Systematics of the temperature-dependent interplane resistivity in Ba(Fe${}_{1-x}{M}_x$)${}_2$As${}_2$ ($M=\text{Co}$, Rh, Ni, and Pd)

Temperature-dependent interplane resistivity ${\rho }_c\left(T\right)$ was measured systematically as a function of transition-metal substitution in the iron-arsenide superconductors Ba(Fe${}_{1-x}$$M$${}_x$)${}_2$As${}_2$, $M=\text{Ni}$, Pd, Rh. The data are compared with the behavior found in Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$, revealing resistive signatures of pseudogap. In all compounds we find resistivity crossover at a characteristic pseudogap temperature $T^{*}$ from nonmetallic to metallic temperature dependence on cooling. Suppression of $T^{*}$ proceeds very similarly in cases of Ni and Pd doping and much faster than in similar cases of Co and Rh doping. In cases of Co and Rh doping an additional minimum in the temperature-dependent ${\rho }_c$ emerges for high dopings, when superconductivity is completely suppressed. These features are consistent with the existence of a charge gap covering part of the Fermi surface. The part of the Fermi surface affected by this gap is notably larger for Ni- and Pd-doped compositions than in Co- and Rh-doped compounds.

Figure 1

(Color online) Temperature dependence of the interplane resistivity ${\rho }_c$ normalized by its value at room temperature ${\rho }_c\left(300\text{K}\right)$, for samples of Ba(Fe${}_{1-x}$Rh${}_x$)${}_2$As${}_2$ with $x⩽0.171$ (slightly above the concentration boundary for the superconducting dome). Lines are offset, from bottom to top, $x_{\mathrm{Rh}}$ = 0, 0.012, 0.026, 0.039, 0.076, 0.096, 0.131, and 0.171 (left panel). Arrows show a position of the resistivity maximum $T^{*}$, crossed arrow shows a position of the resistivity minimum $T_{\mathit{CG}}$. Right panel shows the $T-x_{\mathrm{Rh}}$ phase diagram, in which lines of structural $T_S$, magnetic $T_M$, and superconducting $T_c$ states are determined from in-plane resistivity and magnetization measurements; see Ref. 13.

Figure 2

(Color online) Temperature-concentration phase diagrams of the pseudogap features as revealed from the temperature-dependent interplane resistivity ${\rho }_c$ in $M=\text{Rh}$ (solid symbols, this study) and $M=\text{Co}$ (open symbols, Ref. 8) doped Ba(Fe${}_{1-x}$$M$${}_x$)${}_2$As${}_2$. Pseudogap features for two types of doping overlap within error bars, similar to the lines of structural $T_S$, magnetic $T_M$, and superconducting $T_c$ transitions; Ref. 13. Vertical lines separate composition ranges in which Fermi surface topology changes in $M=\text{Co}$ (Refs. 18–20).

Figure 3

(Color online) Temperature dependence of the interplane resistivity ${\rho }_c$ normalized by its value at room temperature ${\rho }_c\left(300\text{K}\right)$, for samples of Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$ with $x⩽0.072$ (slightly above the concentration boundary for the superconducting dome). Lines are offset, from bottom to top, $x_{\mathrm{Ni}}=0$, 0.0067, 0.016, 0.024, 0.032, 0.054, and 0.072. Arrows show a position of the resistivity maximum $T^{*}$ used to plot the phase diagram; see Fig. 5.

Figure 4

(Color online) Temperature dependence of the interplane resistivity ${\rho }_c$ normalized by its value at room temperature ${\rho }_c\left(300\text{K}\right)$, for samples of Ba(Fe${}_{1-x}$Pd${}_x$)${}_2$As${}_2$ with $x⩽0.077$ (slightly above the concentration boundary for the superconducting dome). Lines are offset, from bottom to top, $x_{\text{Pd}}=0$, 0.012, 0.021, 0.027, 0.030, 0.053, and 0.077. Arrows show a position of the resistivity maximum $T^{*}$ used to plot the phase diagram; see Fig. 5.

Figure 5

(Color online) Comparison of the temperature-concentration phase diagrams of the pseudogap features in $M=\text{Ni}$ (solid symbols) and $M=\text{Pd}$ (open symbols) doped Ba(Fe${}_{1-x}$$M$${}_x$)${}_2$As${}_2$ as determined from interplane resistivity measurements. Lines of structural $T_S$, magnetic $T_M$, and superconducting $T_c$ states are determined from in-plane resistivity and magnetization measurements; see Ref. 13. All characteristic features for two types of doping overlap within error bars.

Figure 6

(Color online) Left panel: comparison of the doping phase diagrams for Rh (solid symbols) and Pd (open symbols) doping, plotted vs concentration of added electrons defined as $n=x_{\text{Rh}}=2x_{\text{Pd}}$. Right panel: Phase diagram of the pseudogap features plotted vs $n=x_{\text{Rh}}=x_{\text{Co}}=2x_{\text{Pd}}=2x_{\text{Ni}}$ for all studied transition metals. Resistivity maximum $T^{*}$ for Rh (blue solid up triangles), Co (black solid diamonds), Pd (open up triangles), and Ni (red open squares) and resistivity minimum $T_{\mathit{CG}}$ for Rh (solid pink star) and Co (open black circles).