{"paper":{"title":"Phase diagram of magnetic $S^3$ Skyrmions on three-dimensional lattices and the toroidal antiSkyrmion","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cond-mat.mes-hall","authors_text":"Niccol\\`o Francini, Roberto Menta, Stefano Bolognesi, Sven Bjarke Gudnason","submitted_at":"2026-06-05T18:00:02Z","abstract_excerpt":"Magnetic Skyrmions are planar solitons stabilized by the Dzyaloshinskii-Moriya interaction (DMI) and realized in chiral magnets. We study their natural three-dimensional generalization: a sigma model from $\\mathbb{R}^3$ to $S^3$ with a four-component magnetization vector, stabilized by a one-derivative term which is a generalized DMI. We utilize two SO(3)-invariant generalized DMIs discovered recently: an \"$\\alpha$-term\" supporting a spherically symmetric hedgehog Skyrmion and a \"$\\beta$-term\" supporting an axially symmetric Skyrmion that splits into two half-Skyrmions connected by a magnetic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07740","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.07740/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}