  We report a detailed investigation of the magnetic order in 192 stable
magnetic two-dimensional materials from the Computational 2D Materials Database
having one magnetic atom in the unit cell. The calculations are based on a
systematic workflow that employs spin spiral calculations and yields the
magnetic order in terms of a two-dimensional ordering vector $\mathbf{Q}$. We
then include spin-orbit coupling to extract the easy and hard axes for
collinear structures and the orientation of spiral planes in non-collinear
structures. Finally, for all predicted ferromagnets we compute the
Dzyaloshinskii-Moriya interactions and determine whether or not these are
strong enough to overcome the magnetic anisotropy and stabilise a chiral spin
spiral ground state. These steps completely determines the ground state order
within the spiralling ansatz. We find 58 ferromagnets, 21 collinear
anti-ferromagnets, and 85 non-collinear ground states of which 15 are chiral
spin spirals driven by Dzyaloshinskii-Moriya interactions. The results show
that non-collinear order is in fact as common as collinear order in these
materials and emphasise the need for detailed investigation of the magnetic
ground state when reporting magnetic properties of new materials. Furthermore,
non-collinear order typically breaks symmetries inherent to the lattice and may
give rise to emergent properties such as multiferroicity, magnetoelectricity or
second order optical effects that would be predicted as absent based on a
collinear assumption.
