  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.
