Influence of doping on the Hall coefficient in ${\text{Sr}}_{14-x}{\text{Ca}}_x{\text{Cu}}_{24}{\text{O}}_{41}$

We present Hall-effect measurements of two-leg ladder compounds ${\text{Sr}}_{14-x}{\text{Ca}}_x{\text{Cu}}_{24}{\text{O}}_{41}$ $\left(0\le x\le 11.5\right)$ with the aim to determine the number of carriers participating in dc transport. Distribution of holes between the ladder and chain subsystems is one of the crucial questions important for understanding the physics of these compounds. Our Hall-effect and resistivity measurements show typical semiconducting behavior for $x<11.5$. However, for $x=11.5$, the results are completely different, and the Hall coefficient and resistivity behavior are qualitatively similar to that of high-temperature copper-oxide superconductors. We have determined the effective number of carriers at room temperature and compared it to the number of holes in the ladders obtained by other experimental techniques. We propose that going from $x=0$ to $x=11.5$ less than 1 hole per f.u. is added to the ladders and is responsible for a pronounced change in resistivity with Ca doping.

Figure 1

(Color online) Temperature dependence of the dc resistivity, $\rho$ vs $1/T$ for different ${\text{Sr}}_{14-x}{\text{Ca}}_x{\text{Cu}}_{24}{\text{O}}_{41}$ compounds measured along $\mathbf{a}$ direction $\mathbf{j}\parallel \mathbf{a}$ (black lines) and along $\mathbf{c}$ direction $\mathbf{j}\parallel \mathbf{c}$ [red (gray) lines]. Inset: Temperature dependence $\rho$ vs $T$ of the resistivity for $x=11.5$ compound for $\mathbf{j}\parallel \mathbf{a}$ and $\mathbf{j}\parallel \mathbf{c}$. Dashed lines present related power laws.

Figure 2

Magnetic-field dependence of the Hall resistivity ${\rho }_{xy}$ of ${\text{Sr}}_{14-x}{\text{Ca}}_x{\text{Cu}}_{24}{\text{O}}_{41}$ for $x=0$ and 11.5 ($\mathbf{j}\parallel \mathbf{c}$ and $\mathbf{B}\parallel \mathbf{b}$ up to 5 T) and for $x=9$ ($\mathbf{j}\parallel \mathbf{a}$ and $\mathbf{B}\parallel \mathbf{b}$ up to 9 T); all at $T=211\text{K}$. Also shown is the sample geometry and the arrangement of contacts.

Figure 3

(Color online) Temperature dependence of the Hall coefficient $R_H$ for different ${\text{Sr}}_{14-x}{\text{Ca}}_x{\text{Cu}}_{24}{\text{O}}_{41}$ compounds. Full symbols are for $\mathbf{j}\parallel \mathbf{a}$ geometry and empty symbols for $\mathbf{j}\parallel \mathbf{c}$ geometry. The gray lines are scaled temperature dependences of resistivity measured in $\mathbf{j}\parallel \mathbf{a}$ geometry. The solid straight horizontal blue (gray) line is the calculated value for the Hall coefficient (see text).

Figure 4

(Color online) High-temperature $R_H$ vs $T$, presented in more detail in order to emphasize the values around 300 K.

Figure 5

(Color online) The effective number of carriers $n_{\text{eff}}=V/\left(4e{R}_H\right)$ (● our data) and the number of holes $n$ per f.u. in the ladder vs calcium content $x$ in ${\text{Sr}}_{14-x}{\text{Ca}}_x{\text{Cu}}_{24}{\text{O}}_{41}$. [Data taken from ◼ Osafune et al. (Ref. 11), ◆ Nücker et al. (Ref. 12), ▲ Piskunov et al. (Ref. 16), and ▼ Rusydi et al. (Ref. 17).]

Figure 6

(Color online) Temperature dependence of the Hall coefficient $R_H$ and resistivity ${\rho }_c$ and ${\rho }_a$ for the $x=11.5$ compound of ${\text{Sr}}_{14-x}{\text{Ca}}_x{\text{Cu}}_{24}{\text{O}}_{41}$. Full symbols are $R_H$ for $\mathbf{j}\parallel \mathbf{a}$ geometry and empty symbols for $\mathbf{j}\parallel \mathbf{c}$ geometry. Red (gray) line: ${\rho }_c$, black line: ${\rho }_a$.

Figure 7

$T^2$ dependence of $\text{cot}{\theta }_H$ (at 5 T) for $x=11.5$ in ${\text{Sr}}_{14-x}{\text{Ca}}_x{\text{Cu}}_{24}{\text{O}}_{41}$.