Scaling Behavior in Thermoelectric Misfit Cobalt Oxides

We investigate both thermoelectric and thermodynamic properties of the misfit cobalt oxide $[{\mathrm{Bi}}_{1.7}{\mathrm{Co}}_{0.3}{\mathrm{Ca}}_2{\mathrm{O}}_4{]}_{0.6}^{\mathrm{RS}}{\mathrm{CoO}}_2$. A large negative magnetothermopower is found to scale with both magnetic field and temperature, revealing a significant spin entropy contribution to thermoelectric properties giving rise to a constant $S_0\approx 60\mu \mathrm{V}{\mathrm{K}}^{-1}$. Specific heat measurements allow us to determine an enhanced electronic part with $\gamma \approx 50\mathrm{mJ}(\mathrm{mol}{\mathrm{K}}^2{)}^{-1}$ attesting to strong correlations. Thereby, the comparison between cobaltites and other materials reveals a universal behavior of the thermopower slope as a function of $\gamma$, testifying to a purely electronic origin. This potentially generic scaling behavior suggests here that the high room temperature value of the thermopower in misfit cobalt oxides results from the addition of a spin entropy contribution to an enlarged electronic one.

Figure 1

Magnetothermopower scaling for a sintered cobalt oxide BiCaCoO. The left and the right insets show, respectively, the temperature and the magnetic field dependences of the hole type thermopower ($S>0$). The collapse of the data of the right inset as a function of $H/T$ illustrates a spin entropy contribution to the thermopower here normalized to its zero magnetic field value for each temperature as $S(H)/S(H=0)$. The dotted line is the free spins $1/2$ entropy following Eq. (1).

Figure 2

Temperature dependence of the specific heat $C$ for a sintered sample as $C/T$ vs $T^2$. The linear variation of $C/T$ as a function of $T^2$ allows us to determine directly $\gamma \approx 50\mathrm{mJ}(\mathrm{mol}{\mathrm{K}}^2{)}^{-1}$. The inset table displays the parameters of the two fitting procedures, namely, with and without the Schottky term.

Figure 3

Scaling plot of the thermopower slope $|S/T|$ as a function of the electronic specific heat coefficient $\gamma$ for the cobaltites BiCaCoO, CaCoO [11], and NaCoO [14], the rhodium misfit oxide BiBaRhO [22], common metals, and organic superconductors [9, 20, 21]. The straight and dotted lines are discussed in the text.

Figure 4

Thermopowers ($S-S_0$) as a function of the reduced temperature $T/T^{*}$, with $S_0$ the asymptotic value of the spin entropy contribution and $T^{*}$ the effective Fermi temperature. A comparison is made between the two cobalt oxides BiCaCoO ($S_0\approx 60\mu \mathrm{V}{\mathrm{K}}^{-1}$, $T^{*}\approx 255\mathrm{K}$) and CaCoO ($S_0\approx 20\mu \mathrm{V}{\mathrm{K}}^{-1}$, $T^{*}\approx 140\mathrm{K}$), while the straight line shows $S^{*}$ following Eq. (3). The inset displays the spin entropy contribution $S_{\mathrm{spin}}=S-S^{*}$ for the two cobaltites.