In this study, we reveal the rich magnon topology in honeycomb bilayer ferromagnets (HBF) induced by the combined effects of interlayer exchange, Dzyaloshinskii-Moriya interactions (DMIs), and electrostatic doping (ED). In particular, we present a systematic study of the Hamiltonian non-adiabatic evolution in the HBF parametric space spanned by the symmetry-breaking terms (DMI and ED) and interlayer exchanges. The parametric space is divided into six subspaces, separated by band closure manifolds, resulting in five distinct topological phases and one trivial phase. We highlight the importance of ED as a simple experimental tool to engineer the band gaps and establish topological phase transitions. Edge spectra, dictated by the bulk-edge correspondence, are also analyzed in the model's nanoribbon version. Both the bulk and edge spectra are nonreciprocal due to the ED and edge magnons counter-propagate on opposite edges. We demonstrate the relevance of our findings for $Cr{I}_3$ and $CrB{r}_3$ bilayers. The predicted results offer new insights on the manipulation of magnonic Chern numbers and magnon topological transport via experimentally tunable parameters.

在这项研究中，我们揭示了由层间交换、Dzyaloshinskii-Moriya 相互作用 (DMI) 和静电掺杂 (ED) 的组合效应引起的蜂窝双层铁磁体 (HBF) 中丰富的磁振子拓扑结构。特别是，我们对对称破坏项（DMI 和 ED）和层间交换所跨越的 HBF 参数空间中的哈密顿非绝热演化进行了系统研究。参数空间被划分为六个子空间，由能带闭合流形分隔，导致五个不同的拓扑阶段和一个平凡的阶段。我们强调了 ED 作为设计带隙和建立拓扑相变的简单实验工具的重要性。由体边缘对应关系决定的边缘光谱也在模型的纳米带版本中进行了分析。magnons 在相对的边缘上反向传播。我们证明了我们的研究结果的相关性$Cr{\mathrm{一世}}_3$ 和 $Cr乙r_3$双层。预测结果为通过实验可调参数操纵磁子陈数和磁子拓扑传输提供了新的见解。