Strong Pauli paramagnetic effect in the upper critical field of KCa${}_2$Fe${}_4$As${}_4$F${}_2$

Recently, 12442 system of Fe-based superconductors has attracted considerable attention owing to its unique double-FeAs-layer structure. A steep increase in the in-plane upper critical field with cooling has been observed near the superconducting transition temperature, $T_c$, in KCa${}_2$Fe${}_4$As${}_4$F${}_2$ single crystals. Herein, we report a high-field investigation on upper critical field of this material over a wide temperature range, and both out-of-plane ($H\mathrm{\parallel }c$, $H_{c2}^c$) and in-plane ($H\mathrm{\parallel }ab$, $H_{c2}^{ab}$) directions have been measured. A sublinear temperature-dependent behavior is observed for the out-of-plane $H_{c2}^c$, whereas strong convex curvature with cooling is observed for the in-plane $H_{c2}^{ab}$. Such behaviors could not be described by the conventional Werthamer–Helfand–Hohenberg (WHH) model. The data analysis based on the WHH model by considering the spin aspects reveals a large Maki parameter $\alpha =9$, indicating that the in-plane upper critical field is affected by a very strong Pauli paramagnetic effect.