Effective carrier type and field dependence of the reduced-$T_c$ superconducting state in ${\text{SrFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$

Measurements of the Hall effect, thermoelectric power, magnetic susceptibility, and upper and lower critical fields were performed on single crystals of ${\text{SrFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$, an FeAs-based superconducting system that exhibits a reduced superconducting transition temperature $T_c$ in comparison to most other iron-pnictide superconductors. Studies of the Hall and thermoelectric responses indicate that Ni substitution in this system results in a dominant electronlike response, consistent with electron doping in other similar systems but with a weaker change in the Hall coefficient and a more gradual change in the thermoelectric response with Ni concentration. For optimally doped samples with full superconducting volume fraction, the lower and upper critical fields were determined to be $H_{c1}\left(1.8\text{K}\right)=0.08\text{T}$ and $H_{c2}\left(0\right)=25\text{T}$, respectively, with lower-$T_c$ samples showing reduced values and indications of inhomogeneous superconductivity. Comparable to other higher-$T_c$ FeAs-based materials, the temperature dependence of the upper critical field, $\partial H_{c2}/\partial T$, is linear over a wide temperature range, and the large values of $H_{c2}\left(0\right)$ greatly exceed conventional estimates of paramagnetic and orbital limits.

Figure 1

(Color online) The phase diagram of ${\text{SrFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$ as determined in Ref. 4. The magnetostructural transition is not observed for $x>0.15$ and superconductivity is found for $0.10\le x\le 0.22$. The maximum $T_c\approx 9\text{K}$.

Figure 2

(Color online) Hall coefficient of ${\text{SrFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$ as a function of temperature. The magnetic transitions in $x=0$ and $x=0.08$ are evident as a drop in $R_H$. Superconducting transitions are evident for $0.08\le x\le 0.22$ at low temperatures. All measurements are consistent with a dominant contribution from negative charge carriers. The error bar on the right illustrates the window of uncertainty of about $\pm 0.2\times {10}^{-9}{\text{m}}^3/\text{C}$. Inset: field dependence of the transverse resistivity is linear to at least 5 T.

Figure 3

(Color online) (a) Thermoelectric power $S$ of ${\text{SrFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$ vs temperature. The Ni-substituted samples exhibit linear $T$ dependence at low temperatures, as would be expected in an electron-dominated metal. Slopes increase with increasing Ni content for $x<0.16$. (b) Magnetic field dependence of $S\left(T\right)$ illustrates the suppression of superconductivity for $x=0.16$.

Figure 4

(Color online) Electrical resistivity of ${\text{SrFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$ vs temperature, showing the suppression of the superconducting transition by increasing magnetic field, applied parallel to the $c$ axis. The resistivity is normalized to the normal-state value just above the transition. For $x=0.12$, 7 T data are not shown.

Figure 5

(Color online) Upper critical field $H_{c2}$ of ${\text{SrFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$, for $H\parallel c$, vs temperature. The points here denote half of the resistive transition. Inset: $H_{c2}$ curves scaled to the zero-field transition temperature $T_{c0}$ and a slope of $-1$. The value of $H_{c2}$ at $T=0\text{K}$ exceeds the WHH estimate.

Figure 6

(Color online) Upper critical field slope $\frac{\partial H_{c2}}{\partial T}$ of ${\text{SrFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$ compared to values from the literature. Solid symbols denote $H$ in plane while open symbols denote $H\parallel c$. For a large class of 122 superconductors, values of $\frac{\partial H_{c2}}{\partial T}$ are comparable despite a wide range of $T_c$ values. Data for ${\text{SrFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$ are from this work. Stoichiometric low-$T_c$ materials include ${\text{SrNi}}_2{\text{P}}_2$ (Ref. 32), ${\text{SrNi}}_2{\text{As}}_2$ (Ref. 33), ${\text{BaNi}}_2{\text{As}}_2$ (Ref. 34), ${\text{KFe}}_2{\text{As}}_2$ (Ref. 35), ${\text{BaNi}}_2{\text{As}}_2$ (Ref. 36), and ${\text{BaNi}}_2{\text{P}}_2$ (Ref. 37). The other superconductors are discussed in the text. Data for “undoped strain” are from Refs. 30, 31, “pressure” from Refs. 20, 21, 38, 39, 40, “electron doped” from Refs. 19, 22, 23, 24, 25, 26, 27, 29 and “hole doped” from Refs. 41, 42, 43, 44, 45, 46, 47, 48.

Figure 7

(Color online) Upper critical field $H_{c2}$ of ${\text{SrFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$, determined via resistivity, for different field orientations. Inset: anisotropy of $H_{c2}$, which shows stronger temperature dependence at optimal doping.

Figure 8

(Color online) Magnetization of ${\text{SrFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$ as a function of applied field at 1.8 K with $H$ applied in plane. (a) Hysteresis loops for optimally doped samples have a large area and values of $H_{c2}$ exceeding 7 T. The $x=0.16$ data exhibit a secondary peak, identified by the arrow. (b) For underdoped and overdoped samples, the loops are smaller and critical fields are lower. $M\left(H\right)$ data for the nonsuperconducting parent compound are shown for comparison. Note the different vertical scales. $10\text{kOe}=1\text{T}$.

Figure 9

(Color online) Direction dependence of the magnetization of ${\text{SrFe}}_{1.85}{\text{Ni}}_{0.15}{\text{As}}_2$ at 1.8 K. Field applied in plane evokes a much larger magnetic response than out of plane and the lower critical field $H_{c1}$ is larger for $H\parallel c$. Demagnetization effects have been corrected for. $10\text{kOe}=1\text{T}$.

Figure 10

(Color online) Concentration dependence of the low-temperature properties of the superconducting state of ${\text{SrFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$. (a) The lower critical field $H_{c1}$, identified with the local minimum in the $M\left(H\right)$ virgin curve. (b) The superconducting volume fraction calculated from the initial slope of the virgin $M\left(H\right)$ curves at 1.8 K. (c) Superconducting critical current $J_c$, calculated using the Bean model.