  For face-centered cubic (fcc) and tetragonal (fct) iron a large number of
magnetic configurations as a function of crystal structural parameters were
studied by means of density functional theory. The stability of magnetic
structures was defined by the magnetic re-orientation energy $\Delta
{E}^i_\text{reor}$ as the difference of the total energy of configuration $i$
and that of the fcc ferromagnetic state. The Cluster Expansion technique was
applied to several volumes deriving $\Delta {E}_\text{reor}$ for more than
90.000 collinear spin structures for each volume. A variety of structures with
promisingly low $\Delta {E}_\text{reor}$ were tetragonally distorted according
to a two-dimensional mesh defined by volume per atom and $c/a$ ratio of the
distortion. At each of the points on this mesh $\Delta E_\text{reor}$ of all
collinear structure were compared to results for non-collinear spin spirals
(SS) which were calculated for a grid of propagation directions. The lowest
$\Delta {E}_\text{reor}$ of all investigated spin structures then defined the
magnetic structure map spanned by volume per atom and $c/a$ ratio. Three local
minima were identified and for each of the minima SS were calculated on a fine
grid of propagation vectors. For the volume per atom of 10.6 \AA$^3$ and the
distortion range $0.94 \le c/a \le 1.01$ we found a new, surprisingly simple
collinear spin structure with four atoms per fct unit cell to be the most
stable one. This structure was called AFM/NM because it consists of two atoms
with anti-ferromagnetically ordered local moments of $\pm 1.8 \mu_\text{B}$ and
of two nonmagnetic atoms with zero local moment. It seems that the newly
detected AFM/NM structure explains a variety of puzzling experimental results.
