Effects of isovalent substitution and pressure on the interplane resistivity of single-crystal $\text{Ba}\left({\mathrm{Fe}}_{1-x}{\mathrm{Ru}}_x\right){}_2{\mathrm{As}}_2$

Temperature-dependent interplane resistivity ${\rho }_c\left(T\right)$ was measured in an isovalent substituted iron-arsenide compound $\text{Ba}\left({\mathrm{Fe}}_{1-x}{\mathrm{Ru}}_x\right){}_2{\mathrm{As}}_2$ over a substitution range from parent compound to slightly below optimal doping $x=0.29$. The feature of interest in the ${\rho }_c\left(T\right)$, a broad resistivity crossover maximum found in the parent compound at $T_{\text{max}}\approx 200$ K, shifts to higher temperatures with Ru substitution, $\sim 340$ K for $x=0.161$ and goes out of the 400 K range for $x=0.29$. Nearly $T$-linear dependence of interplane resistivity is found at the highest substitution level $x=0.29$. This temperature-dependent ${\rho }_c$ and its evolution with substitution bear close similarity to another type of isovalent substituted system ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right){}_2$. Similarly to the isovalent substitutions, the measurements of interplane resistivity in the parent ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ compound under pressures up to 20 kbar also revealed a rapid rise in $T_{\text{max}}$.

Figure 1

Top panel: Doping evolution of the temperature-dependent in-plane resistivity of $\text{Ba}\left({\mathrm{Fe}}_{1-x}{\mathrm{Ru}}_x\right){}_2{\mathrm{As}}_2$. The curves are presented using normalized $\rho /\rho$(300 K) plots and offset for clarity. Top to bottom $x=0$, 0.073, 0.126, 0.21, 0.24, and 0.29. Bottom panel: Temperature-dependent interplane resistivity of $\text{Ba}\left({\mathrm{Fe}}_{1-x}{\mathrm{Ru}}_x\right){}_2{\mathrm{As}}_2$, top to bottom $x=0$, 0.073, 0.126, 0.161, 0.21, 0.24, and 0.29. Down triangles show positions of the coupled structural/magnetic transition, open circles show positions of $T_{\text{max}}$. For the highest substitutions $x=0.24$ and 0.29 no maximum is observed in the range, but a slope change crossover is still clearly visible, as indicated by the square symbols.

Figure 2

Top panel shows the compositional phase diagram of $\text{Ba}\left({\mathrm{Fe}}_{1-x}{\mathrm{Ru}}_x\right){}_2{\mathrm{As}}_2$ as determined from interplane resistivity measurements in this study (down triangles, circles, and open squares, see Fig. 1 for definition) in comparison with magnetization measurements (up triangles and pentagons) of Thaler et al. [26]. Bottom panel compares temperature-composition diagrams for two isovalent substitutions, of Fe with Ru (blue lines and symbols) and of As with P (red lines and symbols) [6, 7].

Figure 3

Comparison of the temperature-dependent interplane resistivity of underdoped samples of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ based superconductors, for the compositions selected to have comparable $T_{sm}$ of about 100 K. Top left panel (a) shows ${\rho }_c\left(T\right)$ for hole-doped $\left({\mathrm{Ba}}_{1-x}{\mathrm{K}}_x\right){\mathrm{Fe}}_2{\mathrm{As}}_2$ [13], top right panel (b) for electron-doped $\text{Ba}\left({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\right){}_2{\mathrm{As}}_2$ [11], bottom left panel (c) for isovalent substituted ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right){}_2$ [7], and bottom right panel (d) for isovalent substituted $\text{Ba}\left({\mathrm{Fe}}_{1-x}{\mathrm{Ru}}_x\right){}_2{\mathrm{As}}_2$ (this study). Note the very different evolution of the position of maximum of interplane resistivity $T_{\text{max}}$, shown with open circles.

Figure 4

Comparison of the temperature-dependent in-plane (blue lines) and interplane (red lines) resistivity of close to optimally doped samples of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ based superconductors. Top left panel (a) shows data for hole-doped $\left({\mathrm{Ba}}_{1-x}{\mathrm{K}}_x\right){\mathrm{Fe}}_2{\mathrm{As}}_2$ [13], top right panel (b) for electron-doped $\text{Ba}\left({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\right){}_2{\mathrm{As}}_2$ [11], bottom left panel (c) for isovalent substituted ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right){}_2$ [6, 7], and bottom right panel (d) for isovalent substituted $\text{Ba}\left({\mathrm{Fe}}_{1-x}{\mathrm{Ru}}_x\right){}_2{\mathrm{As}}_2$ (this study). Note that Ru-doped samples are actually underdoped, which is the most likely reason that the evolution towards $T$-linear dependence is incomplete.

Figure 5

Evolution of the temperature-dependent in-plane (top panel) and interplane (bottom panel) resistivity with pressure in the parent compound of 122 iron-based superconductors ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. Pressure values are changing on cooling, as shown for temperatures of 300 and 4.2 K. The inset in the top panel shows pressure dependence of $T_s$ as determined from ${\rho }_a$ (solid down triangles) and from ${\rho }_c$ (open down triangles) measurements. Inset in the bottom panel shows evolution of $T_s$ (down triangles) and of $T_{\text{max}}$ (circles) with pressure. Symbols in the main panel show the respective temperatures vs actual temperature-dependent resistivity curves.

Figure 6

Evolution of the position of the maximum of the temperature-dependent interplane resistivity $T_{\text{max}}$ as a function of the structural transition temperature $T_S$ for cases of isovalent Ru (blue circles) and P (red diamonds) substitutions and of application of pressure (black right triangles). Note the significantly faster increase of $T_{\text{max}}$ under pressure.