Stability of topological charge of magnetic skyrmion configurations

•We analyze the topological charge of a skyrmion qs and its corresponding Hall conductivity σxy.•We derive the general form of the DM interaction for any arbitrary orientation of the DM vector DD.•We obtain the dependence the skyrmion helicity angle on the orientation of DD.•We show mathematically the topological nature of the skyrmionic charge qs.•We show via numerical micromagnetics the robustness of qs under varying applied B-fields.

We analyze the topological charge of a skyrmion qs, and the corresponding Hall conductivity σxy, which can serve as an electrical read-out for skyrmion-based memory. We derived the general form of the Dzyaloshinskii–Moriya (DM) interaction for any arbitrary orientation of the DM vector DD. Based on the DM interaction energy, we obtained the dependence the skyrmion helicity angle γ   on the orientation of DD. We showed via general mathematical arguments, the topological nature of the skyrmionic charge qs, and its independence of γ and specific details of the interior of the skyrmion (e.g., its core size). Finally, we showed via numerical micromagnetics the stability of qs under varying applied B-fields till the annihilation field, despite the drastic reduction in the skyrmion core size.