Two-gap superconductivity with line nodes in CsCa${}_2$Fe${}_4$As${}_4$F${}_2$

We report the results of a muon-spin rotation ($\mu$SR) experiment to determine the superconducting ground state of the iron-based superconductor CsCa${}_2$Fe${}_4$As${}_4$F${}_2$ with $T_{\mathrm{c}}\approx 28.3$K. This compound is related to the fully-gapped superconductor CaCsFe${}_4$As${}_4$, but here the Ca-containing spacer layer is replaced with one containing Ca${}_2$F${}_2$. The temperature evolution of the penetration depth strongly suggests the presence of line nodes and is best modelled by a system consisting of both an $s$- and a $d$-wave gap. We also find a potentially magnetic phase which appears below $\approx 10$K but does not appear to compete with the superconductivity. This compound contains the largest alkali atom in this family of superconductors and our results yield a value for the in-plane penetration depth of ${\lambda }_{ab}(T=0)=423(5)$nm.