Emergence of coexisting topological spin textures in an all-magnetic van der Waals heterostructure

TL;DR

This work tackles the stabilization and manipulation of topological spin textures in atomically thin van der Waals magnets by introducing a first-principles–based spin-spiral mapping method that can be applied to hexagonal and honeycomb lattices. Using atomistic spin models parameterized from density functional theory, the authors predict the coexistence of Néel-type skyrmions in the Fe$_3$GeTe$_2$ (FGT) layer and bimerons in the Cr$_2$Ge$_2$Te$_6$ (CGT) layer of the all-magnetic FGT/CGT vdW heterostructure, with interfacial DMI and lattice symmetry stabilizing these textures at zero field. They reveal that lattice discretization profoundly affects soliton barriers and pinning energetics, with hexagonal versus honeycomb geometries yielding differences in energy barriers (around a factor of ~2) and translation pinning. These findings highlight the importance of discrete lattice models for topological magnetism in 2D materials and point toward design rules for solitonic devices in vdW heterostructures, including potential pathways to synthetic antiferromagnetic skyrmions and field-tunable texture transformations.

Abstract

Magnetic solitons such as skyrmions and bimerons show great promise for both fundamental research and spintronic applications. Stabilizing and controlling topological spin textures in atomically thin van der Waals (vdW) materials has gained tremendous attention due to high tunability, enhanced functionality, and miniaturization. Here, we present an efficient spin-spiral approach based on first-principles, a method for mapping magnetic interactions from collective models onto arbitrary lattice symmetries, such as hexagonal and honeycomb lattices. Using atomistic spin models parametrized from first-principles, we predict the emergence of multiple topological spin textures in an all-magnetic vdW heterostructure Fe$_3$GeTe$_2$/Cr$_2$Ge$_2$Te$_6$ (FGT/CGT) -- an experimentally feasible system. Interestingly, the FGT layer favors out-of-plane magnetization, whereas the CGT layer prefers in-plane magnetocrystalline anisotropy. Néel-type nanoscale skyrmions are formed at zero field in the FGT layer due to interfacial Dzyaloshinskii-Moriya interaction (DMI), while nanoscale bimerons and antibimerons can co-exist in the CGT layer by the interplay between exchange frustration and DMI. Using the collective approach we apply, we reveal significant discretization effects in hexagonal and honeycomb geometries. In particular, we demonstrate that the lifting of geometric exchange frustration on the honeycomb significantly affects soliton barriers and pinning energetics. These fundamental results not only highlight the importance of spin simulations in discrete models for topological magnetism, especially in 2D materials, but may also help to pave the way for solitonic devices based on atomically thin vdW heterostructures.

Figures (11)

• Figure 1: Crystal structure of the Fe$_3$GeTe$_2$/Cr$_2$Ge$_2$Te$_6$ (FGT/CGT) van der Waals interface. Side view of the atomic structure of FGT/CGT. The induced DMI vectors and easy-axis for the FGT and CGT layers at the interface are shown schematically. On the right, we show the topological solitons stabilized in the FGT/CGT heterostructure: skyrmions form spontaneously in the FGT layer, while bimerons appear in the CGT layer.
• Figure 2: Models for fitting magnetic interactions in FGT and CGT. (a) Spin spiral in a magnetic monolayer model with the spin spiral vector $\mathbf{q}$. (b) Rotated and scaled dense hexagonal layer model, which has 3 magnetic atoms in the chemical unit cell from top view, with the transformed spin spiral vector, which is used as the model for the FGT layer. (c) Honeycomb lattice model (2 magnetic atoms per unit cell) with vacancies that would transform it into a hexagonal layer if they were filled. The honeycomb lattice models the CGT layer. (d) Symmetry zone of the spin spiral vector $\mathbf{q}$. It coincides with the Brillouin zone (BZ) in the case of a magnetic monolayer. The path around the irreducible wedge of the symmetry zone is shown in red. (e) Spin spiral symmetry zone for the denser hexagonal and honeycomb lattice models. It is 3 times bigger than the BZ and slightly rotated. (f) Illustration of the interactions between nearest neighbors in the dense hexagonal and the honeycomb lattice model. On the hexagonal lattice, there are two nearest neighbors for each of the three high symmetry directions (green, blue, and red). In the honeycomb model, there are only half as many interactions. If they had double strength in the honeycomb model, both models would produce the same spin spiral energy dispersions. (g)-(i) Show the states at the high-symmetry points of the different models. For the latter two, the larger BZ leads to new high-symmetry points.
• Figure 3: (a) Triangulation of the hexagonal lattice and (b) the honeycomb lattice for the definition of topological density $q$. The positions of the magnetic moments are depicted in blue, while the dual lattice points are shown in red.
• Figure 4: Comparison between two fitting schemes for the exchange constant of CGT. (a) DFT total energies (dots), with $\mathbf{q}$ restricted to the first BZ, are fitted using the hexagonal monolayer model (cf. Fig. \ref{['fig:CGT-lattices']}(a) and (d)). As an inset, the extended BZ is shown with high-symmetry directions, $\overline{\Gamma \text{M}}$, $\overline{\Gamma \text{KM}}$, $\overline{\Gamma \text{M}^{'}}$, and $\overline{\Gamma \text{K}^{'}\text{M}^{'}}$. The first BZ is marked in yellow. (b) Same as in (a), but with DFT data sampled in the extended BZ and fitted using the CGT model (cf. Fig. \ref{['fig:CGT-lattices']}(c) and (f)).
• Figure 5: Energy dispersion of spin spirals in the extended $\mathbf{q}$ zone for the FGT and CGT layers at FGT/CGT. (a) Four spin spiral configurations used to calculate the energy dispersions. The top three layers represent the Fe atoms in the FGT layer, while the bottom layer represents the Cr atoms in the CGT layer. (b-e) Spin spiral energy dispersions without SOC, $E_{\text{SS}}(\mathbf{q})$ (upper panels), and SOC-induced DMI energy, $E_{\text{DMI}}(\mathbf{q})$ (lower panels), for the FGT layer ((b) and (c)), and the CGT layer ((d) and (e)). Black circles correspond to the DFT total energies for FGT or CGT layers at FGT/CGT, while red circles are the corresponding DFT data for free FGT or CGT layers but with structural deformations as in FGT/CGT. All energies are given respect to the FM state at $\mathbf{q} = 0$. Note that positive and negative DMI energy contributions represent clockwise (CW) and counter-clockwise (CCW) cycloidal spin spiral configurations.