Phase diagrams of $\text{Ba}{\left({\text{Fe}}_{1-x}{M}_x\right)}_2{\text{As}}_2$ single crystals ($M=\text{Rh}$ and Pd)

Single crystalline $\text{Ba}{\left({\text{Fe}}_{1-x}{M}_x\right)}_2{\text{As}}_2$ $\left(M=\text{Rh},\text{Pd}\right)$ series have been grown and characterized by structural, thermodynamic, and transport measurements. These measurements show that the structural/magnetic phase transitions, found in pure ${\text{BaFe}}_2{\text{As}}_2$ at 134 K, are suppressed monotonically by the doping and that superconductivity can be stabilized over a domelike region. Temperature-composition $\left(T-x\right)$ phase diagrams based on electrical transport and magnetization measurements are constructed and compared to those of the $\text{Ba}{\left({\text{Fe}}_{1-x}{M}_x\right)}_2{\text{As}}_2$ $\left(M=\text{Co},\text{Ni}\right)$ series. Despite the generic difference between $3d$ and $4d$ shells and the specific, conspicuous differences in the changes to the unit cell parameters, the effects of Rh doping are exceptionally similar to the effects of Co doping and the effects of Pd doping are exceptionally similar to the effects of Ni doping. These data show that whereas the structural/antiferromagnetic phase-transition temperatures can be parameterized by $x$ and the superconducting transition temperature can be parameterized by some combination of $x$ and $e$, the number of extra electrons associated with the $M$ doping, the transition temperatures of $3d$- and $4d$-doped ${\text{BaFe}}_2{\text{As}}_2$ cannot be simply parameterized by the changes in the unit-cell dimensions or their ratios.

Figure 1

(Color online) The temperature-dependent resistivity, normalized by the room temperature value, for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Rh}}_x\right)}_2{\text{As}}_2$. Inset: low-temperature data for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Rh}}_x\right)}_2{\text{As}}_2$. On- and off-set criteria for $T_c$ are shown.

Figure 2

(Color online) Low magnetic-field $M/H$ for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Rh}}_x\right)}_2{\text{As}}_2$ series. Inset: the criterion used to infer $T_c$ is shown for $\text{Ba}{\left({\text{Fe}}_{0.961}{\text{Rh}}_{0.039}\right)}_2{\text{As}}_2$.

Figure 3

Temperature-dependent heat-capacity data for $\text{Ba}{\left({\text{Fe}}_{0.943}{\text{Rh}}_{0.057}\right)}_2{\text{As}}_2$. Inset: $C_p$ vs $T$ near the superconducting transition with the estimated $\Delta C_p$ shown.

Figure 4

(Color online) The temperature-dependent resistivity, normalized by room temperature value, for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Pd}}_x\right)}_2{\text{As}}_2$. Inset: low-temperature data for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Pd}}_x\right)}_2{\text{As}}_2$.

Figure 5

(Color online) Low magnetic-field $M/H$ for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Rh}}_x\right)}_2{\text{As}}_2$ series.

Figure 6

Temperature-dependent heat-capacity data for $\text{Ba}{\left({\text{Fe}}_{0.957}{\text{Pd}}_{0.043}\right)}_2{\text{As}}_2$. Inset: $C_p$ vs $T$ near the superconducting transition with the estimated $\Delta C_p$ shown.

Figure 7

(Color online) Transition temperature as a function of $x$. (a) $T-x$ phase diagrams of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Rh}}_x\right)}_2{\text{As}}_2$ and $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ series. (b) Phase diagrams of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Pd}}_x\right)}_2{\text{As}}_2$ and $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Ni}}_x\right)}_2{\text{As}}_2$ series. For both plots the transition temperatures were determined in a manner similar to that described in Ref. 11 and illustrated in the inset for $\text{Ba}{\left({\text{Fe}}_{0.961}{\text{Rh}}_{0.039}\right)}_2{\text{As}}_2$. Data for Co and Ni doping are taken from Refs. 11, 17.

Figure 8

(Color online) Normalized structural parameters measured at $\sim 300\text{K}$. (a) $c/c_0$ as a function of transition metal doping, $x$ and (b) $\left(a/c\right)/\left(a_0/c_0\right)$ as a function of extra conduction electrons, $e$. [$a_0=3.9621\left(4\right)\text{Å}$, $c_0=13.0178\left(10\right)\text{Å}$.] Data for Co and Ni doping are taken from Refs. 11, 17.

Figure 9

(Color online) (a) Superconducting transition temperature $T_c$ as a function of $x_{\text{ave}}$. (b) Superconducting transition temperature $T_c$ as a function of extra electrons per Fe/M site. Data for Co and Ni doping are taken from Refs. 11, 17.

Figure 10

(Color online) (a) Superconducting transition temperature $T_c$ as a function of structural phase transition temperature $T_s$. (b) Superconducting transition temperature $T_c$ as a function of magnetic phase transition temperature $T_m$. Data for Co and Ni doping are taken from Refs. 11, 17.

Figure 11

(Color online) Transition temperature as a function of adjusted $x$. $x$ is normalized so as to bring the interpolated values of $T_s$ onto the transition associated with $\text{Ba}{\left({\text{Fe}}_{0.953}{\text{Co}}_{0.047}\right)}_2{\text{As}}_2$ for Co doped ${\text{BaFe}}_2{\text{As}}_2$, $x=x_{\text{ave}}$; for Rh doped ${\text{BaFe}}_2{\text{As}}_2$, $x=x_{\text{ave}}\times 0.047/0.039$; for Pd doped ${\text{BaFe}}_2{\text{As}}_2$, $x=x_{\text{ave}}\times 0.047/0.028$; for Ni doped ${\text{BaFe}}_2{\text{As}}_2$, $x=x_{\text{ave}}\times 0.047/0.03$. Data for Co and Ni doping are taken from Refs. 11, 17.