Tuning the magnetic interactions in van der Waals Fe${}_3$GeTe${}_2$ heterostructures: A comparative study of \textit{ab initio} methods

Abstract

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 Fe${}_3$GeTe${}_2$ 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 Fe${}_3$GeTe${}_2$ 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 $\mathcal{E}=\pm 0.5$~V/Å applied perpendicular to the Fe${}_3$GeTe${}_2$/germanene heterostructure leads to significant changes of the exchange constants. We show that the Dzyaloshinskii-Moriya interaction (DMI) in Fe${}_3$GeTe${}_2$/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 Fe${}_3$GeTe${}_2$/germanene heterostructure.

arXiv comment15 pages, 12 figures

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• Prediction of stable nanoscale skyrmions in monolayer Fe${}_5$GeTe${}_2$
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• Above room-temperature two-dimensional ferromagnetic half-metals in Mn-based Janus magnets
• Flat bands and magnetism in $\mathbf{F}{\mathbf{e}}_4\mathbf{GeT}{\mathbf{e}}_2$ and $\mathbf{F}{\mathbf{e}}_5\mathbf{GeT}{\mathbf{e}}_2$ due to bipartite crystal lattices
• Unconventional hybrid-order topological insulators
• Long lifetimes of nanoscale skyrmions in lithium-decorated van der Waals ferromagnet Fe${}_3$GeTe${}_2$
• Why Fe${}_3$GaTe${}_2$ has higher Curie temperature than Fe${}_3$GeTe${}_2$?
• A new skyrmion topological transition driven by higher-order exchange interactions in Janus MnSeTe