Effect of interlayer coupling on the coexistence of antiferromagnetism and superconductivity in Fe pnictide superconductors: A study of ${\mathrm{Ca}}_{0.74\left(1\right)}{\mathrm{La}}_{0.26\left(1\right)}\left({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\right){\mathrm{As}}_2$ single crystals

We report the transport, thermodynamic, muon spin relaxation, and neutron study of the ${\mathrm{Ca}}_{0.74\left(1\right)}{\mathrm{La}}_{0.26\left(1\right)}$(${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$)${\mathrm{As}}_2$ single crystals, mapping out the temperature-doping level phase diagram. Upon Co substitution on the Fe site, the structural and magnetic phase transitions in this 112 compound are suppressed and superconductivity up to 20 K occurs. Our measurements of the superconducting and magnetic volume fractions show that these two phases coexist microscopically in the underdoped region, in contrast to the related ${\mathrm{Ca}}_{10}$(${\mathrm{Pt}}_3{\mathrm{As}}_8$)((${\mathrm{Fe}}_{1-x}{\mathrm{Pt}}_x$)${}_2{\mathrm{As}}_2$)${}_5$ (10-3-8) compound, where coexistence is absent. Supported by model calculations, we discuss the differences in the phase diagrams of the 112 and 10-3-8 compounds in terms of the FeAs interlayer coupling, whose strength is affected by the character of the spacer layer, which is metallic in the 112 compound and insulating in the 10-3-8 compound.

Figure 1

${\mathrm{Ca}}_{0.74\left(1\right)}{\mathrm{La}}_{0.26\left(1\right)}$(${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$)${\mathrm{As}}_2$: (a) The $x_{\mathrm{nominal}}$ vs $x_{\mathrm{WDS}}$ and the evolution of the FeAs interlayer distance $d$ with $x_{\mathrm{WDS}}$. Inset: single crystals against the 1-mm scale. (b) The temperature-dependent normalized resistance $R/R_{300\text{K}}$ for representative samples. The 50% criterion to infer $T_c$ from resistivity is depicted for the $x=0.025$ sample. (c) The derivative of $R/R_{300\text{K}}$ vs $T$ for the $x=0$ and $x=0.008$ samples. The criteria to infer $T_s$ and $T_m$ are depicted. (d) The temperature-dependent zero-field-cooled (ZFC) and field-cooled (FC) data with $H\parallel ab$. For the $x=0.025$ sample, the value of $4\pi \chi$ is averaged on four pieces. The criterion to infer $T_c$ from susceptibility is depicted. (e) The temperature-dependent Hall coefficient for the $x=0$ and $x=0.033$ samples.

Figure 2

${\mathrm{Ca}}_{0.74\left(1\right)}{\mathrm{La}}_{0.26\left(1\right)}$(${\mathrm{Fe}}_{0.954}{\mathrm{Co}}_{0.046}$)${\mathrm{As}}_2$: (a) The $H_{c2}$ data inferred using the 50% criterion. Inset: the anisotropy parameter of the upper critical field ${\gamma }_H=H_{c2}^{\perp ab}/H_{c2}^{\parallel ab}$. (b) $C_p/T$ vs $T$. (c) The field-dependent critical current density $J$ at various temperatures with $H^{ab}$. (d) Normalized pinning force $f=F_p/F_{p,\text{max}}$ vs reduced field $h=H/H_{\text{irr}}$ at various temperatures. The data were fitted by $f=A{h}^p{(1-h)}^q$ with the parameters $p=1.14$ and $q=3.24$.

Figure 3

${\mathrm{Ca}}_{0.74\left(1\right)}{\mathrm{La}}_{0.26\left(1\right)}$(${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$)${\mathrm{As}}_2$: (a) The representative ZF $\mu \mathrm{SR}$ data of the $x=0.033$ sample. (b) The temperature-dependent ordered magnetic volume fraction $V_{\mathrm{mag}}$ determined from the fitting of the ZF $\mu \mathrm{SR}$ asymmetry spectra. (c) The fast transverse relaxation rate $\sigma$ inferred from the ZF $\mu \mathrm{SR}$ asymmetry spectra. (d) The integrated intensity of the (0,2,0) nuclear neutron peak and the intensity of the (0.5,0.5,0.5) magnetic neutron peak. (e) The temperature-doping level ($T-x$) phase diagram of ${\mathrm{Ca}}_{0.74\left(1\right)}{\mathrm{La}}_{0.26\left(1\right)}$(${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$)${\mathrm{As}}_2$. For $x=0$ and 0.008, $T_s$ and $T_m$ are the structural and magnetic phase transition determined from $dR/R_{300\mathrm{K}}/dT$, respectively. For $x=0.025$ and 0.033, $T_m$ is inferred by the ZF $\mu \mathrm{SR}$ data. $T_c^{50\%}$ is the SC transition temperature determined using the 50% criterion shown in Fig. 1. $T_c^{\text{Mag}}$ is determined from the susceptibility data using the criterion shown in Fig. 1.

Figure 4

The coefficient $g$ as function of the tight-binding parameters $t_0$ and $t_1$ in Eq. (4), under the constraint $t_2=-t_0-t_1$ to maintain the perfect nesting condition at $k_z=0$. Note that $g=0$ at the black lines, whereas $g<0$ in the blue-shaded region (implying AFM-SC microscopic phase coexistence) and $g>0$ and in the red-shaded region (implying AFM-SC macroscopic phase separation).