shown as red circles, and the molar magnetic susceptibility for CoSb${}_3$ shown as green triangles, after corrections; see text. The errors are the size of the data points. Inset: the effective magnetic moment of FeSb${}_3$.

Figure 3

Hysteresis loop of FeSb${}_3$ measured at 300 K. The negative slope is indicative of diamagnetic behavior. The inset shows the hysteresis loop obtained after the diamagnetic correction that is discussed in the text.

Figure 4

X-ray diffraction pattern of FeSb${}_3$ obtained at 10 K (red dots), the corresponding Rietveld refinement (black line), the difference plot (blue line), and the peak positions for FeSb${}_3$ and Si (green ticks). Inset: A quarter of the corresponding detector image.

Figure 5

The structure of unfilled CoSb${}_3$ or FeSb${}_3$ (left) and filled $R$Fe${}_4$Sb${}_{12}$ (right) skutterudite. Co or Fe, Sb, and $R$ are shown in red, blue, and yellow, respectively. The blue rectangle indicates one of the Sb rings; see text.

Figure 6

Top: The temperature dependence of the lattice parameter $a$ for FeSb${}_3$ (red) and CoSb${}_3$ (green), and the corresponding polynomial fit (black). Bottom: The thermal expansion coefficient $\alpha$ of FeSb${}_3$ and CoSb${}_3$.

Figure 7

Top: The Mössbauer spectra of FeSb${}_3$ obtained on a 1.5 $\mu$m film. Bottom: The fit parameters obtained from the spectra of the $\sim$1 and $\sim$1.5 $\mu$m films (open and closed symbols), respectively. The errors are the size of the symbols. The crossed square indicates the $f_{\mathit{LM}}$ obtained directly from the ${}^{57}$Fe NIS at 295 K. The dashed line indicates the second-order Doppler shift obtained from the DPS; see text. The lines for the Doppler shift and $f_{\mathit{LM}}$ are Debye model fits.[41] The lines for $\Delta E_Q$ and $\Gamma$ are quadratic polynomial fits given as a guide for the eye.

Figure 8

The nuclear inelastic scattering (NIS) spectra and the instrumental functions (dashed lines) measured by nuclear forward scattering (NFS) obtained with the ${}^{57}$Fe resonance of FeSb${}_3$ (top graph) and with the ${}^{121}$Sb resonance of FeSb${}_3$, CoSb${}_3$, and EuFe${}_4$Sb${}_{12}$ (bottom three graphs).

Figure 9

Comparison of the DPS measured with the ${}^{57}$Fe resonance at 295 K for FeSb${}_3$ and EuFe${}_4$Sb${}_{12}$ (top) and with the ${}^{121}$Sb resonance at 25 K for FeSb${}_3$, CoSb${}_3$, and EuFe${}_4$Sb${}_{12}$ (bottom). The insets show the reduced partial DPS $g\left(E\right)/E^2$ in units of 10${}^{-4}/$meV${}^3$, and the low-energy fit between 0 and 4 meV for the Debye levels, indicated by the same type of lines. The differences in the Debye levels for Fe and Sb in FeSb${}_3$ and EuFe${}_4$Sb${}_{12}$ are due to the different masses of the elements; see Eq. (1).

Figure 10

A comparison of the total heat capacity, calculated from the DPS of FeSb${}_3$ (red solid lines) and from the DPS and theoretical calculations for CoSb${}_3$ (green dash-dotted lines), and the macroscopic measured heat capacity of CoSb${}_3$ (blue dotted lines).