Tuning superconductivity and spin-vortex fluctuations in CaKFe${}_4$As${}_4$ through in-plane antisymmetric strains

Lattice strains of appropriate symmetry have served as an excellent tool to explore the interaction of superconductivity in the iron-based superconductors with nematic and stripe spin-density wave (SSDW) order, which are both closely tied to an orthorhombic distortion. In this work, we contribute to a broader understanding of the coupling of strain to superconductivity and competing normal-state orders by studying CaKFe${}_4$As${}_4$ under large, in-plane strains of $B_{1g}$ and $B_{2g}$ symmetry. In contrast to the majority of iron-based superconductors, pure CaKFe${}_4$As${}_4$ exhibits superconductivity with relatively high transition temperature of $T_c\sim$35 K in proximity of a non-collinear, tetragonal, hedgehog spin-vortex crystal (SVC) order. Through experiments, we demonstrate an anisotropic in-plane strain response of $T_c$, which is reminiscent of the behavior of other pnictides with nematicity. However, our calculations suggest that in CaKFe${}_4$As${}_4$, this anisotropic response correlates with the one of the SVC fluctuations, highlighting the close interrelation of magnetism and high-$T_c$ superconductivity. By suggesting moderate $B_{2g}$ strains as an effective parameter to change the stability of SVC and SSDW, we outline a pathway to a unified phase diagram of iron-based superconductivity.