First- and second-order magnonic topologies in the ferromagnetic breathing SSH model modulated by non-Hermitian effects

We investigate magnonic topology in the breathing Su–Schrieffer–Heeger (SSH) model, incorporating non-Hermitian effects. Our results demonstrate the coexistence of first- and second-order magnonic topologies, with non-Hermitian effects exhibiting size-dependent behavior. In two-dimensional systems, non-Hermitian terms induce a flat band and gap closure along high-symmetry paths, whereas in one-dimensional systems, a finite band gap persists for small system sizes. Additionally, the corner states remain robust, and a pronounced non-Hermitian skin effect emerges. Our findings provide new insights into magnon-based devices, emphasizing the impact of non-Hermitian effects on their design and functionality.