Classification of field-driven topological magnon transitions in triangular and honeycomb skyrmion crystals

We investigate field-driven topological magnon transitions in two-dimensional ferromagnetic skyrmion crystals (SkXs) on triangular and honeycomb lattices. Using atomistic spin simulations and linear spin-wave calculations, we track the evolution of the lowest magnon bands and their Chern numbers as functions of magnetic field, Dzyaloshinskii-Moriya interaction (DMI), and easy-axis single-ion anisotropy (SIA). Building on the previously identified breathing (Br)-counterclockwise (CCW) band inversion mechanism in triangular-lattice SkXs and its anisotropy dependence, we systematically map the Br-CCW gap behavior across the SkX stability window for both lattice geometries. We find that closure and reopening of the Br-CCW gap at the Brillouin-zone center provide a common framework for topological switching in both lattices, although the evolution may proceed either through a direct Br-CCW transition or through intermediate crossings involving other low-energy modes. This leads to three characteristic patterns on each lattice, with lattice-dependent differences in the order of low-energy modes, the sequence of Chern-number redistribution, and the location of the phase boundaries. The resulting phase diagrams identify the parameter regimes in which the Br-CCW transition occurs or is suppressed and show how lattice geometry, anisotropy, and DMI together shape the low-energy topological magnon spectrum and the associated topological edge states in SkXs.