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

Abstract

We suggest here the method of the mapping of DFT calculations on the multiorbital model in a following way: the parameters of the formulated multiorbital model should be determined from the requirement that the self-consistent charge and spin densities found from the ab initio and model calculations have to be as close to each other as possible. The analysis of the model allows for detailed understanding of the role played by different parameters of the model in the physics of interest. As an example of the approach we present the study of the effect of silicon atoms substitution by the iron atoms and vice versa on the magnetic properties in the iron silicide alpha-FeSi2. The DFT+GGA calculations are mapped to the model with intraatomic Coulomb and exchange interactions, hoppings to nearest and next nearest atoms and exchange of the delocalized electrons between iron atoms; the magnetic moments on atoms and charge densities of the material are found self-consistently within the Hartree-Fock approximation. We find that while the stoichiometric alpha-FeSi2 is nonmagnetic, the substitutions generate different magnetic structures. For example, the substitution of three Si atoms by the Fe atoms results in the ferrimagnetic structure whereas the substitution of four Si atoms by Fe atoms gives rise to either the nonmagnetic or the ferromagnetic state depending on the type of local enviroment 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-neighbors. This finding led us to the counterintuitive conclusion: an increase of Si concentration in Fe1-xSi2+x ordered alloys may lead to a ferromagnetism. This conclusion is confirmed by the calculation within GGA-to-DFT.