{"paper":{"title":"Complete Hierarchy of Nonrelativistic Odd-Parity Spin Splitting in Collinear Magnets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mes-hall"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Cheng-Cheng Liu, Junxi Yu, Pu Zhang, Yichen Liu","submitted_at":"2026-07-21T17:15:03Z","abstract_excerpt":"Momentum-dependent nonrelativistic spin splitting provides a symmetry fingerprint of collinear magnets and can govern unconventional electronic, magnonic, and transport phenomena. Whereas even-parity $s$-, $d$-, $g$-, and $i$-wave splittings in collinear magnets have been extensively studied, odd-parity counterparts remain unexplored beyond the $p$-wave and $f$-wave classes. Here, using group theory, we establish the complete classification of odd-parity spin splitting in collinear magnets. We show that, in addition to the $p$-wave and $f$-wave forms, $h$- and $k$-wave splittings with $\\ell=5$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19303","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/2607.19303/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"}