Thermodynamic, thermoelectric, and magnetic properties of FeSb${}_2$: A combined first-principles and experimental study

We analyze the thermodynamic, magnetic, and transport properties of the narrow band-gap semiconductor FeSb${}_2$ using density functional theory calculations corroborated by nuclear inelastic spectroscopy and ultrasound experiments. The vibrational properties (phonon spectrum, density of states, heat capacity) and elastic constants are computed through response function calculations and are in good agreements with the measurements. The electron-phonon coupling effects are also studied. The estimations of linewidth broadening due to electron-phonon coupling along the high-symmetry directions in the first Brillouin zone are given. The linewidth broadening reaches the largest value for Fe optical modes in the vicinity of the $X[0.5,0,0]$ point. The broadening, when compared to those obtained at the other symmetry points, differs by up to two orders of magnitude. From the Boltzmann theory applied to our electronic band structure, we investigate the electrical transport properties. It is found that a purely electronic structure description is incompatible with the record value of the Seebeck coefficient experimentally observed at $T\approx$ 12 K. The diamagnetic to paramagnetic crossover at a temperature around 100 K is also described from the calculation of the magnetic susceptibility, and results compare well with experiment.

Figure 1

Calculated electronic band structure and density of states of FeSb${}_2$ using GGA. The red dotted line indicates the Fermi level. The inset right figure shows the small direct band gap at the $R$ [0.5,0.5,0.5] point (corner of the first Brillouin zone), and the overlap between the maximum of the valence band, which is located at $R$ point and the minimum of the conduction band lying between the $\Gamma$ and $Z$ [0 0 0.5] points.

Figure 2

The temperature evolution of the magnetic susceptibility compared with experimental results extracted from Ref. 3. $\chi$ evolves from a constant value $=-4.{510}^{-5}$ emu/mol at low temperatures (diamagnetic region) toward positive values (paramagnetic region) above $T=80$ K.

Figure 3

Seebeck coefficient $S$ vs temperature $T$. The inset shows the low-temperature curve between 0 and 40 K for $S$.

Figure 4

Seebeck coefficient $S$ vs chemical potential $\mu$ at different temperatures. $S$ is very sensitive to small changes in $\mu$.

Figure 5

Calculated electrical resistivity $\rho$ vs temperature in a logarithmic scale. $\rho \left(T\right)$ is computed using a constant relaxation time $\tau =0.225$ ps for the whole temperature range.

Figure 6

Comparison of the DPS obtained by calculation (Theor.) and by NIS (Expt.) measured with the ${}^{57}$Fe resonance at 50 K and with the ${}^{121}$Sb resonance at 67 K. In the inset, the reduced partial DPS, $g\left(E\right)/\left(E^2\right)$, is shown in units of 10${}^{-4}/$meV${}^3$ with the low-energy fit, between 0 and 4 meV, for the Debye levels indicated by the same line style. The Debye level is proportional to the mass of the element and hence different for Fe and Sb.

Figure 7

Temperature dependence of the shear modulus $c_{44}$ in a sintered polycrystalline sample of FeSb${}_2$.

Figure 8

Plot of the specific heat of ${\mathrm{FeSb}}_2$ (full line) as a function of temperature. Results are in very good agreement with measurements (dotted line).

Figure 9

Calculated phonon spectrum of FeSb${}_2$ along the high-symmetry lines of the Brillouin zone. The points' size indicates the line broadening due to electron-phonon coupling.

Figure 10

Electron-phonon spectral function for FeSb${}_2$. The results are based on the calculated frequencies.