{"paper":{"title":"Enumeration of spin-space groups: Towards a complete description of symmetries of magnetic orders","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mes-hall","cond-mat.str-el"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Chen Fang, Hongming Weng, Jian Yang, Tiannian Zhu, Yi Jiang, Zheng-Xin Liu, Zhong Fang, Ziyin Song","submitted_at":"2023-07-19T18:00:03Z","abstract_excerpt":"Symmetries of three-dimensional periodic scalar fields are described by 230 space groups (SGs). Symmetries of three-dimensional periodic (pseudo-) vector fields, however, are described by the spin-space groups (SSGs), which were initially used to describe the symmetries of magnetic orders. In SSGs, the real-space and spin degrees of freedom are unlocked in the sense that an operation could have different spacial and spin rotations. SSGs gives a complete symmetry description of magnetic structures, and have natural applications in the band theory of itinerary electrons in magnetically ordered s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.10371","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/2307.10371/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"}