Topological Magnetic Phases and Magnon-Phonon Hybridization in the Presence of Strong Dzyaloshinskii-Moriya Interaction

In recent years, the interplay between quantum magnetism and topology has attracted growing interest, both for its fundamental importance and its technological potential. Topological magnons, quantized spin excitations with nontrivial band topology, hold particular promise for spintronics, offering routes to robust, low-dissipation devices for next-generation information processing and storage. While topological magnons in honeycomb ferromagnets with weak next-nearest-neighbor Dzyaloshinskii-Moriya interactions (DMI) have been extensively investigated, the strong-DMI regime remains largely unexplored. In this work, we examine topological magnetic phases and magnon-phonon hybridization in a two-dimensional magnetic system with strong DMI. We show that strong DMI drives a transition from a ferromagnetic ground state to a 120$^\circ$ noncollinear order. An additional Zeeman field further induces noncoplanar spin textures, giving rise to a diverse set of topological phases. We demonstrate that these topological phases can be directly probed through the anomalous thermal Hall effect. Finally, we find that the spin-spin interactions in the strong-$D$ phase enable magnon-phonon coupling that yields hybridized topological bands, whereas such coupling vanishes in the weak-$D$ phase.

💡 Research Summary

In this work the authors investigate the interplay between strong Dzyaloshinskii‑Moriya interaction (DMI), external magnetic fields, and magnon‑phonon coupling in a two‑dimensional honeycomb magnetic lattice. The Hamiltonian comprises a nearest‑neighbor ferromagnetic Heisenberg exchange (J < 0), a next‑nearest‑neighbor DMI term (strength D), and a Zeeman term (field h). By analytically solving the classical energy in the limits D → 0 and D → ∞, they identify two distinct magnetic ground states: a conventional collinear ferromagnet for weak DMI and a 120° non‑collinear order for strong DMI. Between these limits a first‑order transition occurs at D = D_c(h) = −J√3 + |h|/(3S√3), which they confirm numerically by minimizing the classical energy on large lattices. The order parameter M_z = (1/N)∑S_z distinguishes the two phases; it is saturated in the ferromagnetic region and vanishes in the strong‑D regime, signalling a breaking of the U(1) spin‑rotation symmetry.

Linear spin‑wave theory (LSWT) is then applied to each phase. In the weak‑D region the system has two magnon bands. A finite D opens a gap at the K points, and the lower band acquires a Chern number C₁ = sgn(S_z) sgn(D). Thus the sign of the DMI determines the chirality of the magnon edge modes, while the Zeeman term fixes the overall sign through the magnetization direction. In the strong‑D regime the enlarged magnetic unit cell contains six spins, leading to six magnon branches. Quantum order‑by‑disorder selects relative azimuthal angles ϕ₂ − ϕ₁ = 0, 2π/3, or 4π/3, minimizing the zero‑point energy. When a finite out‑of‑plane field h is applied, the spins become non‑coplanar, generating a finite scalar chirality χ = S₁·(S₃×S₅) = S₂·(S₄×S₆). This breaks the combined symmetry ˜T = exp(−iπS_z) T (time reversal followed by a π‑rotation about z) and allows all six bands to acquire non‑zero Chern numbers. The authors find that the sum of the Chern numbers of the three lowest bands satisfies Σ_{α=1}^{3} C_α = sgn(S_z) sgn(D), while the sum over the three highest bands is the opposite, ensuring the total Chern number vanishes as required by lattice periodicity. Gap closings at specific high‑symmetry points (e.g., E₆ = E₅, E₅ = E₄) drive cascades of topological phase transitions, changing individual Chern numbers while preserving the summed constraints.

The topological nature of the magnon bands manifests directly in the thermal Hall conductivity κ_xy, which is proportional to the integral of the Berry curvature weighted by the Bose occupation factor. The authors argue that κ_xy provides an experimentally accessible probe of the magnetic phase diagram: a sign change of κ_xy signals either a reversal of D or of the external field, while its magnitude tracks the size of the magnon band gaps. In the strong‑D, finite‑h regime, κ_xy is expected to be sizable due to multiple chiral edge channels.

A central novelty of the paper is the analysis of magnon‑phonon hybridization. The authors show that the distance‑dependent exchange interaction, when expanded to linear order in lattice displacements, yields a quadratic magnon‑phonon coupling term that is non‑zero only in the strong‑D phase where the spin texture is non‑collinear. This coupling mixes magnon and acoustic phonon modes, producing hybrid topological bands that inherit the Chern numbers of the underlying magnon bands. In contrast, in the weak‑D ferromagnetic phase the symmetry of the collinear ground state eliminates the quadratic coupling, leaving pure magnon and phonon spectra. The hybridization opens additional gaps and could be probed via inelastic neutron scattering or Raman spectroscopy, offering a route to engineer topological bosonic quasiparticles beyond pure magnons.

Overall, the study maps out a rich phase diagram controlled by DMI strength and magnetic field, demonstrates multiple topological magnon phases with tunable Chern numbers, predicts a measurable anomalous thermal Hall response, and uncovers a DMI‑induced magnon‑phonon coupling mechanism that generates hybrid topological excitations. The work provides a concrete theoretical framework for future experiments on two‑dimensional magnetic materials with strong spin‑orbit coupling, such as transition‑metal halides or engineered heterostructures where DMI can be enhanced via substrate engineering or heavy‑atom intercalation.