Iron-based superconductors (FeSCs) include several families, such as 1111 family,^[1–3] 122 family,^[4] 111 family,^[5] and 112 family.^[6] Among them, Ca_1–xLa_xFeAs₂ (CaLa112) is the first example of FeSCs which crystallizes in a monoclinic lattice with the space group of P21 (No. 4).^[6] The presence of one-dimensional zig-zag As chains is the most prominent feature of the metallic block layer between the FeAs layers. Such metallic layers make the structure and electronic of CaLa112 distinct from other FeSCs. The temperature-doping phase diagram of CaLa112 is in stark contrast to many existing FeSCs, since the Neel temperature T_N of CaLa112 is found to increase with increasing x (0.15 < x < 0.25).^[7] Intriguingly, T_N is gradually suppressed with electron doping (Co, Ni, or Pd substitution on the Fe site) and another superconducting phase is resolved.^[8–10] The metallic spacer layers and the interesting phase diagram make CaLa112 particularly interesting.

The superconducting anisotropy parameter γ is an important quantity for characterizing superconductivity. From the standard anisotropic Ginzburg–Landau theory, γ≡mc∗/ma∗=Hc2||ab/Hc2||c=λc/λab=ξab/ξc, where m is the effective mass, c and a are crystallographic axes, respectively, H_c2 is the upper critical field, λ is the penetration depth, and ξ is the coherence length. For CaLa112 system, the anisotropy parameter γ is reported in a very limited temperature range close to T_c. For example, in Ca_0.82La_0.18FeAs₂, γ is 2 – 4 at 0.90 < t(T/T_c) < 0.96.^[11] For Ca_0.8La_0.2Fe_0.98Co_0.02As₂, γ is 2–6 at 0.95 < t < 0.98.^[12] In addition, the γ reported is based on transport measurement which is not a thermodynamic approach. Among many different techniques, torque magnetometry is the most sensitive one to detect anisotropy parameter especially with small single crystals.^[13,14] Torque is a thermodynamic approach, which is defined by the angular derivative of the free energy.^[15] It has been successfully applied to investigate the anisotropy of FeSCs, cuprates, heavy fermion superconductors,and intermetallic compounds, see our previous work^[16–19] and other reports.^[20–23]

Ca_0.73La_0.27FeAs₂ is regarded as a parent compound of 112 type iron-based superconductors. With Co substitution on Fe site, superconductivity is induced in the system. Here, we performed torque measurements on single crystal samples of Ca_0.73La_0.27(Fe_0.96Co_0.04)As₂. Based on Kogan’s model,^[15] we obtained the anisotropy parameter γ and estimated the in-plane penetration depth λ_ab, an important characteristic length scale of a superconductor, which parameterizes the ability of a superconductor to screen an applied field by the diamagnetic response of the superconducting condensate. It was found that at the reduced temperature t = 0.85, γ ≃ 7.5. Thus, this material is more anisotropic compared to 11 and 122 families of FeSCs, whose γ is about 2–3.^[24] It was found that γ is not constant, instead, it shows an obvious temperature dependence, which suggests a multiband picture.^[25]

High quality single crystal samples of Ca_0.73La_0.27(Fe_0.96 Co_0.04)As₂ were grown by the self-flux method.^[26] Electrical resistance measurements were performed in a physical property measurement system (PPMS). Magnetization measurements were performed by using a superconducting quantum interference device (SQUID). The sample for which the torque data is shown in this paper has a mass of 0.40 mg. Angular dependent torque measurements were performed by using a piezoresistive torque magnetometer in the PPMS. The angle θ is defined as the angle between the magnetic field and the c-axis of the single crystal. In this technique, a piezoresistor measures the torsion, or twisting, of the torque lever about its symmetry axis as a result of the magnetic moment of the sample. Note that the torque due to gravity and puck should always be subtracted from the total measured torque signal.^[19]

Figure 1(a) shows the temperature T dependent resistance R. The onset of the superconducting transition appears at Tconset=20.0K and the zero resistance is reached at T_c0 = 17.5 K. The magnetization M curves were measured under field-cooled (FC) and zero-field- cooled (ZFC) conditions with a magnetic field H of 10 Oe applied along the ab-plane of the crystal, as shown in Fig. 1(b). Tcm determined from the magnetization measurements is 17.9 K, which is consistent with the T_c0 obtained from the resistance measurements.

Figure 2(a) shows selected torque data measured in the normal state. It is found that torque τ is sinusoidal and can be well fitted by

$$ \begin{eqnarray}\tau (T,H,\theta )={\tau }_{0}(T,H)\sin 2\theta,\end{eqnarray}$$ (1)

$$ \begin{eqnarray}{\tau }_{0}(T,H)=A(T){H}^{2},\end{eqnarray}$$ (2)

$$ \begin{eqnarray}\tau (T,H,\theta )={\tau }_{0}\sin 2\theta =A(T){H}^{2}\sin 2\theta .\end{eqnarray}$$ (3)

$$ \begin{eqnarray}{\tau }_{p}=\displaystyle \frac{{\chi }_{c}-{\chi }_{ab}}{2}{H}^{2}\sin 2\theta,\end{eqnarray}$$ (4)

The anisotropy parameter γ is an important quantity for characterizing superconductivity. Here we examine the anisotropy γ of Ca_0.73La_0.27(Fe_0.96Co_0.04)As₂ by studying the torque data in the mixed state for T < T_c. Figure 3(a) shows the torque data measured at T = 17 K and H = 3 T, which is the typical behavior in the mixed state. With increasing and decreasing angular sweeps, a large hysteresis is observed, which is a result of intrinsic pinning of vortices. The reversible part of the torque can be obtained by τ_rev = (τ_inc + τ_dec)/2, where τ_inc and τ_dec indicate torque data measured with increasing and decreasing angle sweeps, respectively. Only τ_rev reflects the equilibrium state which allows the determination of thermodynamic parameters. Figure 3(b) plots τ_rev for the data measured at T = 17 K with different applied magnetic fields. The symbols are data points and the solid lines are fitting curves by the following equation:

$$ \begin{eqnarray}{\tau }_{{\rm{rev}}}(\theta )=a\sin 2\theta +\displaystyle \frac{{\varphi }_{0}HV}{16\pi {\mu }_{0}{\lambda }_{ab}^{2}}\displaystyle \frac{{\gamma }^{2}-1}{\gamma }\displaystyle \frac{\sin 2\theta }{\varepsilon (\theta )}\mathrm{ln}\left\{\displaystyle \frac{\gamma \eta {H}_{{\rm{c}}2}^{||c}}{H\varepsilon (\theta )}\right\},\,\end{eqnarray}$$ (5)

The magnetic field dependence of the anisotropy parameter γ is summarized in Fig. 3(c). It is found that, γ exhibits weak magnetic field dependence. At the reduced temperature t = 0.85, γ ≃ 7.5. The anisotropy parameter γ of the 11 and 122 families of FeSCs stays in the range of 2–3,^[24] like for FeSe_0.5Te_0.5, γ ≃ 3.1 at t = 0.86 determined by torque measurements.^[27] For 1111 family of FeSCs, like SmFeAsO_0.8F_0.2, γ ≃ 12 at t = 0.8,^[25] CaFe_0.88Co_0.12AsF γ ≃ 15 at t = 0.83.^[16] So, the sample examined in this work is more anisotropic compared to 11 and 122 families, but less anisotropic than 1111 families of FeSCs. Similar conclusion can be reached based on γ_H (=Hc2||ab/Hc2||c) of 11, 122, and 1111 families of FeSCs.^[24,28] The relatively large anisotropy of CaLa112 may result from the large distance d (∼ 1.035 nm) between the adjacent FeAs layers.^[11] Note that this material crystallizes in a low symmetry crystal structure with an additional metallic spacer-layer which significantly increases the distance between the superconducting FeAs layers.^[29] Figure 3(d) is a plot of the field dependence of β. Note that β displays linear behavior with zero y-intercept, as it should be, and based on which the penetration depth can be obtained.

Figure 4(a) plots τ_rev for the data measured with H = 9 T at different temperatures. Figure 4(b) summarizes the temperature T dependence of the anisotropy parameter γ. Note that with increasing temperature, γ decreases fast, at t = 0.75, γ ≃ 11.45, and at t = 0.9, γ ≃ 6.84. The fact that γ is not a constant suggests that Ca_0.73La_{0.2 7}(Fe_0.96Co_0.04)As₂ is probably a multiband/multigap superconductor. This multiband picture is consistent with other reports. For example, Xing et al. reported that a two-band model is required to fully reproduce the behavior of μ0Hc2||c(T) in Ca_0.8La_0.2Fe_0.98Co_0.02As₂, in which μ0Hc2||c(T) presents a sublinear temperature dependence with decreasing temperature.^[30] Note that multiband picture is also reported in other FeSCs, such as LaFeAsO_0.9F_0.1,^[20] SmFeAsO_0.8F_0.2,^[25] and FeSe_0.5Te_0.5.^[27]

In Fig. 4(b), we also compare our data and other reports for similar compounds.^[11,12,30] It is found that the Co-doped 112 system is more anisotropic than the one without doping at temperature close to T_c. Furthermore, it is found that for Co-doped 112 system, the anisotropy determined from our torque measurements γ_λ, and the one based on upper critical field γ_H, show opposite temperature dependence at low temperatures. Note that for a multiband superconductor at arbitrary temperatures, γ_H and γ_λ are not necessarily the same, since the former determines the anisotropy of the coherence length, while the latter describes the ellipticity of the current distribution far from the core.^[31] However, the anisotropy parameters determined by different techniques tend to meet at T_c as shown in Fig. 4(b).

From Eq. (2), we can also obtain the temperature dependence of penetration depth λ_ab, as shown in Fig. 4(c). It is found that λ_ab increases with increasing temperature. At t = 0.75, λ_ab = 347 nm. At t = 0.9, λ_ab = 475 nm. This is consistent with an earlier report λ_ab(0) = 300 – 500 nm.^[32] In addition, λ⁻² shows a pronounced positive curvature (Fig. 4(d)), similar to that of MgB₂^[33] and LaFeAsO_0.9F_0.1.^[20] Such an upward curvature is consistent with the s^± scenario with interband impurity scattering.^[34]

In summary, we performed detailed angular dependent torque measurements on Ca_0.73La_0.27(Fe_0.96Co_0.04)As₂. A large paramagnetic effect is observed in the normal state. In the mixed state, we obtain the anisotropy parameter from the reversible torque. The moderate anisotropy shows that this 112 FeSC is more anisotropic in the mixed state compared to 11 and 122 families of FeSCs, but less anisotropic than 1111 families of FeSCs. We also investigate its temperature and magnetic field evolution. The fact that the anisotropy parameter is not a constant points to a possible multiband picture. At low temperatures, our anisotropy parameter shows different behavior from the one determined by transport measurements, similar to the iron-based superconductor FeSe_0.5Te_0.5, Ba_1–xK_xFe₂As₂^[24] and the two-gap superconductor MgB₂.^[23]