Impact of the honeycomb spin-lattice on topological magnons and edge states in ferromagnetic 2D skyrmion crystals

Magnons have been intensively studied in two-dimensional (2D) ferromagnetic (FM) skyrmion crystals (SkXs) stabilized on Bravais lattices, particularly triangular and square lattices. In these systems, topological edge states (TESs) have been reported in higher-energy magnon gaps, while the first magnon gap is found to be topologically trivial. In this context, antiferromagnetic (AFM) SkXs on the triangular spin lattice have been considered potentially more interesting for applications, since TESs emerge already in the first magnon gap. Meanwhile, the magnon topology of SkXs stabilized on non-Bravais spin lattices remains largely unexplored. In this work, we theoretically investigate the magnon band structure and TESs in 2D FM SkXs stabilized on the honeycomb spin lattice, including experimentally motivated parameter sets relevant to van der Waals magnets. We show that chiral TESs emerge in the first magnon gap over significant ranges of the Dzyaloshinskii-Moriya interaction and single-ion magnetic anisotropy. Magnetic-field-driven topological phase transitions modify the number of these TESs before eventually trivializing them. In addition, we find that TESs can coexist in the first and higher magnon gaps, which could enable frequency-multiplexed magnonic edge transport. These findings highlight the role of lattice geometry in shaping the magnon topology and edge transport in noncollinear spin textures.

💡 Research Summary

This paper presents a comprehensive theoretical study of magnon excitations and topological edge states (TES) in two‑dimensional ferromagnetic (FM) skyrmion crystals (SkXs) that are stabilized on a honeycomb (non‑Bravais) spin lattice. While previous works have focused on SkXs formed on Bravais lattices such as triangular or square, where the lowest magnon gap is topologically trivial, the authors explore how the bipartite geometry of the honeycomb lattice reshapes the magnon band topology.

The authors construct a spin Hamiltonian that includes nearest‑neighbor (NN) ferromagnetic Heisenberg exchange (J), interfacial NN Dzyaloshinskii‑Moriya interaction (DMI) (D), intrinsic next‑nearest‑neighbor (NNN) DMI (D′), and single‑ion magnetic anisotropy (SIMA) (K), together with a Zeeman term for an out‑of‑plane magnetic field B. Six parameter sets (Models 1–6) are defined; Models 2, 4 and 6 correspond to experimentally measured values for monolayer CrI₃·FeCl₃, CrGeTe₃ and related van‑der‑Waals magnets, while Models 1, 3 and 5 serve as interpolations mainly varying K. The Hamiltonian is normalized by setting J = 1 and D = 1, so all energies are expressed in units of J D.

Skyrmion crystals are generated using stochastic Landau‑Lifshitz‑Gilbert (sLLG) simulations (Vampire code). At the lowest field (B ≈ 0) the SkX forms a dense triangular lattice of skyrmions with a characteristic width R₀; as B increases, each skyrmion shrinks while remaining pinned, until a critical field B_c annihilates the texture and the system becomes a uniform FM. The authors devise an analytical extraction of the field‑dependent skyrmion width from the out‑of‑plane spin density, providing a quantitative mapping between B and the magnetic texture used for subsequent magnon calculations.

To quantize magnons, a local spin‑axis rotation aligns each spin with its equilibrium direction, after which Holstein‑Primakoff bosonization is applied. Because the honeycomb lattice has two sublattices (A, B), the magnon Hamiltonian becomes a 2N × 2N Bogoliubov matrix (N ≈ R² spins per sublattice in a single skyrmion unit cell). The matrix incorporates exchange, D, D′, and K contributions; the NNN DMI opens gaps at Dirac points in the collinear limit but, as the authors find, has only a minor effect on the SkX magnon topology because the emergent gauge field of the non‑collinear texture already generates large Berry curvature.

Diagonalization via Colpa’s bosonic Bogoliubov method yields magnon band energies εₙ(k) and eigenvectors. Berry curvature Ωₙ(k) and Chern numbers Cₙ are computed using the discretized gauge‑invariant algorithm of Fukui, Hatsugai, and Suzuki. The key findings are:

1. First‑gap topology – For models with sufficiently large K (e.g., Model 1, K ≈ 0.07 J), and for D exceeding a threshold (≈ 0.07 J), the lowest magnon gap acquires a non‑zero Chern number (±1). Consequently, chiral edge modes appear in this gap, a situation never reported for triangular‑lattice FM SkXs.

2. Magnetic‑field‑driven topological phase transitions – As B is increased, the Chern number of the first gap follows a sequence 0 → ±1 → 0. Each transition is accompanied by the appearance or disappearance of TESs, demonstrating that the external field can switch edge transport on and off.

3. Coexistence of TESs in multiple gaps – Higher‑energy magnon gaps (second, third, etc.) also become topologically non‑trivial for certain D and B values, allowing edge states to exist simultaneously in the first and higher gaps. This opens the possibility of frequency‑multiplexed magnonic edge channels, where different information channels are carried at distinct energies without mutual interference.

4. Parameter dependence – The single‑ion anisotropy K is identified as the dominant intrinsic parameter controlling the existence of first‑gap TESs. Larger K expands the D‑range where Chern numbers are non‑zero, while small K (as in CrGeTe₃‑like models) suppresses topological gaps entirely. The NNN DMI D′, despite being crucial for topological magnon bands in collinear honeycomb ferromagnets, plays a negligible role in the SkX case for experimentally realistic values.

5. Experimental relevance – Using realistic parameters for CrI₃·FeCl₃ (Model 2), the authors predict robust first‑gap TESs, suggesting that existing van‑der‑Waals magnets could host low‑energy topological magnon edge transport. Conversely, materials with weak anisotropy (e.g., CrGeTe₃) are unlikely to exhibit such edge modes.

Overall, the work demonstrates that lattice geometry—specifically the bipartite honeycomb structure—fundamentally alters magnon topology in non‑collinear spin textures. By revealing that the first magnon gap can become topologically non‑trivial and that edge states can be tuned by magnetic field and anisotropy, the study provides a concrete pathway toward low‑energy, low‑dissipation magnonic devices based on 2D van‑der‑Waals skyrmion crystals. Future directions include experimental verification via Brillouin light scattering or inelastic neutron scattering, exploration of magnon‑magnon interactions, and engineering of DMI or anisotropy through strain, electric fields, or heterostructuring to realize reconfigurable topological magnonic circuits.