Topological Magnon-Phonon Hybrid Bands in Ferromagnetic Skyrmion Crystals

Abstract: We investigate magnon-phonon (MP) excitations in a Neel-type two-dimensional ferromagnetic skyrmion crystal (SkX) stabilized on a triangular spin lattice by Dzyaloshinskii-Moriya interaction (DMI). Although the lowest two magnon bands of the bare SkX are topologically trivial, we show that coupling to lattice vibrations reconstructs the low-energy sector and generates topological MP hybrid bands. Starting from a spin-lattice Hamiltonian in which phonons couple to magnons through fluctuations of the DMI vectors, we derive the bosonic Hamiltonian for the SkX and compute the hybrid band structure by Bogoliubov diagonalization. MP coupling opens gaps at low-energy magnon-phonon crossings, lifts phonon degeneracies associated with supercell folding, and yields nontrivial Chern numbers for the lowest hybrid bands. The resulting low-energy topology and associated edge states remain robust under magnetic-field variation, while higher-energy hybrid bands can undergo field-driven topological phase transitions. These results extend topological magnon-phonon hybridization to noncoplanar SkXs.

• The paper demonstrates that magnon-phonon hybridization reconstructs trivial magnon and phonon bands into nontrivial Chern bands with protected edge states.
• It employs a spin-lattice Hamiltonian and Colpa’s method for numerical diagonalization to reveal field-tunable hybridization gaps and topological transitions.
• The study highlights potential applications in low-dissipation bosonic transport and thermal Hall effects, paving the way for quantum device engineering.

Topological Magnon-Phonon Hybrid Bands in Ferromagnetic Skyrmion Crystals

Overview

This work addresses the generation of topological bosonic excitations via magnon-phonon hybridization in a two-dimensional Néel-type ferromagnetic skyrmion crystal (SkX) on a triangular spin lattice with strong Dzyaloshinskii-Moriya interaction (DMI). By focusing on a regime where the lowest bare magnon bands are topologically trivial, the paper demonstrates that coupling these modes to lattice vibrations reconstructs the low-energy sector and induces nontrivial Chern bands and topological edge states, even in a parameter regime where pure magnon or phonon spectra are themselves trivial.

Model and Formalism

The system is modeled with a spin-lattice Hamiltonian $H = H_m + H_p + H_{mp}$, where $H_m$ represents the Heisenberg-DMI Hamiltonian on a triangular lattice, $H_p$ captures harmonic lattice vibrations, and $H_{mp}$ incorporates magnetoelastic coupling via DMI vector fluctuations. Quantization proceeds via Holstein-Primakoff bosonization and a local spin-axis rotation, yielding a quadratic bosonic Hamiltonian block-diagonal in magnon and phonon sectors, with off-diagonal blocks from $H_{mp}$.

Parameter regimes are chosen such that the energy scales of phonon and magnon bands overlap, ensuring band crossings amenable to hybridization. The bosonic Hamiltonian is diagonalized using Colpa's method, producing band structures and associated Berry curvatures throughout the reduced Brillouin zone of the SkX superlattice.

Band Topology Induced by Magnon-Phonon Coupling

Numerical diagonalization reveals that, in the absence of hybridization, the lowest magnon and phonon bands are both topologically trivial (Chern numbers zero) and phonon bands display degeneracies due to the supercell. Introduction of MP coupling lifts these degeneracies, opens gaps at magnon-phonon crossing points, and generates finite Chern numbers in the hybrid bands. For the lowest five hybrid bands, calculated Chern numbers are found to be $\{0, 1, 0, 2, 1\}$ at the minimal magnetic field stabilizing the SkX phase.

MP coupling reconstructs the low-energy excitation window, relocating nontrivial topology from typically higher-energy, purely magnonic states to the lowest sector, which is beneficial for experimental detection and manipulation, including edge state engineering. The topological gaps created by hybridization, particularly the global second gap separating the second and third hybrid bands, are explicitly shown to host protected edge states, as required by the nonzero sum of Chern numbers below the gap.

Magnetic Field Dependence and Topological Transitions

The topology of the lowest hybrid bands is robust under variation of the perpendicular magnetic field. Increasing the field enlarges the global hybridization gap without altering the band Chern numbers in the low-energy sector. However, at higher energies, field-driven band inversion leads to topological phase transitions detectable as gap closures and exchange of Chern numbers. These transitions specifically occur in hybrid bands above the low-energy manifold, enabling selective tuning of band topology without affecting robust low-energy chiral edge states.

The field-driven transitions are ascribed to the complex interplay between magnon band reshaping (due to Zeeman splitting and DMI) and the folding and degeneracy of phonon bands inherent to the SkX magnetic superstructure. The authors confirm that these conclusions are insensitive to the DMI strength, aside from scaling considerations, as long as umklapp scattering is suppressed.

Implications and Future Perspectives

This work provides theoretical validation that noncoplanar skyrmion crystals present a robust platform for realizing low-energy topological magnon-phonon hybridization. The activation of nontrivial Chern bands in an otherwise trivial low-energy window is significant for several domains:

• Bosonic Transport: Enabling low-dissipation edge channel engineering for application in magnonics and phononics, leveraging the robustness of chiral edge states against disorder and field fluctuations.
• Thermal Hall Effects: The emergence of topological MP bands with finite Berry curvature is poised to yield observable signatures in thermal Hall and related transport measurements, extending the phenomenology known from antiferromagnets and collinear magnets to SkX phases.
• Hybrid Quantum Information Processing: The controllable nature of MP hybridization across different field regimes suggests potential for dynamic manipulation and braiding of edge states, offering a route to magnon-phonon-based bosonic quantum devices.

Future studies may address extensions to moiré-engineered lattices, inclusion of spin-orbit phonon coupling, quantum fluctuation effects in the vicinity of phase transitions, and the detailed structure of hybrid edge modes in finite geometries. Experimental realization will require precise tuning of magnon-phonon band crossings; however, precedent exists in recent measurements of strong MP hybridization and topological magnon polarons in both bulk and truly 2D magnets.

Conclusion

In summary, this study establishes that magnon-phonon hybridization can endow a topologically trivial low-energy sector of a ferromagnetic skyrmion crystal with nontrivial topological character, manifested via nonzero Chern numbers and protected edge states. The resulting topological features are resilient under tuning of external field and interaction parameters, positioning noncoplanar SkXs as promising candidates for topological magnonics and hybrid bosonic band engineering.