Interplane resistivity of isovalent doped BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$

Temperature-dependent interplane resistivity ${\rho }_c\left(T\right)$ was measured for the iron-based superconductor BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ over a broad isoelectron phosphorus substitution range from $x=0$ to $x=0.60$, from nonsuperconducting parent compound to heavily overdoped superconducting composition with $T_c\approx 10\text{K}$. The features due to structural and magnetic transitions are clearly resolved in ${\rho }_c\left(T\right)$ of the underdoped crystals. A characteristic maximum in ${\rho }_c\left(T\right)$, found in the parent BaFe${}_2$As${}_2$ at around 200 K, moves rapidly with phosphorus substitution to high temperatures. At the optimal doping, the interplane resistivity shows $T$-linear temperature dependence without any crossover anomalies, similar to the previously reported in-plane resistivity. This observation is in stark contrast with dissimilar temperature dependencies found at optimal doping in electron-doped Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$. Our finding suggests that despite similar values of the resistivity and its anisotropy, the temperature-dependent transport in the normal state is very different in electron and isoelectron-doped compounds. Similar temperature dependence of both in-plane and interplane resistivities, in which the dominant contributions are coming from different parts of the Fermi surface, suggests that scattering is the same on the whole Fermi surface. Since magnetic fluctuations are expected to be much stronger on the quasinested sheets, this observation may point to the importance of the interorbital scattering between different sheets.

Figure 1

Temperature-dependent interplane resistivity of BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ for (top to bottom) $x=0$ (parent compound, black curve), underdoped compositions $x=0.23$ (green) and $x=0.25$ (blue), optimally doped $x=0.33$ (red), and overdoped $x=0.48$ (magenta) and $x=0.60$ (dark yellow). The data are plotted on the normalized resistivity scale, ${\rho }_c\left(T\right)/{\rho }_c\left(300\text{K}\right)$, and offset progressively downwards for higher $x$ to avoid overlapping. Arrows show a position of the resistivity crossover temperature $T_{\max }$ and of the structural $T_S$ and magnetic $T_N$ transitions.

Figure 2

Temperature-composition $x$-phase diagram of electron-doped BaFe${}_{1-x}$Co${}_x$As${}_2$ and isoelectron-substituted BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ as determined from temperature-dependent interplane resistivity measurements. The crossover maximum temperature $T_{\max }$ found in the ${\rho }_c\left(T\right)$ of the parent BaFe${}_2$As${}_2$ (see top curve in Fig. 1) shifts in a very different way for various types of doping: it is rapidly suppressed with electron doping (green solid circles)[14] but rapidly increases (green down triangles) for isoelectron substitution. An additional minimum feature in ${\rho }_c\left(T\right)$ of heavily overdoped BaFe${}_{1-x}$Co${}_x$As${}_2$ defines a characteristic temperature $T_{CG}$, not found in isoelectron-doped BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$. Magenta crosses show an onset temperature of nematic anomaly in in-plane resistivity and torque measurements,[17] and black and red lines show temperatures of structural tetragonal-to-orthorhombic $T_S$ and antiferromagnetic $T_N$ transitions, respectively.

Figure 3

Comparison of the temperature-dependent in-plane (data from Ref. 5) and interplane resistivity of isoelectron-substituted BaFe${}_2$As${}_{1-x}$P${}_x$ (top panel) with the, e.g., electron- doped BaFe${}_{1-x}$Co${}_x$As${}_2$ (bottom panel) at optimal doping level, with $x$ as indicated. Note that both ${\rho }_a\left(T\right)$ and ${\rho }_c\left(T\right)$ are close to linear just above superconducting $T_c$ for both types of doping; however, the temperature range of the $T$-linear dependence is restricted at higher temperatures by an onset of the crossover in electron-doped composition, similar to in-plane transport in Ba${}_{1-x}$K ${}_x$Fe${}_2$As${}_2$, LiFeAs,[31] and NaFeAs.[20, 21]