  The magnetic order in CaK(Fe[1-x]Ni[x])4As4 (1144) single crystals (x = 0.051
and 0.033) has been studied by neutron diffraction. We observe magnetic Bragg
peaks associated to the same propagation vectors as found for the collinear
stripe antiferromagnetic (AFM) order in the related BaFe2As2 (122) compound.
The AFM state in 1144 preserves tetragonal symmetry and only a commensurate,
non-collinear structure with a hedgehog spin-vortex crystal (SVC) arrangement
in the Fe plane and simple AFM stacking along the c direction is consistent
with our observations. The SVC order is promoted by the reduced symmetry in the
FeAs layer in the 1144 structure. The long-range SVC order coexists with
superconductivity, however, similar to the doped 122 compounds, the ordered
magnetic moment is gradually suppressed with the developing superconducting
order parameter. This supports the notion that both collinear and non-collinear
magnetism and superconductivity are competing for the same electrons coupled by
Fermi surface nesting in iron arsenide superconductors.
