Phonon-drag effect in ${\mathrm{FeGa}}_3$

The thermoelectric properties of single-crystalline and polycrystalline ${\mathrm{FeGa}}_3$ are systematically investigated over a wide temperature range. At low temperatures, below 20 K, previously not known pronounced peaks in the thermal conductivity $(400–800\text{W}{\mathrm{K}}^{-1}$ ${\mathrm{m}}^{-1})$ with corresponding maxima in the thermopower (in the order of $-16000$ $\mu \text{V}$ ${\mathrm{K}}^{-1}$) were found in single-crystalline samples. Measurements in single crystals along [100] and [001] directions indicate only a slight anisotropy in both the electrical and thermal transports. From susceptibility and heat-capacity measurements, a magnetic or structural phase transition was excluded. Using density functional theory based calculations, we have revisited the electronic structure of ${\mathrm{FeGa}}_3$ and compared the magnetic (including correlations) and nonmagnetic electronic densities of states. Thermopower at fixed carrier concentrations is calculated using semiclassical Boltzmann transport theory, and the calculated results match fairly with our experimental data. The inclusion of strong electron correlations treated in a mean field manner (by LSDA + $U$) does not improve this comparison, rendering strong correlations as the sole explanation for the low-temperature enhancement unlikely. Eventually, after a careful review, we assign the peaks in the thermopower as a manifestation of the phonon-drag effect, which is supported by thermopower measurements in a magnetic field.

Figure 1

Secondary electron microstructure pictures of ${\mathrm{FeGa}}_3$ specimens: (a) flux-grown single crystal, (b) polycrystalline specimen after SPS of flux-grown single crystal, (c) single crystal obtained from Czochralski method and oriented along [001], and (d) single crystal obtained from Czochralski method and oriented along [100].

Figure 2

Tetragonal crystal structure of ${\mathrm{FeGa}}_3$ according to Ref. [19]. The large (gray) atoms are Fe, while the smaller (Ga1, red; Ga2, light blue) atoms are Ga [Fe at $4f$ (0.3437,0.3437,0); Ga1 at $4c$ (0,0.5,0); Ga2 at $8j$ (0.1556,0.1556,0.2620)]. The polyhedra surrounding the Fe atom are composed of eight Ga atoms: two nearest-neighbor Ga at a distance of 2.37 Å (Ga1), two next-nearest-neighbor Ga at a distance of 2.39 Å (Ga2), and four third-nearest-neighbor Ga at a distance of 2.50 Å (Ga2). Each Fe atom also has one another Fe atom at a distance of 2.77 Å, forming so-called “dimers” in the (001) plane. The polyhedrons of the iron atoms belonging to the same “dimer” are sharing a common face, while polyhedrons of different “dimers” are corner sharing.

Figure 3

Electrical resistivity in dependence on the temperature for single-crystalline and polycrystalline ${\mathrm{FeGa}}_3$ specimens. For comparison, single-crystal data [3] are included in the inset. Band-gap calculation with the Arrhenius law $\rho$($T$) = exp($Eg/2k{}_{B}T$) gives energy gaps of 0.38–0.51 eV.

Figure 4

Charge carrier concentration $n$ as a function of temperature for the oriented ${\mathrm{FeGa}}_3$ single crystals (Czochralski method).

Figure 5

Top: Temperature dependence of the thermal conductivity for ${\mathrm{FeGa}}_3$ specimens. The inset represents the contribution of the electronic part to the total thermal conductivity estimated with the Wiedemann-Franz law ${\kappa }_{\mathrm{el}}$ = $\rho$ $L_0$ $T$. Bottom: Seebeck coefficient of ${\mathrm{FeGa}}_3$ specimens depending on the temperature. The inset shows high values for the flux-grown single crystal. The black solid curve in the inset represents the error for the Seebeck coefficient measurement, with $\Delta T$ = ${10}^{-3}$ K.

Figure 6

Nonmagnetic total and site-projected electronic density of states of ${\mathrm{FeGa}}_3$.

Figure 7

Comparison of the nonmagnetic LDA and the AFM LSDA + $U$ band structures of ${\mathrm{FeGa}}_3$. The nearest-neighbor Fe atoms are ordered antiferromagnetically in the LSDA + $U$ calculation. A $U$ value of 2 eV and a $J$ value of 0.625 eV were used.

Figure 8

Calculated thermopower as a function of temperature for ${\mathrm{FeGa}}_3$ for the two scenarios: LDA (nonmagnetic) and LSDA + $U$ (antiferromagnetic, $U=2$ eV). There is a significant difference in the calculated thermopower between LDA and LSDA + $U$, with the LDA curve being more in accordance with the experimentally measured thermopower.

Figure 9

Top: Magnetic field dependence of the specific heat for a ${\mathrm{FeGa}}_3$ single crystal (Czochralski method) oriented along [001] in zero field (ZF) and high field $(H=9$ T). The inset shows a log-log plot. Bottom: Specific-heat data below 10 K in a $C_p/T$ vs $T^2$ representation resulting in a Sommerfeld coefficient of $\gamma =0.03$ mJ ${\mathrm{mol}}^{-1}$ ${\mathrm{K}}^{-1}$.

Figure 10

Top: Temperature dependence of magnetic susceptibility for ${\mathrm{FeGa}}_3$ single crystal (Czochralski method) oriented along [001] and powder made of the single crystal (flux grown), which was additionally washed with hydrochloric acid in (top) low external field of $H=0.1$ T and (bottom) high external fields of 3.5 and 7.0 T. The inset in the upper panel shows the magnification of temperatures below 20 K.

Figure 11

Comparison of the measured Seebeck coefficient with the calculated values of the diffusive $\left(S_d\right)$ and phonon-drag $\left(S_p\right)$ parts as a function of temperature for a single crystal of ${\mathrm{FeGa}}_3$ (Czochralski method) along [100]. The $S_p$ term dominates the low-temperature regime, indicative of a significant phonon-drag effect in this system.

Figure 12

Temperature dependence of the Seebeck coefficient for a single crystal of ${\mathrm{FeGa}}_3$ (Czochralski method) oriented along the [100] direction, measured both at 0- and 9-T magnetic fields. The magnetic field was applied along [100], parallel to the crystallographic orientation. The lack of significant changes in $S$ at 0 and 9 T supports the nonelectronic origin of the colossal low-temperature values and thus can be attributed to phonon-drag mechanism. The slight difference in the thermopower data compared to Fig. 5 is due to the change in the shape of the sample to improve the heat flow (see inset).