Dual electronic states in thermoelectric cobalt oxide ${\left[{\text{Bi}}_{1.7}{\text{Ca}}_2{\text{O}}_4\right]}_{0.59}{\text{CoO}}_2$

We investigate the low-temperature magnetic-field dependence of the resistivity in the thermoelectric misfit cobalt oxide ${\left[{\text{Bi}}_{1.7}{\text{Ca}}_2{\text{O}}_4\right]}_{0.59}{\text{CoO}}_2$ from 60 K down to 3 K. The scaling of the negative magnetoresistance demonstrates a spin dependent transport mechanism due to a strong Hund’s coupling. The inferred microscopic description implies dual electronic states, which explain the coexistence between localized and itinerant electrons both contributing to the thermopower. By shedding light on the electronic states, which lead to a high thermopower, this result likely provides potential way to optimize the thermoelectric properties.

Figure 1

(Color online). Schematic picture of the crystal structure of the cobaltate ${\left[{\text{Bi}}_{1.7}{\text{Ca}}_2{\text{O}}_4\right]}_{0.59}{\text{CoO}}_2$.

Figure 2

(Color online). Temperature dependences of the single-crystal in-plane resistivity $\rho$ at 0 and 9 T, the magnetic field being parallel to the conducting plane. The inset displays a transport crossover from a high-temperature metalliclike behavior to a low-temperature insulatinglike one.

Figure 3

(Color online). Scaling plot of the single-crystal in-plane resistivity $\rho \left(H,T\right)$ as a function of ${\mu }_{0}H/T$. The inset displays the magnetic-field dependence of the normalized resistivity over the whole temperature range. The applied magnetic field is parallel to the conducting plane.

Figure 4

(Color online). Schematic picture of the electronic energy levels involved in an elementary spin dependent hopping from site $i$ to site $j$. The magnetic potential barrier ${\Delta }_{ij}$ results from the misorientation ${\theta }_{ij}$ between the quasiparticle spin $s_i$ (thin red arrow) and the localized spin ${\sigma }_j$ (bold black arrow) as explained in the text.

Figure 5

(Color online). (a): Crystal-field effect in the ${\text{Co}}^{3+}$ $\left(d^6\right)$. (b): The structural distortion along the $z$ axis illustrated by the two upper octahedrons reduces the gap between the $d_{z^2}$ and the $d_{xy}$ levels. A strong Hund’s coupling is, besides, represented with the splitting of the two spin states in the $d_{z^2}$ and $d_{xy}$ levels, respectively. (b) and (c): Spin dependent hopping mechanism between the ${\text{Co}}^{3+}$ and the ${\text{Co}}^{4+}$. The thin red arrow represents the quasiparticle spin and the bold black arrows the localized spin.

Figure 6

(Color online). Comparison between the experimental temperature dependence of the thermopower $S$ (Ref. 14) and the theoretical predictions including both localized spins $S_{\text{spin}}$ and quasiparticles $S_{\text{QP}}$ contributions. It is worth noting that the latter is plotted from the two limiting cases, namely, with $S_{\text{QP}}\approx {\pi }^2/6$, $k_B/e$, and $T/T_F^{\ast }$ if $T⪡T_F^{\ast }$ and $S_{\text{QP}}=k_B/e\text{ln}\left[\delta /\left(1-\delta \right)\right]$ if $T>T_F^{\ast }$.