Robustness of topological magnons in disordered arrays of skyrmions

The effects of disorder on the robustness of topological magnon states of two-dimensional ferromagnetic skyrmions is investigated. It is diagnosed by evaluating a real space topological invariant, the bosonic Bott index (BI). The disorder simultaneously breaks the axially symmetric shape and the crystalline ordering of the skyrmions array. The corresponding magnonic fluctuations and band spectrum are determined in terms of magnetic field and strength of disorder. We observe the closing of the existing band gaps as the individual skyrmions start to occupy random positions. The analysis reveals that topological states (TSs) persist beyond the perturbative limit when skyrmions reach the glassy phase. In addition, the localization of topologically protected edge states is weakened by the disordered skyrmion structure with increasing localization length. Our findings shed light on the physical understanding of the coexistence of disordered magnetic textures and their topological spin fluctuations.