  The magnetic properties of monolayer FeSe films are investigated via
first-principles spin-spiral calculations. Although the (pi,pi) collinear
antiferromagnetic (CL-AFM) mode is lowest in energy, the spin-wave energy E(q)
- which exhibits intrinsic non-Heisenberg behavior - is found to be extremely
very flat over a large region of the two-dimensional Brillouin zone centered at
the checkerboard antiferromagnetic (CB-AFM) q=0 configuration, giving rise to a
sharp peak in the spin density of states. Considering the paramagnetic state as
an incoherent average over spin-spiral states, we find that resulting
electronic band states around the Fermi level closely resemble the bands of the
CB-AFM configuration - not the CL-AFM one - and thus providing a natural
explanation of the angle-resolved photoemission observations. The presence of
the SrTiO3(001) substrate, both with and without interfacial oxygen vacancies,
is found to reduce the energy difference between the CB-AFM and CL-AFM states
and hence enhancing the CB-AFM-like fluctuations.
