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

Abstract

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 $\hat{I}”E_{\text{reor}}^i$ 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 $\hat{I}”E_{\text{reor}}$ for more than 90.000 collinear spin structures for each volume. A variety of structures with promisingly low $\hat{I}”E_{\text{reor}}$ 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 $\hat{I}”E_{\text{reor}}$ 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 $\hat{I}”E_{\text{reor}}$ 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 à ${}^3$ 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 $\pm 1.8\hat{I}{¼}_{\text{B}}$ 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.