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, where the first two magnon gaps are topologically trivial and do not support topological edge states (TESs). Meanwhile, the third gap can host TESs, which may be trivialized through field-induced topological phase transitions (TPTs), enabling controlled magnonic edge transport. However, the magnon topology in non-Bravais spin lattices remains largely unexplored. In this work, we theoretically investigate the influence of the honeycomb lattice structure on magnon band topology and associated TESs in FM SkXs, employing realistic parameters for monolayer CrI₃ and CrBr₃. We reveal unique magnonic topological features arising specifically from the honeycomb lattice. Characteristic magnon modes, such as elliptical and triangular distortion modes, acquire nontrivial Chern numbers, contrasting their trivial counterparts in triangular-based SkXs. Moreover, the second magnon gap in honeycomb-based SkXs consistently hosts TESs at low magnetic fields, unlike triangular SkXs. These TESs can be trivialized above a critical magnetic field. Conversely, the third gap is generally trivial at higher magnetic fields but becomes topological at low fields only when the SkX periodicity falls below a critical threshold dependent on Dzyaloshinskii-Moriya interaction (DMI) strength and magnetic anisotropy. Our study further demonstrates a rich magnonic topological phase diagram accessible by magnetic fields, potentially enabling selective control of low-energy chiral edge modes. These findings underscore the pivotal role of lattice geometry in shaping the topology of magnons in noncollinear spin textures.