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The spin-orbit coupling (SOC) is a key to understand the magnetically drivensuperconductivity in iron-based superconductors, where both local and itinerantelectrons are present and the orbital angular momentum is not completelyquenched. Here, we report a neutron scattering study on the bilayer compoundCaK(Fe$_{0.96}$Ni$_{0.04}$)$_4$As$_4$ with superconductivity coexisting with anon-collinear spin-vortex crystal magnetic order that preserves the tetragonalsymmetry of Fe-Fe plane. In the superconducting state, two spin resonance modeswith odd and even $L$ symmetries due to the bilayer coupling are found similarto the undoped compound CaKFe$_4$As$_4$ but at lower energies. Polarizationanalysis reveals that the odd mode is $c-$axis polarized, and the low-energyspin anisotropy can persist to the paramagnetic phase at high temperature,which closely resembles other systems with in-plane collinear and $c-$axisbiaxial magnetic orders. These results provide the missing piece of the puzzleon the SOC effect in iron-pnictide superconductors, and also establish a commonpicture of $c-$axis preferred magnetic excitations below $T_c$ regardless ofthe details of magnetic pattern or lattice symmetry.

Preferred Spin Excitations in the Bilayer Iron-Based Superconductor CaK(Fe$_{0.96}$Ni$_{0.04}$)$_4$As$_4$ with Spin-Vortex Crystal Order