Thermoelectric properties of $\text{Ce}\left(\text{La}\right){\text{Fe}}_4{\text{Sb}}_{12}$ skutterudites under a magnetic field

We show that ${\text{LaFe}}_4{\text{Sb}}_{12}$ is a ferromagnetic quantum critical point system and that ${\text{CeFe}}_4{\text{Sb}}_{12}$ is a moderate heavy fermion compound. This is supported by our thermoelectric and thermodynamic experiments under magnetic field on both compounds, and a comparison with other physical properties of these compounds. For ${\text{LaFe}}_4{\text{Sb}}_{12}$, the quenching of the ferromagnetic spin fluctuations explains both the negative magnetothermopower and the decrease in the electronic heat capacity under magnetic field. We propose that the negative magnetothermopower is a generic property of compounds with ferromagnetic spin fluctuations when the diffusion term by spin fluctuations dominates at low temperature. On the other hand these critical ferromagnetic fluctuations are smeared out in ${\text{CeFe}}_4{\text{Sb}}_{12}$ due to the antiferromagnetic coupling between the $d$ electrons of Fe and the $4f$ electron of Ce. As a result, ${\text{CeFe}}_4{\text{Sb}}_{12}$ is a moderate heavy fermion compound with Kondo temperature $T_K$ of about 80 K, which is consistent with the fact that cerium is almost trivalent in this material, and the partially screened magnetic moment of the cerium ions at $T⪡T_k$ is $0.3{\mu }_{\text{B}}$. Finally, in both compounds, the power laws observed at low temperature in the lattice thermal conductivity ${\kappa }_l$ could be explained by electron-phonon scattering.

Figure 1

XRD pattern of the skutterudite Compound ${\text{LaFe}}_4{\text{Sb}}_{12}$.

Figure 2

Thermal variation in the thermal conductivity $\kappa$ and its different contributions in zero field for ${\text{CeFe}}_4{\text{Sb}}_{12}$ and ${\text{LaFe}}_4{\text{Sb}}_{12}$. ${\kappa }_e$ is the electronic contribution provided the Wiedemann-Franz law is valid (see discussion in the text), and ${\kappa }_l=\kappa -{\kappa }_e$.

Figure 3

(Color online) Double logarithmic plot of the thermal variation in the lattice thermal conductivity ${\kappa }_l$ for ${\text{CeFe}}_4{\text{Sb}}_{12}$ and ${\text{LaFe}}_4{\text{Sb}}_{12}$.

Figure 4

Thermal variation in the thermopower $S$ in zero field for ${\text{CeFe}}_4{\text{Sb}}_{12}$ and ${\text{LaFe}}_4{\text{Sb}}_{12}$. Also shown is the Ce contribution of the thermopower estimated as $\Delta S=S\left({\text{CeFe}}_4{\text{Sb}}_{12}\right)-S\left({\text{LaFe}}_4{\text{Sb}}_{12}\right)$. Inset: thermal variation in the thermopower $S$ at $H=0$ and 9 T for ${\text{LaFe}}_4{\text{Sb}}_{12}$.

Figure 5

Magnetic field variation in the thermopower at $T=40\text{K}$ for ${\text{LaFe}}_4{\text{Sb}}_{12}$.

Figure 6

Magnetic field dependence of the Sommerfeld coefficient in ${\text{LaFe}}_4{\text{Sb}}_{12}$. The full curve is the fit by a power series (see text).

Figure 7

Magnetic field dependence of the $\beta$ parameter of the specific heat in ${\text{LaFe}}_4{\text{Sb}}_{12}$.

Figure 8

Temperature dependence of the specific heat $C_p$ in ${\text{LaFe}}_4{\text{Sb}}_{12}$ at different magnetic fields ($H=0$, 4, and 7 T). The straight lines that fit the data at $T\le 6\text{K}$, in agreement with Eq. (1), merge at $T=6\text{K}$, and $C_p$ does not depend on $H$ above 7 K, which also means that spin-fluctuations contribution is negligible above 7 K.

Figure 9

Temperature dependence of the thermal dilatation $\alpha$ of ${\text{CeFe}}_4{\text{Sb}}_{12}$, ${\text{LaFe}}_4{\text{Sb}}_{12}$ and their difference ${\alpha }_{\text{Ce}}$, together with the Ce part of the heat capacity, $C_p\left(\text{Ce}\right)$ defined by Eq. (5), showing the scaling of $C_p\left(\text{Ce}\right)$ with ${\alpha }_{\text{Ce}}$.

Figure 10

Plot of $\left(C_p-\beta T^3\right)/T$, with a $T$ and $H$ independent value $\beta =1.17\times {10}^{-3}\text{J}/\text{mole}{\text{K}}^4$, as a function of the temperature $T$ in ${\text{CeFe}}_4{\text{Sb}}_{12}$. If Eq. (1) would have still be valid, this quantity should have been reduced to the Sommerfeld constant of this compound. The temperature dependence is then attributable to the Schottky resonance Due to Zeeman splitting of the ground state.

Figure 11

Temperature $T_{max}$ of the maximum of the Shottky anomaly shown in Fig. 10 as a function of the magnetic field $H$. Note that $T_{max}\propto H$ hints for the influence of the Zeeman effect.