{"paper":{"title":"Exact Hopfion Vortices in a 3D Heisenberg Ferromagnet","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"nlin.SI","authors_text":"Avadh Saxena, Radha Balakrishnan, Rossen Dandoloff","submitted_at":"2022-02-15T05:05:05Z","abstract_excerpt":"We find exact static soliton solutions for the unit spin vector field of an inhomogeneous, anisotropic three-dimensional Heisenberg ferromagnet. Each soliton is labeled by two integers $n$ and $m$. It is a (modified) skyrmion in the $z=0$ plane with winding number $n$, which twists out of the plane $m$ times in the $z$-direction to become a 3D soliton. Here $m$ arises due to the periodic boundary condition at the $z$-boundaries. We use Whitehead's integral expression to find that the Hopf invariant of the soliton is an integer $H =nm$. It represents a hopfion vortex. Plots of the preimages of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.07195","kind":"arxiv","version":2},"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/2202.07195/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"}