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 of the exact energy functional to a model one provided that their charge densities coincide. We suggest here to use a mapping in a similar spirit: 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. 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 as hybrid self-consistent mapping approach (HSCMA). 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 α − F eSi2. 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 α − F eSi2 is nonmagnetic, the substitutions generate different magnetic structures. For example, the substitution of three Si atoms by the F e atoms results in the ferrimagnetic structure whereas the substitution of four Si atoms by F e atoms gives rise to either the nonmagnetic or the ferromagnetic state depending on the type of local enviroment of the substitutional F e atoms. Besides, contrary to the commonly accepted statement that the destruction of the magnetic moment is controlled only by the number of F e − Si nearest neighbors, we find that actually it is controlled by the F e − F e next-nearest-neighbors' hopping parameter. This finding led us to the counterintuitive conclusion: an increase of Si concentration in F e1−xSi2+x ordered alloys may lead to a ferromagnetism. This conclusion is confirmed by the calculation within GGA-to-DFT.

Approach to form planar structures based on epitaxial Fe1−xSix films grown on Si(111)

“…Besides, Fe3Si lattice parameter of 0.564 nm [7] allows for performing epitaxial growth on semiconductor substrates of GaAs [8],Ge [9],Si [10,11] and on dielectric MgO(001) substrates [12] or on a several-nanometer-thick MgO tunneling barrier on GaAs(001) [13], which can improve spin injection efficiency into semiconductor. Moreover, the magnetic and electronic properties of such iron-rich epitaxial Fe1 − xSix thin films (x=0-0.4) can be tuned by varying the chemical order [14,15]. In these crystalline systems, three different bcc-like structures (D03, B2, A2), each with a different degree of chemical order, are possible.…”

Effect of the Local Environment on the Magnetic Properties of Mn3Si: Hybrid Ab Initio and Model Study

“…The strong dependence of the magnetic moments of MnII atom on the hopping integral t3 results in the appearance of the sharp boundary between magnetic and nonmagnetic states of MnII atom and the ab initio magnetic state is located in instability region near this sharp boundary (Figure b). It should be noted that such sharp dependence of the magnetic moment on the hopping parameter t3 is characteristic not only for iron and manganese silicides but also for nickel . It can be assumed that this feature of the model phase diagrams will be preserved for other compounds with transition 3d‐metals.…”

“…Here, we give only the Hamiltonian of the model. The detailed description of the model approach can be found in previous studies . The model Hamiltonian is where the Coulomb part of the Hamiltonian …”

“…All these parameters ( U; U'; J, J' , , , , ) are fitting parameters of the model, and they are determined by the requirement that the model charge densities, obtained self‐consistently, have to be as close as possible to the GGA ones. The model parameters can be found from minimization of the difference Δ = [ ρ GGA ( k,σ ) − ρ model ( k, σ ; U; U'; J, J' , )] 2 between the ab initio electron density ρ GGA ( k, σ ) and the model one ρ model ( k, σ ; U; U'; J, J' , ) with respect to interaction parameters . Since the Hartree–Fock equations have to be solved self‐consistently for each set of the model parameters, we simplified the problem further and instead of minimization of function Δ (i.e., the differences of the model and VASP electron spin densities in each point of space), we have chosen to fit the occupation numbers of d‐electrons, the magnetic moments of Mn‐atoms, and partial d‐densities of states for Mn atoms (see Equation in the study by Zhandun et al).…”

Lattice dynamics and polarization-dependent phonon damping in α -phase FeSi2 nanostructures

“…In a similar manner, the tetragonal high-temperature phase α-FeSi 2 can be stabilized at room temperature in epitaxial nanostructures by deposition of a few Fe monolayers on the Si surface [10][11][12][13][14][15][16]. Several experimental and theoretical studies investigated the magnetic [17][18][19] and electronic [14,[20][21][22] properties of α-FeSi 2 nanostructures. The discovery of superparamagnetic behavior in nanoislands and nanostripes [23,24], the indication of a ferromagneticsemiconductor-like behavior below 50 K [25] and the fa- * svetoslav.stankov@kit.edu brication of α-FeSi 2 nanobars [26] and nanowires [27] suggested applications of this material in nanoelectronics.…”