We report combined experimental and theoretical analysis of superconductivity in $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_4{\mathrm{As}}_4$ (CaK1144) for $x=0$, 0.017, and 0.034. To obtain the superfluid density $\rho ={\left[1+\mathrm{\Delta }{\lambda }_L\left(T\right)/{\lambda }_L\left(0\right)\right]}^{-2}$, the temperature dependence of the London penetration depth $\mathrm{\Delta }{\lambda }_L\left(T\right)$ was measured by using a tunnel-diode resonator (TDR) and the results agreed with the microwave coplanar resonator (MWR) with the small differences accounted for by considering a three orders of magnitude higher frequency of MWR. The absolute value of ${\lambda }_L(T\ll T_c)\approx {\lambda }_L\left(0\right)$ was measured by using MWR, ${\lambda }_L\left(5\mathrm{K}\right)\approx 170\pm 20$ nm, which agreed well with the NV centers in diamond optical magnetometry that gave ${\lambda }_L\left(5\mathrm{K}\right)\approx 196\pm 12$ nm. The experimental results are analyzed within the Eliashberg theory, showing that the superconductivity of CaK1144 is well described by the nodeless $s_{\pm }$ order parameter and that upon Ni doping the interband interaction increases.

• Received 13 May 2019
• Revised 12 July 2019
• Corrected 6 April 2021

DOI:https://doi.org/10.1103/PhysRevB.100.094513