Strongly correlated properties of the thermoelectric cobalt oxide ${\mathrm{Ca}}_3{\mathrm{Co}}_4{\mathrm{O}}_9$

We have performed both in-plane resistivity, Hall effect, and specific heat measurements on the thermoelectric cobalt oxide ${\mathrm{Ca}}_3{\mathrm{Co}}_4{\mathrm{O}}_9$. Four distinct transport regimes are found as a function of temperature, corresponding to a low temperature insulating one up to $T_{\mathit{min}}\approx 63\mathrm{K}$, a strongly correlated Fermi liquid up to $T^{*}\approx 140\mathrm{K}$, with $\rho ={\rho }_0+A{T}^2$ and $A\approx 3.63\times {10}^{-2}\mu \Omega \mathrm{cm}∕{\mathrm{K}}^2$, followed by an incoherent metal with $k_{F}l⩽1$ and a high temperature insulator above $T^{**}\approx 510\mathrm{K}$. The specific heat Sommerfeld coefficient $\gamma =93\mathrm{mJ}∕\left(\mathrm{mol}{\mathrm{K}}^2\right)$ confirms a rather large value of the electronic effective mass and fulfils the Kadowaki-Woods ratio $A∕{\gamma }^2\approx 0.45\times {10}^{-5}\mu \Omega \mathrm{cm}{\mathrm{K}}^2∕\left({\mathrm{mJ}}^2{\mathrm{mol}}^{-2}\right)$. Resistivity measurements under pressure reveal a decrease of the Fermi liquid transport coefficient A with an increase of $T^{*}$ as a function of pressure while the product $A{\left(T^{*}\right)}^2∕b_2$ remains constant and of order $h∕e^2$. Both thermodynamic and transport properties suggest a strong renormalization of the quasiparticles coherence scale of order $T^{*}$ that seems to govern also thermopower.

Figure 1

(Color online) Temperature dependence of the in-plane single crystal resistivity. The three temperatures $T_{\mathit{min}}$, $T^{*}$, and $T^{**}$ separate, respectively, a low-temperature insulatinglike behavior, a strongly correlated Fermi liquid, an incoherent metal, and a high-temperature insulator, while $T_a$ indicates an anomaly explained in the text. The inset displays $\rho$ vs $T^2$ below $T^{*}$.

Figure 2

(Color online) Temperature dependence of the in-plane resistivity under pressure, with, from the bottom to the top, $1\text{bar}$, $6\mathrm{kbar}$, and $12\mathrm{kbar}$ (only three pressures are selected for clarity). The inset displays $\rho -{\rho }_0$ vs $T^2$ with the fitted lines.

Figure 3

(Color online) Pressure dependences of the Fermi liquid transport coefficient $A$ (upper panel) and the coherence temperature $T^{*}$ (middle panel). The lower panel exhibits the pressure independence of the product $A{\left(T^{*}\right)}^2∕b_2$ in unit of $(h∕e^2)$, $b_2$ being an in-plane lattice parameter.

Figure 4

(Color online) Temperature dependence of the specific heat for a sintered sample as $C∕T$ vs $T^2$. It’s noteworthy that the $9\text{−}\mathrm{T}$ magnetic field reveals the lattice contribution to the specific heat reducing a magnetic one (Ref. 9), and improve the quality of the determination of $\gamma$. The inset displays C vs T.

Figure 5

(Color online) Magnetic-field dependence of the single crystal transverse resistivity for different temperatures (upper panel) and temperature dependence of Hall resistance (lower panel).

Figure 6

(Color online) Temperature dependence of the single crystal thermopower $S_{\mathit{exp}}$ (Ref. 7) compared to a renormalized free electron prediction $S^{*}$ involving the quasiparticle coherence scale $T^{*}$ (Fig. 1). Agreement is more apparent if a constant contribution $S^0$ is added to $S^{*}$.