Superconducting state coexisting with a phase-separated static magnetic order in $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$, $\left(\text{Sr},\text{Na}\right){\text{Fe}}_2{\text{As}}_2$, and ${\text{CaFe}}_2{\text{As}}_2$

By muon spin-relaxation measurements on single-crystal specimens, we show that superconductivity in the $A{\text{Fe}}_2{\text{As}}_2$ $\left(A=\text{Ca},\text{Ba},\text{Sr}\right)$ systems, in both the cases of composition and pressure tunings, coexists with a strong static magnetic order in a partial volume fraction. The superfluid response from the remaining paramagnetic volume fraction of $\left({\text{Ba}}_{0.5}{\text{K}}_{0.5}\right){\text{Fe}}_2{\text{As}}_2$ exhibits a nearly linear variation in $T$ at low temperatures, suggesting an anisotropic energy gap with line nodes and/or multigap effects.

Figure 1

(Color online) Temperature dependences of the resistivity and the magnetic susceptibility of our specimens of (a) $\left({\text{Ba}}_{0.5}{\text{K}}_{0.5}\right){\text{Fe}}_2{\text{As}}_2$ $\left(T_c\sim 37\text{K}\right)$ and (b) $\left({\text{Sr}}_{0.5}{\text{Na}}_{0.5}\right){\text{Fe}}_2{\text{As}}_2$ $\left(T_c\sim 35\text{K}\right)$. Due to the irregular shape of the specimen which prevents accurate estimate of the demagnetizing factor, we put the results of the latter system on a relative (arbitrary) scale. The inset figure of (b) shows the magnetic susceptibility obtained in the field-cooling and zero-field-cooling procedures.

Figure 2

(Color online) Temperature dependences of (a) the muon spin precession frequency observed in ZF $\mu \text{SR}$ and (b) the paramagnetic volume fraction determined from WTF-$\mu \text{SR}$ measurements of single-crystal specimens of $\left({\text{Ba}}_{0.5}{\text{K}}_{0.5}\right){\text{Fe}}_2{\text{As}}_2$ $\left(T_c\sim 37\text{K}\right)$ and $\left({\text{Sr}}_{0.5}{\text{Na}}_{0.5}\right){\text{Fe}}_2{\text{As}}_2$ $\left(T_c\sim 35\text{K}\right)$. The results from the present work (solid and open symbols) are compared with those of the undoped parent compounds ${\text{BaFe}}_2{\text{As}}_2$ (Ref. 15) and ${\text{SrFe}}_2{\text{As}}_2$ (Ref. 10) (solid and broken lines).

Figure 3

(Color online) (a) Temperature dependence of the muon spin-relaxation rate $\sigma$ observed in a single-crystal specimen of $\left({\text{Ba}}_{0.5}{\text{K}}_{0.5}\right){\text{Fe}}_2{\text{As}}_2$ $\left(T_c\sim 37\text{K}\right)$ in TF $\mu \text{SR}$ with $\text{TF}=500\text{G}$ (closed circles, present work), compared with the temperature dependence expected for the isotropic energy gap of BCS $s$-wave pairing (broken line), scaled results from YBCO (Ref. 25) (solid line), and our previous results in a different crystal of ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$ (Ref. 15) (open circles). (b) A plot of the relaxation rate $\sigma \left(T\to 0\right)$ versus $T_c$, including the point for $\left({\text{Ba}}_{0.5}{\text{K}}_{0.5}\right){\text{Fe}}_2{\text{As}}_2$ from the present work as well as those for the FeAs-based 1111 superconductors published in Refs. 12, 14, various cuprates, and $A_3{\text{C}}_{60}$ superconductors (Ref. 18).

Figure 4

(Color online) (a) The volume fraction of regions without static magnetic order in ${\text{CaFe}}_2{\text{As}}_2$, as a function of temperature and pressure, determined by WTF-$\mu \text{SR}$ measurements with WTF $\sim 50\text{G}$. The points with closed (open) symbols were obtained in measurements with (without) a pressure cell. (b) Pressure dependence of the volume fraction of the magnetically ordered region (purple closed circles; left axis) from WTF $\mu \text{SR}$ and the muon spin precession frequency (blue triangles; right axis) from ZF $\mu \text{SR}$ at $T\sim 2\text{K}$ in ${\text{CaFe}}_2{\text{As}}_2$. (c) The phase diagram as a function of pressure and temperature in ${\text{CaFe}}_2{\text{As}}_2$. The $T_c$ values are taken from the reported resistivity results (Ref. 4). Upper, middle, and lower temperatures attached to the closed circle symbols for $T_N$ represent temperatures at which the volume fraction with static magnetic order becomes 30%, 50%, and 70% of the value at $T\to 0$, respectively.