We investigate the impact of mechanical strain, stacking order, and external electric fields on the magnetic interactions of a two-dimensional (2D) van der Waals (vdW) heterostructure in which a 2D ferromagnetic metallic Fe3GeTe2 monolayer is deposited on germanene. Three distinct computational approaches based on \textit{ab initio} methods are used, and a careful comparison is given: (i) The Green's function method, (ii) the generalized Bloch theorem, and (iii) the supercell approach. First, the shell-resolved exchange constants are calculated for the three Fe atoms within the unit cell of the freestanding Fe3GeTe2 monolayer. We find that the results between methods (i) and (ii) are in good qualitative agreement and also with previously reported values. An electric field of E=±0.5~V/{\AA} applied perpendicular to the Fe3GeTe2/germanene heterostructure leads to significant changes of the exchange constants. We show that the Dzyaloshinskii-Moriya interaction (DMI) in Fe3GeTe2/germanene is mainly dominated by the nearest neighbors, resulting in a good quantitative agreement between methods (i) and (ii). Furthermore, we demonstrate that the DMI is highly tunable by strain, stacking, and electric field, leading to a large DMI comparable to that of ferromagnetic/heavy metal (FM/HM) interfaces. The geometrical change and hybridization effect explain the origin of the high tunability of the DMI at the interface. The electric-field driven DMI obtained by method (iii) is in qualitative agreement with the more accurate \textit{ab initio} method used in approach (ii). However, the field-effect on the DMI is overestimated by method (iii) by about 50\%. The magnetocrystalline anisotropy energy can also be drastically changed by the application of compressive or tensile strain in the Fe3GeTe2/germanene heterostructure.
@article{arxiv.2210.15351,
title = {Tuning the magnetic interactions in van der Waals Fe$_3$GeTe$_2$ heterostructures: A comparative study of \textit{ab initio} methods},
author = {Dongzhe Li and Soumyajyoti Haldar and Tim Drevelow and Stefan Heinze},
journal= {arXiv preprint arXiv:2210.15351},
year = {2023}
}