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

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.

💡 Research Summary

**
This paper introduces a comprehensive first‑principles‑based framework for predicting and analyzing multiple topological spin textures in a fully magnetic van der Waals (vdW) heterostructure composed of Fe₃GeTe₂ (FGT) and Cr₂Ge₂Te₆ (CGT). The authors develop an efficient spin‑spiral approach that maps density‑functional‑theory (DFT) total‑energy data onto Heisenberg‑type spin Hamiltonians defined on arbitrary two‑dimensional lattices, specifically dense hexagonal and honeycomb lattices. By constructing a (√3 × √3) FGT supercell matched to a (1 × 1) CGT cell (lattice mismatch <0.15 %), they obtain a realistic interface model containing nine Fe atoms and two Cr atoms per supercell.

The methodology proceeds in three stages. First, flat spin‑spiral calculations without spin‑orbit coupling (SOC) yield isotropic exchange constants J via the generalized Bloch theorem. Second, DMI vectors D are extracted by treating SOC as a first‑order perturbation on the spin‑spiral dispersion. Third, magnetocrystalline anisotropy energies (MAE) are obtained using the magnetic force theorem. To handle the multi‑atom unit cell, the authors introduce collective lattice models: the FGT layer is represented by a dense hexagonal lattice with three magnetic sites per cell, while the CGT layer is mapped onto a honeycomb lattice with two sites per cell. The mapping accounts for the different numbers of nearest‑neighbor bonds by scaling the exchange parameters (e.g., J_honeycomb = 2 J_hexagonal for bonds that are halved in the honeycomb geometry). This reduces the number of independent fitting parameters while preserving the full spin‑spiral energy landscape E(q).

Using the parametrized Hamiltonian
H = −∑_ij J_ij m_i·m_j − ∑_ij D_ij·(m_i×m_j) − K∑_i (m_i^z)^2 − μ∑_i m_i·B,
the authors perform large‑scale atomistic spin dynamics simulations (120 × 120 lattices, 10⁻⁸ eV torque convergence) and compute minimum‑energy paths (MEPs) with the geodesic nudged elastic band (GNEB) method.

Key physical findings are:

1. FGT layer – The interfacial DMI is counter‑clockwise (CCW) with magnitude ≈0.45 meV·Å, while the MAE strongly favors out‑of‑plane magnetization (K > 0). These conditions stabilize Néel‑type skyrmions of ~1–2 nm radius at zero external field. The collapse barrier, obtained from GNEB, is ~45 meV, and the annihilation proceeds via a core‑spin reversal (a “hedgehog” transition).

2. CGT layer – The DMI switches to clockwise (CW) and the MAE favors in‑plane orientation (K < 0). Combined with frustrated exchange (next‑nearest‑neighbor antiferromagnetic coupling), this leads to the spontaneous formation of bimerons and antibimerons (in‑plane analogues of skyrmions) with typical lengths of 3–4 nm. Their energy barriers exceed 60 meV, and the collapse follows a continuous shear of the meron‑antimeron pair rather than a core reversal.

3. Lattice‑discretization effects – Although the underlying magnetic interactions are identical, the dense hexagonal lattice (FGT) exhibits twice as many nearest‑neighbor bonds as the honeycomb lattice (CGT). Consequently, skyrmions on the hexagonal lattice experience lower pinning and smaller migration barriers, whereas bimerons on the honeycomb lattice are strongly pinned to lattice sites and defects. This “discretization effect” dramatically influences soliton mobility and stability, suggesting that lattice geometry can be used as a design knob for device engineering.

4. Interlayer coupling – Van der Waals forces produce only weak interlayer exchange and DMI (J⊥, D⊥ ≈ 0.1 meV). The authors therefore neglect interlayer terms in the spin dynamics, confirming that each layer behaves almost independently while still sharing the same interface‑induced DMI sign reversal.

5. Experimental relevance – The FGT/CGT heterostructure has already been fabricated experimentally. The predicted zero‑field coexistence of Néel skyrmions (out‑of‑plane) and bimerons (in‑plane) should be observable with spin‑polarized scanning tunneling microscopy or magnetic force microscopy. Moreover, the distinct pinning characteristics imply that electric‑field or strain tuning could selectively manipulate one texture without affecting the other, opening pathways toward multi‑state memory or logic devices that exploit both out‑of‑plane and in‑plane topological bits.

In summary, the paper delivers (i) a versatile spin‑spiral‑to‑Heisenberg mapping technique for complex 2D magnetic heterostructures, (ii) a detailed quantitative analysis of how exchange frustration, DMI, and magnetic anisotropy cooperate to generate coexisting skyrmions and bimerons, and (iii) insight into how lattice symmetry governs soliton energy barriers and pinning. These results advance the fundamental understanding of topological magnetism in vdW materials and provide concrete guidelines for designing next‑generation spintronic devices based on atomically thin magnetic heterostructures.