Magnetic structure map for face-centered tetragonal iron: Appearance of a collinear spin structure

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.