Nontrivial Topological Properties of a One-dimensional Magnonic Crystal

A magnonic crystal provides a promising realization of a bosonic topological insulator with length scales much shorter than photonic ones. We derive the non-trivial topological phase diagram of a one-dimensional magnonic crystal that is a magnonic analogue of the Su-Schrieffer-Heeger model. We studied a YIG based semi-infinite magnonic crystal polarized with an out-of-plane magnetic field. We obtained dispersion relations of the magnonic crystal using the linearized Landau-Lifshitz-Gilbert equation. We used an analytic calculation to obtain Zak phases and confirmed a change to the non-trivial phase in certain magnon bands. Finally, we employed a micromagnetic modeling program to simulate the finite structure and excitation of topologically non-trivial and robust magnonic edge states, which may have applications to quantum information science.