Quasi-two-dimensional behavior of 112-type iron-based superconductors

Fluctuation magnetoconductivity and magnetization above the superconducting transition temperature ($T_c$) are measured on the recently discovered 112 family of iron-based superconductors (IBS), ${\mathrm{Ca}}_{1-x}{\mathrm{La}}_x{\mathrm{Fe}}_{1-y}{\mathrm{Ni}}_y{\mathrm{As}}_2$, which presents an extra As-As chain spacer-layer. The analysis in terms of a generalization of the Lawrence-Doniach approach to finite applied magnetic fields indicates that these compounds are among the most anisotropic IBS ($\gamma$ up to $\sim 30$) and provides compelling evidence of a quasi-two-dimensional behavior for doping levels near the optimal one.

Figure 1

Examples of EDX spectrum measured in the studied crystals.

Figure 2

XRD pattern of the studied crystals (already corrected for a background contribution).

Figure 3

$T$ dependence of the resistivity around $T_c$ of the studied crystals for both field orientations. The lines are examples (for ${\mu }_{0}H=9$ T) of the background contribution, as determined by a linear fit above 35 K, where fluctuation effects are expected to be negligible.

Figure 4

Analysis of the results for crystal 9. (a) $T$ dependence of $\mathrm{\Delta }\sigma$ for $H\perp ab$. The lines are the best fit of Eq. (1) to the data up to the $\mathrm{\Delta }\sigma$ value indicated by the arrow. (b) $T$ dependence of $\mathrm{\Delta }\sigma$ for $H\parallel ab$. Inset: $H$ dependence for different temperatures above $T_c$. The lines in the main panel and in the inset were evaluated by using in Eq. (1) the superconducting parameters obtained in (a). See the main text for details.

Figure 5

Analysis of the results for crystal 6. (a) $T$ dependence of $\mathrm{\Delta }\sigma$ for $H\perp ab$. The lines are the best fit of Eq. (3) to the data up to the $\mathrm{\Delta }\sigma$ value indicated by the arrow. Inset: Comparison of the $H=0$ data with the 2D, 3D, and LD approaches (see the main text for details). (b) $T$ dependence for $H\parallel ab$. The line was evaluated with the zero-field LD expression, Eq. (4), by using the $r$ value obtained in (a). Inset: $H$ dependence of $\mathrm{\Delta }\sigma$ above $T_c$ for both field orientations. The data for $H\parallel ab$ are almost $H$ independent, as expected for a (quasi)-2D superconductor. The lines correspond to $H\perp ab$ and were evaluated by using in Eq. (3) the same parameters as in (a).

Figure 6

(a) $T$ dependence of the low-field (0.3 mT) ZFC magnetic susceptibility of crystal 11 (already corrected for demagnetizing effects). (b) Detail of the $T$ dependence of the as-measured magnetic moment around $T_c$. Solid and open symbols were obtained under ZFC and FC conditions, respectively. The diamagnetism above $T_c$ is unobservable in this scale. (c) Examples of the $T$ dependence up to 50 K, where the normal-state backgrounds (lines) were determined by a linear fit in the indicated region.

Figure 7

3D-GL scaling of the magnetization in the critical region. For clarity the noisy data for 6 T and 7 T were not included in the representation, but they are still consistent with the scaling. Inset: $T$ dependence of the unscaled $\mathrm{\Delta }M$ data around $T_c$. The circle is the prediction for the crossing point of 2D superconductors. See the main text for details.

Figure 8

Temperature dependence just above $T_c$ of the fluctuation magnetic susceptibility obtained with ${\mu }_{0}H=1$ T. The solid line is the best fit of Eq. (7) above 22 K with $r$ as the only free parameter. For comparison, the results for the 2D and 3D approaches are also included (see the main text for details).

Figure 9

$T_c$ dependence of the coherence lengths and of the anisotropy factor of the studied samples.