Preferred spin excitations in the bilayer iron-based superconductor CaK ( Fe$_{0.96}$Ni$_{0.04}$)$_4$As$_4$ with spin-vortex crystal order

International audienceSpin-orbit coupling (SOC) is a key to understand the magnetically driven superconductivity in iron-based superconductors, where both local and itinerant electrons are present and the orbital angular momentum is not completely quenched. Here, we report a neutron scattering study on the bilayer compound CaK Fe$_{0.96}$Ni$_{0.04}$$_4$As$_4$ with superconductivity coexisting with a noncollinear spin-vortex crystal magnetic order that preserves the tetragonal symmetry of the Fe-Fe plane. In the superconducting state, two spin resonance modes with odd and even L symmetries due to the bilayer coupling are found similar to the undoped compound CaKFe$_4$As$_4$ but at lower energies. Polarization analysis reveals that the odd mode is c-axis polarized, and the low-energy spin anisotropy can persist to the paramagnetic phase at high temperature, which closely resembles other systems with in-plane collinear and c-axis biaxial magnetic orders. These results provide the missing piece of the puzzle on the SOC effect in iron-pnictide superconductors, and also establish a common picture of c-axis preferred magnetic excitations below Tc regardless of the details of magnetic pattern or lattice symmetry