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The electronic energy structures and magnetic properties of iron-based compounds with group VI elements (FeTe, BiFeO3, SrFe12O19 and SrCoTiFe10O19) are studied using the density functional theory (DFT) methods. Manifestations of different types of chemical bonds in magnetism of these compounds are studied theoretically. Calculations of electronic structures of these systems are performed, by using the generalized gradient approximation (GGA) for the description of the exchange and correlation effects within DFT. For SrFe12O19 and SrCoTiFe10O19 hexaferrites, the GGA+ 𝑈 method is also employed to deal with strongly correlated 3𝑑-electrons. The calculations have revealed distinctive features of the electronic structure of the investigated iron-based compounds with strongly correlated 3𝑑-electrons, which can be responsible for their peculiar structural and magnetic properties.