Giant contribution of the ligand states to the magnetic properties of the Cr2Ge2Te6 monolayer

The magnetic properties of the Cr2Ge2Te6 monolayer - an important two-dimensional (2D) ferromagnetic (FM) material - are systematically investigated on the basis of ab initio electronic structure calculations within density functional theory (DFT). For these purposes we construct a minimal tight-binding model in the basis of maximally localized Wannier functions, which describes the behavior of the magnetic Cr 3d, Ge 4p, and Te 5p electrons. This model allows us to rationalize the results of conventional DFT calculations at the microscopic level. We explore the abilities of different techniques, including the Green's function perturbation theory and constraint calculations with an external magnetic field, for the analysis of magnetic interactions, that allow us to decompose these interactions in terms of partial contributions coming from different atomic sites. We argue that, although the magnetism of Cr2Ge2Te6 originates from the Hund's rule effects in the partially filled Cr 3d shell, the contributions of the ligand - and particularly Te 5p - states are crucially important and have a significant effect on the behavior of isotropic exchange interactions, magnetocrystalline anisotropy energy (MAE), and antisymmetric Dzyaloshinskii-Moriya (DM) interactions induced by an electric field. In particular, the Te 5p states increase dramatically the FM coupling and DM interactions between the Cr spins. They are also largely responsible for the behavior of MAE, manifesting themselves in non-Heisenberg type effects, which go beyond the scopes of the conventional Mermin-Wagner theorem for the analysis of 2D magnetism of Cr2Ge2Te6.