  The spin-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
non-collinear spin-vortex crystal magnetic order that preserves the tetragonal
symmetry of 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 $T_c$ regardless of
the details of magnetic pattern or lattice symmetry.
