Abstract
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 D. Based on the DM interaction energy, we obtained the dependence the skyrmion helicity angle γ on the orientation of D. 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.
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