Self-consistent mapping: Effect of local environment on formation of magnetic moment in α−FeSi2

Abstract

The Hohenberg-Kohn theorem establishes a basis for mapping the exact energy functional to a model one provided that their charge densities coincide. We suggest to use a mapping in a similar spirit, but here the parameters of the formulated multiorbital model should minimize the difference between the self-consistent charge and spin densities. The analysis of the model allows for detailed understanding of the role played by different parameters of the model in the physics of interest. After finding the areas of interest in the phase diagram of the model, we return to the ab initio calculations and check if the effects discovered are confirmed or not. Because of the last controlling step, we call this approach hybrid self-consistent mapping approach (HSCMA). As an example of the approach we present a study of the effect of silicon atoms substitution by the iron atoms and vice versa on the magnetic properties in the iron silicide $\ensuremath{\alpha}\ensuremath{-}{\mathrm{FeSi}}_{2}$. We find that while the stoichiometric $\ensuremath{\alpha}\ensuremath{-}{\mathrm{FeSi}}_{2}$ is nonmagnetic, the substitutions generate different magnetic structures depending on the type of local environment of the substitutional Fe atoms. Besides, contrary to the commonly accepted statement that the destruction of the magnetic moment is controlled only by the number of Fe-Si nearest neighbors, we find that actually it is controlled by the Fe-Fe next-nearest-neighbor hopping parameter. This finding led us to the counterintuitive conclusion: an increase of Si concentration in ${\mathrm{Fe}}_{1\ensuremath{-}x}{\text{Si}}_{2+x}$ ordered alloys may lead to ferromagnetism. The calculation within GGA-to-DFT confirms this conclusion.