{
  "abstract": "Conventional approaches classify symmetry-allowed magnetic configurations but do not by themselves establish a direct, mode-resolved correspondence with parent-lattice vibrations. Here, we formulate a universal determinant-induced pseudoscalar twist for all 32 crystallographic point groups, establishing an exact representation-to-geometry correspondence between parent vibrations and magnetic order. Within the paramagnetic gray group $G\\timesΘ_{\\mathcal{T}}$, the spatial twist determines symmetry-defined magnetic geometry, while time-reversal parity independently specifies magnetic character. Each parent phonon irrep $Γ$ maps to $Γ_{\\mathrm{mag}}=Γ\\otimesΓ_{\\mathrm{ps}}$, preserving multiplicities and yielding the projection identity $P_{\\mathrm{mag},mn}^{(Γ\\otimesΓ_{\\mathrm{ps}})}=P_{\\mathrm{ph},mn}^{(Γ)}$ under the common Cartesian realization. This establishes the \\textit{Template Principle}: parent vibrational modes furnish real-space templates whose symmetry-enforced nodal manifolds are inherited exactly. Applied to monolayer $\\mathrm{Cd}_2\\mathrm{N}_3$, the framework identifies the ferrimagnetic ground state from the parent $A_{2u}$ sector, confirmed by first-principles calculations, alongside cluster magnetic octupoles and antiferromagnetic manifolds. It further provides an \\textit{a priori} parent-group criterion for screening symmetry-allowed linear magnetic responses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18449",
  "author_total": 3,
  "authors": [
    {
      "name": "Yachao Liu"
    },
    {
      "name": "Haibo Niu"
    },
    {
      "name": "Vei Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/11s136wdr3rrh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18449",
  "fulltext_url": null,
  "id": "11s136wdr3rrh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18449",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "openalex",
      "3104|Advanced Condensed Matter Physics"
    ]
  ],
  "openalex": "W7213498292",
  "pdf_url": "https://arxiv.org/pdf/2609.18449",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/11s136wdr3rrh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.18449",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18449"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "A Pseudoscalar Representation Mapping from Parent-Group Vibrational Normal Modes to Symmetry-Adapted Magnetic Structures",
  "title_text": "A Pseudoscalar Representation Mapping from Parent-Group Vibrational Normal Modes to Symmetry-Adapted Magnetic Structures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/11s136wdr3rrh",
  "venue": "arXiv",
  "versions": []
}