Temperature versus doping phase diagrams for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{TM}}_x\right)}_2{\text{As}}_2\left(\text{TM}=\text{Ni},\text{Cu},\text{Cu}/\text{Co}\right)$ single crystals

Microscopic, structural, transport, and thermodynamic measurements of single crystalline $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{TM}}_x\right)}_2{\text{As}}_2$ ($\text{TM}=\text{Ni}$ and Cu) series, as well as two mixed $\text{TM}=\text{Cu}/\text{Co}$ series, are reported. In addition, high-magnetic field, anisotropic $H_{c2}\left(T\right)$ data were measured up to 33 T for the optimally Ni-doped ${\text{BaFe}}_2{\text{As}}_2$ sample. All the transport and thermodynamic measurements indicate that the structural and magnetic phase transitions at 134 K in pure ${\text{BaFe}}_2{\text{As}}_2$ are monotonically suppressed and increasingly separated in a similar manner by these dopants. In the $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Ni}}_x\right)}_2{\text{As}}_2$ $\left(x\le 0.072\right)$, superconductivity, with $T_c$ up to 19 K, is stabilized for $0.024\le x\le 0.072$. In the $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Cu}}_x\right)}_2{\text{As}}_2$ $\left(x\le 0.356\right)$ series, although the structural and magnetic transitions are suppressed, there is only a very limited region of superconductivity: a sharp drop of the resistivity to zero near 2.1 K is found only for the $x=0.044$ samples. In the $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ series, superconductivity, with $T_c$ values up to 12 K ($x\sim 0.022$ series) and 20 K ($x\sim 0.047$ series), is stabilized. Quantitative analysis of the detailed temperature-dopant concentration $\left(T-x\right)$ and temperature-extra electrons $\left(T-e\right)$ phase diagrams of these series shows that there exists a limited range of the number of extra electrons added, inside which the superconductivity can be stabilized if the structural and magnetic phase transitions are suppressed enough. Moreover, comparison with pressure-temperature phase diagram data, for samples spanning the whole doping range, further re-enforces the conclusion that suppression of the structural/magnetic phase transition temperature enhances $T_c$ on the underdoped side, but for the overdoped side $T_C^{\text{max}}$ is determined by $e$. Therefore, by choosing the combination of dopants that are used, we can adjust the relative positions of the upper phase lines (structural and magnetic phase transitions) and the superconducting dome to control the occurrence and disappearance of the superconductivity in transition metal, electron-doped ${\text{BaFe}}_2{\text{As}}_2$.

Figure 1

(Color online) (a) Measured Ni concentration vs nominal Ni concentration for the $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Ni}}_x\right)}_2{\text{As}}_2$ series. (b) Enlarged measured Cu concentration vs nominal Cu concentration for $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ ($x=0$, $x\sim 0.022$, and $x\sim 0.047$). Inset: $x_{\text{WDS}}$ vs $x_{\text{nominal}}$ for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Cu}}_x\right)}_2{\text{As}}_2$ in the whole doping range.

Figure 2

(Color online) Powder x-ray diffraction patterns for $\text{Ba}{\left({\text{Fe}}_{0.644}{\text{Cu}}_{0.356}\right)}_2{\text{As}}_2$, $\text{Ba}{\left({\text{Fe}}_{0.895}{\text{Co}}_{0.047}{\text{Cu}}_{0.058}\right)}_2{\text{As}}_2$, $\text{Ba}{\left({\text{Fe}}_{0.928}{\text{Ni}}_{0.072}\right)}_2{\text{As}}_2$, and pure ${\text{BaFe}}_2{\text{As}}_2$.

Figure 3

(Color online) Room temperature lattice parameters of the $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Ni}}_x\right)}_2{\text{As}}_2$ series, $a$ and $c$ as well as unit cell volume, $V$, normalized to the values of pure ${\text{BaFe}}_2{\text{As}}_2$ [$a_0=3.9621\left(8\right)\text{Å}$, $c_0=13.018\left(2\right)\text{Å}$, and $V_0=204.357{\text{Å}}^3$] as a function of measured Ni concentration, $x_{\text{WDS}}$.

Figure 4

(Color online) The $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Ni}}_x\right)}_2{\text{As}}_2$ series: (a) The temperature-dependent resistivity, normalized to the room temperature value. Each subsequent data set is shifted downward by 0.3 for clarity. (b) $d\left(\rho \left(T\right)/{\rho }_{300\text{K}}\right)/dT$ for $y\le 0.032$. The criteria to infer $T_s$ and $T_m$ from the resistivity data are shown. (c) Enlarged low temperature $\rho \left(T\right)/{\rho }_{300\text{K}}$. The offset and onset criteria to infer $T_c$ are shown.

Figure 5

(Color online) The $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Ni}}_x\right)}_2{\text{As}}_2$ series: (a) $M\left(T\right)/H$ data taken at 1 T with $H\perp c$. (b) Field-cooled (FC) and zero-field-cooled (ZFC) low field $M\left(T\right)/H$ data taken at 2.5 mT with $H\perp c$. The criterion to infer $T_c$ is shown. (c) $d\left(M\left(T\right)/H\right)/dT$ for $x\le 0.024$. The criteria to infer $T_s$ and $T_m$ are shown. (d) The criterion to infer $T_s$ for $x=0.032$ sample.

Figure 6

(Color online) $T-x$ phase diagram of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Ni}}_x\right)}_2{\text{As}}_2$ single crystals for $x\le 0.072$. The precise form of $T_s$ and $T_m$ lines are not yet determined in the superconducting dome region, but we assume that they intersect with the superconducting dome near $T_c^{\text{max}}$ (Ref. 28), which is implied by the shading plotted in the superconducting dome.

Figure 7

(Color online) $R\left(H\right)$ data of $\text{Ba}{\left({\text{Fe}}_{0.954}{\text{Ni}}_{0.046}\right)}_2{\text{As}}_2$ with $H\perp c$ (left panel) and $H\parallel c$ (right panel).

Figure 8

(Color online) (a) $H_{c2}$ vs $T$ from offset criterion (upper panel) and onset criterion (lower panel) of $\text{Ba}{\left({\text{Fe}}_{0.954}{\text{Ni}}_{0.046}\right)}_2{\text{As}}_2$ and $\text{Ba}{\left({\text{Fe}}_{0.953}{\text{Co}}_{0.047}\right)}_2{\text{As}}_2$ (Ref. 20). (b) $H_{c2}$ vs. $T/T_c$ from offset criterion (upper panel) and onset criterion (lower panel) of $\text{Ba}{\left({\text{Fe}}_{0.954}{\text{Ni}}_{0.046}\right)}_2{\text{As}}_2$ and $\text{Ba}{\left({\text{Fe}}_{0.926}{\text{Co}}_{0.074}\right)}_2{\text{As}}_2$ (Ref. 20). (c) $\gamma =H_{c2}^{\perp c}/H_{c2}^{\parallel c}$ vs $T/T_c$ for $\text{Ba}{\left({\text{Fe}}_{0.954}{\text{Ni}}_{0.046}\right)}_2{\text{As}}_2$. For each composition, data inferred from $R\left(H\right)$ measurements on two samples are shown.

Figure 9

(Color online) Lattice parameters of the $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Cu}}_x\right)}_2{\text{As}}_2$ series, $a$ and $c$ as well as unit cell volume, $V$, normalized to the values of pure ${\text{BaFe}}_2{\text{As}}_2$ ($a_0=3.9621\left(8\right)\text{Å}$, $c_0=13.0178\left(20\right)\text{Å}$, and $V_0=204.357{\text{Å}}^3$) as a function of measured Cu concentration, $x_{\text{WDS}}$

Figure 10

(Color online) The temperature-dependent resistivity, normalized to the room temperature value, for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Cu}}_x\right)}_2{\text{As}}_2$. Each subsequent data set is shifted downward by 0.3 for clarity, respectively, for (a) and (b).

Figure 11

(Color online) (a) $d\left(\rho \left(T\right)/{\rho }_{300\text{K}}\right)/dT$ of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Cu}}_x\right)}_2{\text{As}}_2$ for $0.05\ge x$. (b) Enlarged low temperature $\rho \left(T\right)/{\rho }_{300\text{K}}$ data of $\text{Ba}{\left({\text{Fe}}_{0.956}{\text{Cu}}_{0.044}\right)}_2{\text{As}}_2$

Figure 12

(Color online) The $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Cu}}_x\right)}_2{\text{As}}_2$ series: (a) $M\left(T\right)/H$ taken at 1 T with $H\perp c$ for $0\le x\le 0.035$. (b) $M\left(T\right)/H$ taken at 1 T with $H\perp c$ for $0.035<x\le 0.068$. (c) $d\left(M\left(T\right)/H\right)/dT$ for $x\le 0.026$. The criteria to infer $T_s$ and $T_m$ are shown. (d) The criteria to infer $T_s$ and $T_m$ for $x=0.035$ sample.

Figure 13

(Color online) (a) Temperature-dependent heat capacity of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Cu}}_x\right)}_2{\text{As}}_2$ ($x=0$, 0.0077, 0.02, and 0.026). Inset: $C_p$ vs $T^2$ for $\text{Ba}{\left({\text{Fe}}_{0.956}{\text{Cu}}_{0.044}\right)}_2{\text{As}}_2$. (b) $d{C}_p/dT$ vs. $T$ for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Cu}}_x\right)}_2{\text{As}}_2$ ($x=0.0077$, 0.02, and 0.026).

Figure 14

(Color online) $T-x$ phase diagram of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Cu}}_x\right)}_2{\text{As}}_2$ single crystals for $x\le 0.061$. Superconductivity is only determined below 2 K, the extent of the superconducting region is unknown, but is bounded by $x=0.035$ on the underdoped side and $x=0.05$ on the overdoped side.

Figure 15

(Color online) Lattice parameters of the $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ $\left(x\sim 0.022\right)$ series, $a$ and $c$ as well as unit cell volume, $V$, normalized to the values of $\text{Ba}{\left({\text{Fe}}_{0.976}{\text{Co}}_{0.024}\right)}_2{\text{As}}_2$ ($a_0=3.9598\left(6\right)\text{Å}$ and $c_0=13.004\left(3\right)\text{Å}$) as a function of measured Cu concentration, $y_{\text{WDS}}$. The solid lines represent the values of $a/a_0$ and $c/c_0$ for the $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ $\left(x=0\right)$ series shown in Fig. 9.

Figure 16

(Color online) The $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ $\left(x\sim 0.022\right)$ series. (a) The temperature-dependent resistivity, normalized to the room temperature values. Each subsequent data set is shifted downward by 0.3 for clarity. (b) $d\left(\rho \left(T\right)/{\rho }_{300\text{K}}\right)/dT$ for $y\le 0.019$. (c) Enlarged, low temperature, $\rho \left(T\right)/{\rho }_{300\text{K}}$.

Figure 17

(Color online) The $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ $\left(x\sim 0.022\right)$ series: (a) $M\left(T\right)/H$ data taken at 1 T with $H\perp c$. (b) $d\left(M/H\right)/dT$ for $y=0.005$, 0.01, and 0.019 samples. Each subsequent data set is shifted downward by $1\times {10}^{-6}$ for clarity. (c) FC and ZFC low-field $M\left(T\right)/H$ data taken at 2.5 mT with $H\perp c$.

Figure 18

(Color online) Temperature-dependent heat capacity of $\text{Ba}{\left({\text{Fe}}_{0.953}{\text{Co}}_{0.021}{\text{Cu}}_{0.026}\right)}_2{\text{As}}_2$. Inset: $C_p/T$ vs $T$.

Figure 19

(Color online) $T-y$ phase diagram of $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ $\left(x\sim 0.022\right)$ single crystals. The shading in the superconducting dome implies the existence of a crossover from tetragonal/paramagnetic phase to orthorhombic/antiferromagnetic phase, as used in Fig. 6.

Figure 20

(Color online) (a) Low-temperature-dependent resistivity, normalized by room temperature value, for $\text{Ba}{\left({\text{Fe}}_{0.953}{\text{Co}}_{0.021}{\text{Cu}}_{0.026}\right)}_2{\text{As}}_2$ with 0, 1, 3, 5, and 7 T magnetic field perpendicular to $c$ axis (upper panel) and along $c$ axis (lower panel). (b)Critical field $H_{c2}$ vs $T$ determined from onset and offset criteria. (c) The ratio of anisotropic critical field $\gamma =H_{c2}^{\perp c}/H_{c2}^{\parallel c}$ vs $T/T_c$.

Figure 21

(Color online) Lattice parameters of the $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ $\left(x\sim 0.047\right)$ series, $a$ and $c$ as well as unit cell volume, $V$, normalized to the values of $\text{Ba}{\left({\text{Fe}}_{0.953}{\text{Co}}_{0.047}\right)}_2{\text{As}}_2$ $\left[a_0=3.9605\left(6\right)\text{Å},c_0=12.992\left(4\right)\text{Å}\right]$ as a function of measured Cu concentration, $y_{\text{WDS}}$. The dash lines and solid lines represent the values for the $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ $\left(x\sim 0.022\right)$ and $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ $\left(x=0\right)$ series shown in Figs. 9, 15, respectively.

Figure 22

(Color online) The $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ $\left(x\sim 0.047\right)$ series: (a) The temperature dependent resistivity, normalized to the room temperature value. Each subsequent data set is shifted downward by 0.3 for clarity. (b) $d\left(\rho \left(T\right)/{\rho }_{300\text{K}}\right)/dT$ for $y=0$ and 0.0045. (c) Enlarged low temperature $\rho \left(T\right)/{\rho }_{300\text{K}}$.

Figure 23

(Color online) The $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ $\left(x\sim 0.047\right)$ series: (a) FC and ZFC low field $M\left(T\right)/H$ data taken at 2.5 mT with $H\perp c$. (b) $M\left(T\right)/H$ data taken at 1 T with $H\perp c$ for $0\le y\le 0.034$.

Figure 24

(Color online) Temperature-dependent heat capacity of $\text{Ba}{\left({\text{Fe}}_{0.934}{\text{Co}}_{0.047}{\text{Cu}}_{0.019}\right)}_2{\text{As}}_2$. Inset: $C_p/T$ vs $T$ near the superconducting transition with the estimated $\Delta C_p$ shown.

Figure 25

(Color online) $T-y$ phase diagram of $\text{Ba}{\left({\text{Fe}}_{1-x-y}{\text{Co}}_x{\text{Cu}}_y\right)}_2{\text{As}}_2$ $\left(x\sim 0.047\right)$ single crystals. The shading in the superconducting dome implies the existence of a crossover from tetragonal/paramagnetic phase to orthorhombic/antiferromagnetic phase, as used in Fig. 6. Note: Given the rapid loss of features associated with the antiferromagnetic transition, the AFM phase line is speculative.

Figure 26

(Color online) (a) $T-x$ phase diagrams for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{TM}}_x\right)}_2{\text{As}}_2$ $\left(\text{TM}=\text{Co},\text{Ni},\text{Cu},\text{Co}/\text{Cu}\right)$. (a) $T-e$ phase diagrams for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{TM}}_x\right)}_2{\text{As}}_2$ $\left(\text{TM}=\text{Co},\text{Ni},\text{Cu},\text{Co}/\text{Cu}\right)$.

Figure 27

(Color online) The comparison of the effects of chemical doping (Ref. 41) and application of pressure (Ref. 40) for the $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ series.