Transport properties of the quasi-one-dimensional barium ruthenates

We measured the resistivity, thermoelectric power, and Hall coefficient of polycrystalline samples of $4H\text{−}{\mathrm{Ba}}_{0.8}{\mathrm{Sr}}_{0.2}\mathrm{Ru}{\mathrm{O}}_3$ and $9R\text{−}\mathrm{Ba}{\mathrm{Ru}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_3$ $(0⩽x⩽0.35)$ with a quasi-one-dimensional crystallographic structure made of corner- and face-shared $\mathrm{Ru}{\mathrm{O}}_6$ octahedrons in different proportions. The magnitude of the thermoelectric power is as small as that of metals, but the sign changes from positive to negative with decreasing temperature. In contrast, the Hall coefficient is positive in the range of $4.2–300\mathrm{K}$, and its increase at low temperatures reflects a pseudogap opening in the hole band. A simple two-carrier model is used as a qualitative explanation for the transport properties.

Figure 1

(Color online) Crystal structure of $4H$ (left) and $9R$ (right) $\mathrm{Ba}\mathrm{Ru}{\mathrm{O}}_3$.

Figure 2

X-ray diffraction patterns of the polycrystalline samples of ${\mathrm{Ba}}_{0.8}{\mathrm{Sr}}_{0.2}\mathrm{Ru}{\mathrm{O}}_3$ and $\mathrm{Ba}{\mathrm{Ru}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_3$. The $\mathrm{Cu}K\alpha$ is used as an x-ray source.

Figure 3

(a) The resistivity $\rho$, (b) the thermoelectric power $S$, and (c) the Hall coefficient $R_H$ (left axis, small symbols) of $4H\text{−}{\mathrm{Ba}}_{0.8}{\mathrm{Sr}}_{0.2}\mathrm{Ru}{\mathrm{O}}_3$ and $9R\text{−}\mathrm{Ba}\mathrm{Ru}{\mathrm{O}}_3$. For both samples, the Drude weight (right axis, crossed squares for $9R\text{−}\mathrm{Ba}\mathrm{Ru}{\mathrm{O}}_3$ and crossed circles for $4H\text{−}{\mathrm{Ba}}_{0.8}{\mathrm{Sr}}_{0.2}\mathrm{Ru}{\mathrm{O}}_3$) is taken from Refs. 10, 11. In order to compare $R_H$ with $1∕{\omega }_p^2$, the magnitude of $1∕{\omega }_p^2$ in (c) is properly chosen.

Figure 4

(Color online) (a) The resistivity $\rho$, (b) the thermoelectric power $S$, and (c) the Hall coefficient $R_H$ of $9R\text{−}\mathrm{Ba}{\mathrm{Ru}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_3$. Black, $x=0$; red, $x=0.05$; green, $x=0.1$; blue, $x=0.15$; cyan, $x=0.2$; and magenta, $x=0.35$.

Figure 5

$(p∕n-1)∕{(p∕n+1)}^2$, $1∕(p∕n+1)$, and $n∕p$ calculated as a function of $p∕n$. $p$ and $n$ are the carrier concentrations for the hole and electron bands, respectively.