The coexistence of a new-type antiferromagnetic (AFM) state, the so-called hedgehog spin-vortex crystal (SVC), and superconductivity (SC) is evidenced by an ${}^{75}\mathrm{As}$ nuclear magnetic resonance study on single-crystalline $\mathrm{CaK}{\left({\mathrm{Fe}}_{0.951}{\mathrm{Ni}}_{0.049}\right)}_4{\mathrm{As}}_4$. The hedgehog SVC order is clearly demonstrated by the direct observation of internal magnetic induction along the $c$ axis at the As1 site (close to K) and a zero net internal magnetic induction at the As2 site (close to Ca) below an AFM ordering temperature $T_{\mathrm{N}}\sim 52$ K. The nuclear spin-lattice relaxation rate $1/T_1$ shows a distinct decrease below $T_{\mathrm{c}}\sim 10$ K, providing also unambiguous evidence for the microscopic coexistence. Furthermore, based on the analysis of the $1/T_1$ data, the hedgehog SVC-type spin correlations are found to be enhanced below $T\sim 150$ K in the paramagnetic state. These results indicate the hedgehog SVC-type spin correlations play an important role for the appearance of SC in the new magnetic superconductor.

• Received 26 October 2017
• Revised 11 December 2017

DOI:https://doi.org/10.1103/PhysRevB.96.220510