Pseudogap and its critical point in the heavily doped $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ from $c$-axis resistivity measurements

Temperature-dependent interplane resistivity, ${\rho }_c\left(T\right)$, was used to characterize the normal state of the iron-arsenide superconductor $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ over a broad doping range $0\le x<0.50$. The data were compared with in-plane resistivity, ${\rho }_a\left(T\right)$, and magnetic susceptibility, $\chi \left(T\right)$, taken in $H\perp c$, as well as Co NMR Knight shift, ${}^{59}K$, and spin-relaxation rate, $1/T_{1}T$. The interplane resistivity data show a clear correlation with the NMR Knight shift, assigned to the formation of the pseudogap. Evolution of ${\rho }_c\left(T\right)$ with doping reveals two characteristic energy scales. The temperature of the crossover from nonmetallic, increasing on cooling, behavior of ${\rho }_c\left(T\right)$ at high temperatures to metallic behavior at low temperatures, $T^{\ast }$, correlates well with an anomaly in all three magnetic measurements. This characteristic temperature, equal to approximately 200 K in the parent compound, $x=0$, decreases with doping and vanishes near $x^{\ast }\approx 0.25$. For doping levels $x\ge 0.166$, an additional feature appears above $T^{\ast }$ with metallic behavior of ${\rho }_c\left(T\right)$ found above the low-temperature resistivity increase. The characteristic temperature of this charge-gap formation, $T_{\text{CG}}$, vanishes at $x_{\text{CG}}\simeq 0.30$, paving the way to metallic, $T$ linear, ${\rho }_c\left(T\right)$ close to $x_{\text{CG}}$ and superlinear $T$ dependence for $x>x_{\text{CG}}$. None of these features are evident in the in-plane resistivity ${\rho }_a\left(T\right)$. For doping levels $x<x_{\text{CG}}$, $\chi \left(T\right)$ shows a known, anomalous, $T$-linear dependence, which disappears for $x>x_{\text{CG}}$. These features are consistent with the existence of a charge gap, accompanying formation of the magnetic pseudogap, and its critical suppression with doping. The inferred $c$-axis charge gap reflects the three-dimensional character of the electronic structure and of the magnetism in the iron arsenides.

Figure 1

Room-temperature interplane resistivity, ${\rho }_c\left(300\text{K}\right)$, of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ as a function of doping (top panel). Lower panel shows doping dependence of the ratio of resistivities at low temperatures and at room temperature, ${\rho }_c\left(0\right)/{\rho }_c\left(300\text{K}\right)$.

Figure 2

(Color online) Room-temperature in-plane resistivity, ${\rho }_a\left(300\text{K}\right)$, of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ as a function of doping (top panel). Red stars show resistivity values taken from Ref. 31. Lower panel shows doping dependence of the resistivity ratio, ${\rho }_a\left(0\right)/{\rho }_a\left(300\text{K}\right)$.

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 $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ with $x\le 0.166$ (slightly above the concentration boundary for the superconducting dome) as shown in the figure (top panel). The curves are offset to avoid overlapping. Arrows show a position of the resistivity maximum, presented as a function of dopant concentration in the $T\text{−}x$ phase diagram (see Fig. 5 below), cross arrows show position of the resistivity minimum, $T_{\text{CG}}$, appearing at high doping levels. Bottom panel shows doping evolution of the temperature-dependent in-plane resistivity, ${\rho }_a$, normalized by room-temperature value ${\rho }_a\left(300\text{K}\right)$. Arrows show positions of $T^{\ast }$ and $T_{\text{CG}}$ as determined from ${\rho }_c\left(T\right)$, revealing no discernible features in the in-plane resistivity.

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 $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ with high doping levels $x\ge 0.127$ as shown in the figure (top panel). The curves are offset to avoid overlapping. Cross arrows and straight arrows show positions of the resistivity minimum, $T_{\text{CG}}$, and maximum, $T^{\ast }$, respectively. Lines with $x=0.343$ and $x=0.370$ curves show a second order polynomial fit through the data, as discussed in the text. Bottom panel shows evolution of the temperature-dependent in-plane resistivity, ${\rho }_a$, normalized by room-temperature value ${\rho }_a\left(300\text{K}\right)$. Arrows show positions of $T_{\text{CG}}$ and $T^{\ast }$ as determined from the interplane resistivity temperature dependence, revealing no discernible features in the in-plane resistivity.

Figure 5

(Color online) Temperature-doping phase diagram of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ as determined from interplane resistivity measurements. Inset shows comparison of $T^{\ast }$ and $T_{\text{CG}}$, corresponding to the maxima and minima in ${\rho }_c\left(T\right)$ with $T_{PG}$ as found in NMR study by fitting the temperature-dependent Knight shift (Refs. 24, 34). Arrow in the inset shows a minimum estimate for $T_{\text{CG}}$ for the border composition $x=0.127$.

Figure 6

(Color online) Comparison of the temperature-dependent interplane resistivity ${\rho }_c$ (solid lines, left scale) with the temperature-dependent ${}^{59}\text{C}\text{o}$ NMR Knight shift $K\left(T\right)$ (solid symbols) and relaxation rate, $1/T_{1}T$, (open symbols) from Ref. 24 (two right scales) for ${\text{BaFe}}_2{\text{As}}_2$ (top left panel) and $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ with $x=0.04$ (top right panel), $x=0.074–0.08$ (bottom left panel), and $x=0.105–0.108$ (bottom right panel). A broad maximum in the temperature dependence of the interplane resistivity clearly correlates with pseudogap features in NMR measurements: a crossover slope change in $K\left(T\right)$ and the onset of a low-temperature rapid rise in $1/T_{1}T$.

Figure 7

(Color online) Top panel: temperature-dependent molar magnetic susceptibility, ${\chi }_{mole}\left(T\right)$, measured in magnetic field $H\perp c=5\text{T}$. The data for low dopings are from Ref. 19. On doping increase the slope of the $T$-linear increase in $\chi \left(T\right)$ (shown with orange line for pure composition $x=0$ at $T=250\text{K}$) decreases and for $x=0.313$ the dependence becomes flat at $T>\sim 150\text{K}$. Bottom panel: doping evolution of the slope of ${\chi }_{mole}\left(T\right)$, $d{\chi }_{mole}\left(T\right)/dT$, at $T=250\text{K}$.