A Pseudoscalar Representation Mapping from Parent-Group Vibrational Normal Modes to Symmetry-Adapted Magnetic Structures
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×Θ𝒯, the spatial twist determines symmetry-defined magnetic geometry, while time-reversal parity independently specifies magnetic character. Each parent phonon irrep Γ maps to Γmag=Γ⊗Γps, preserving multiplicities and yielding the projection identity Pmag,mn(Γ⊗Γps)=Pph,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 Cd2N3, the framework identifies the ferrimagnetic ground state from the parent A2u 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.
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BibTeX
@misc{liu2026pseudoscalar,
title = {{A Pseudoscalar Representation Mapping from Parent-Group Vibrational Normal Modes to Symmetry-Adapted Magnetic Structures}},
author = {Yachao Liu and Haibo Niu and Vei Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18449},
eprint = {2609.18449},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18449},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Pseudoscalar Representation Mapping from Parent-Group Vibrational Normal Modes to Symmetry-Adapted Magnetic Structures
AU - Yachao Liu
AU - Haibo Niu
AU - Vei Wang
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18449
UR - https://arxiv.org/abs/2609.18449
AB - 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×Θ_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_mag=Γ⊗Γ_ps, preserving multiplicities and yielding the projection identity P_mag,mn^(Γ⊗Γ_ps)=P_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 Cd_2N_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.
ER -