Resistivity anisotropy of $A{\text{Fe}}_2{\text{As}}_2$ ($A=\text{Ca}$, Sr, Ba): Direct versus Montgomery technique measurements

The anisotropy of electrical resistivity was measured in parent compounds of the iron-arsenic high-temperature superconductors $A{\text{Fe}}_2{\text{As}}_2$ with alkali earth elements $A=\text{Ca}$, Sr, and Ba. Measurements were performed using both the Montgomery technique and direct resistivity measurements on samples cut along principal crystallographic directions. The anisotropy ratio ${\gamma }_{\rho }={\rho }_c/{\rho }_a$ is well below ten for all compounds in the whole temperature range studied (4–300 K), in notable contrast to previous reports. The anisotropy at room temperature increases from about two in Ca to about four in Sr and Ba. In all compounds the resistivity ratio decreases on cooling through the structural/antiferromagnetic transition temperature $T_{SM}$, with the change mainly coming from stronger variation in ${\rho }_a$ as compared with ${\rho }_c$. This suggests that the transition affects stronger the two-dimensional parts of the Fermi surface. We compare our experimental observations with band-structure calculations, and find similar trend in the evolution of anisotropy with the size of $A$ ion. Our results show that the electronic structure of the iron pnictides has large contribution from three-dimensional areas of the Fermi surface.

Figure 1

(Color online) Temperature dependence of ${\rho }_a$ measured on four different samples of ${\text{CeFe}}_2{\text{As}}_2$ (main panel). The inset shows the same data normalized to a value at 300 K. Samples are labeled A–D in line with increase in the room-temperature resistivity value.

Figure 2

(Color online) Temperature dependence of ${\rho }_c$ measured on three samples of ${\text{CaFe}}_2{\text{As}}_2$ (main panel). The inset shows the same data normalized by the value of ${\rho }_c$ at 300 K. The curves are labeled alphabetically in line with room-temperature resistivity increase.

Figure 3

(Color online) Temperature dependence of the ratio of resistivities ${\gamma }_{\rho }\equiv {\rho }_c/{\rho }_a$ as determined from the Montgomery technique (solid symbols), and from the ratio of independently measured ${\rho }_a$ and ${\rho }_c$ for samples with the lowest resistivities, $\text{A-}{\rho }_c$ and $\text{A-}{\rho }_a$ (open symbols). The inset shows raw $R_1$ and $R_2$ data for sample A-M, and schematics of contact configuration during anisotropy measurements using Montgomery technique. Sample has rectangular cross section in the $ac$ plane with dimensions $l_1$ (along $a$) and $l_2$ (along $c$). Contacts are located at the corners of the rectangle and run in the direction perpendicular to the plane of the figure along $l_3$ (parallel $b$). Two sets of four-probe resistivity measurements are performed: in the first run current $I_1$ is flowing between contacts 1 and 4 along $l_1$ while voltage $V_1$ is measured between contacts 2 and 3, their ratio determines resistance $R_1=V_1/I_1$; in the second run direction of the current $I_2$ is along $l_2$ between contacts 1 and 2 while voltage $V_2$ is measured between contacts 3 and 4, and $R_2=V_2/I_2$. The anisotropy ${\gamma }_{\rho }$ is calculated using $R_2/R_1$ and $l_2/l_1$ ratios as discussed in Refs. 19, 20.

Figure 4

(Color online) Temperature dependence of ${\rho }_a$ measured on four different samples of ${\text{SrFe}}_2{\text{As}}_2$ (main panel). The inset shows the same data normalized to a value at 300 K. Samples are labeled A–D in line with increase in the room-temperature resistivity value.

Figure 5

(Color online) Temperature dependence of ${\rho }_c$ measured on five samples of ${\text{SrFe}}_2{\text{As}}_2$ (main panel). Sample C was measured twice to check the effect of thermal cycling on resistivity value, the lower curve represents initial run. The inset shows the same data normalized by the value of ${\rho }_c$ at 300 K. The curves are labeled alphabetically in line with room-temperature resistivity increase.

Figure 6

(Color online) Temperature dependence of the ratio of resistivities ${\gamma }_{\rho }\equiv {\rho }_c/{\rho }_a$ as determined from the Montgomery technique (solid symbols), and from the ratio of independently measured ${\rho }_a$ and ${\rho }_c$ for several different samples (open symbols). The inset shows raw $R_1$ and $R_2$ data for sample C-M measured in Montgomery configuration.

Figure 7

(Color online) Temperature dependence of ${\rho }_a$ measured on five different samples of ${\text{BaFe}}_2{\text{As}}_2$ (main panel). The inset shows the same data normalized to the resistivity values at 300 K. Samples are labeled A–E in line with increase in the room-temperature resistivity.

Figure 8

(Color online) Temperature dependence of ${\rho }_c$ measured on five samples of ${\text{BaFe}}_2{\text{As}}_2$ (main panel). The inset shows the same data normalized by the values of ${\rho }_c$ at 300 K. The curves are labeled alphabetically in line with room-temperature resistivity increase.

Figure 9

(Color online) Temperature dependence of the ratio of resistivities ${\gamma }_{\rho }\equiv {\rho }_c/{\rho }_a$ as determined from the Montgomery technique (solid symbols), and from the ratio of independently measured ${\rho }_a$ and ${\rho }_c$ for some representative samples (open symbols). The inset shows raw $R_1$ and $R_2$ data for sample C-M measured in Montgomery configuration.

Figure 10

(Color online) Temperature dependence of the anisotropy ratio ${\gamma }_{\rho }={\rho }_c/{\rho }_a$ for ${\text{CaFe}}_2{\text{As}}_2$, ${\text{SrFe}}_2{\text{As}}_2$, and ${\text{BaFe}}_2{\text{As}}_2$. The error bars represent the evaluated systematic error of the anisotropy determination.

Figure 11

(Color online) Cross section of the Fermi surface of ${\text{BaFe}}_2{\text{As}}_2$ by the $\Gamma XZ$ plane in the Brillouin zone. The position of the As atom in the lattice, $Z_{\text{As}}$, was assumed corresponding to experimentally measured (Ref. 23) (top panel) or to the minimum of the total crystal energy (bottom panel). Variation in $Z_{\text{As}}$ affects most strongly the sheets of the Fermi surface surrounding the $\Gamma$ point in the Brillouin zone.

Figure 12

(Color online) Temperature dependence of the in-plane (top panel) and interplane (bottom panel) resistivity for ${\text{CaFe}}_2{\text{As}}_2$, ${\text{SrFe}}_2{\text{As}}_2$, and ${\text{BaFe}}_2{\text{As}}_2$. The curves were selected as corresponding to a minimum room-temperature resistivity value for each type of the curves. The insets show the same data normalized by the resistivity values at 300 K.