Rich Magnon Topology in Triangular Lattice Magnets.

The two-dimensional magnet has been an emerging and rapidly growing field. The nontrivial topological phenomenon in these materials is an attracting subject. Yet, the realization of such magnets exhibiting topological magnons remains a challenge. Here, employing the linear spin-wave theory and the first-principles calculations, we propose that variety of topological phases exist in the trian gular ferromagnet. These include magnon Chern insulators and high-order topological insulators. Interestingly, these topological states can coexist within a certain parameter space, leading to a hybrid topological state. We propose that these novel topological phases can be realized via atomic substitutions in MnSe₂or MnTe₂single-layers. The following detailed analysis suggests that non-uniform Dzyaloshinsky-Moriya interactions are crucial in achieving topological magnons. Our work unveil a novel approach to obtaining non-trivial topological magnons in two-dimensional materials.