Magnon band modulations in monolayer and bilayer honeycomb ferromagnets with the Kekulé coupling texture

We study the combined effect exerted by the Kekulé coupling (KC) texture and Dzyaloshinskii-Moriya (DM) interactions in both monolayer and bilayer Heisenberg models. With the help of an analysis of the energy band gap and Chern number, we characterize the corresponding topological property, which is inherent to the ferromagnetic system. By measuring the magnon spectra of two types of honeycomb ferromagnets and comparing the differences between them, we prove that different topological phases can exist in both monolayer and bilayer honeycomb ferromagnets by varying the KC parameter or the DM interaction strength. However, properties of the magnetic topological phase transition in monolayer and bilayer honeycomb ferromagnets are quite different. We also identify the parameter domains where the system undergoes transitions between trivial and nontrivial topological magnon insulator phases. Our results suggest a potential for inducing novel topological phases through the KC texture and the DM interaction in layered magnetic materials.