  We calculated the structural, electronic and magnetic properties of FeSe
within density-functional theory at the generalized gradient approximation
level. First, we studied how the bandwidth of the d-bands at the Fermi energy
are renormalized by adding simple corrections: Hubbard U, Hunds J and by
introducing long-range magnetic orders. We found that introducing either a
striped or a staggered dimer antiferromagnetic order brings the bandwidths --
which are starkly overestimated at the generalized gradient approximation level
-- closer to those experimentally observed. Second, for the ferromagnetic, the
striped, checkerboard and the staggered dimer antiferromagnetic order, we
investigate the change in magnetic formation energy with local magnetic moment
of Fe at a pressure up to 6 GPa. The bilinear and biquadratic exchange energies
are derived from the Heisenberg model and noncollinear first-principles
calculations, respectively. We found a non-trivial behavior of the
spin-exchange parameters on the magnetization, and we put forward a
field-theory model that rationalizes these results in terms of two-dimensional
spin and orbital fluctuations. The character of these fluctuations can be
either that of a standard density wave or a topological vortex. Topological
vortexes can result in mesoscopic magnetization structures.
