Employment of Green’s functions with reciprocal space resolution to study magnetocrystalline anisotropy in systems with itinerant electrons

Abstract In this work we suggest a theoretical approach, that allows to study the effects of magnetocrystalline anisotropy (MCA) using the Green’s functions formalism in real systems with the electronic states near the Fermi level. Previously known approaches based on the inter-site Green’s functions could not be reliably applicable for these systems due to slow or even absent convergence of the spatial sum over the atoms of the lattice. We demonstrate that employment of the Green’s functions with reciprocal space resolution essentially improves the situation and grants robuster stability by means Monkhorst–Pack grid density. The problem of spatial convergence is completely removed due to rigorous analytical replacement of pairwise atomic summation by simple composition of sublattices contributions, which could be calculated as a whole. It leads to significant economy of the required computational expenses, which can be up to two orders of magnitude in comparison with previously known methods. The basic validation of the suggested approach is performed on the effective model of single atom, which nevertheless inherits the qualitative MCA picture of Co monolayer and Au/Co/Au sandwiched material. The improved numerical convergence is confirmed by the model of the simple atomic chain in the strong metallic regime. For monoxides CoO and FeO, described by ab initio calculations using GGA +U , the MCA energy angular profile reveals the prevailing role of ferromagnetically aligned TM sublattices in forming of the easy axis.