发表机构
Xi’an University of Technology; Xi’an Jiaotong University City College（西安理工大学; 西安交通大学城市学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于行列式赝标量扭转的普适框架，将32个晶体点群的母振动模式映射为对称自适应磁性结构，并应用于单层Cd2N3识别亚铁磁基态，为筛选线性磁响应提供先验判据。
AI 中文摘要
传统方法对对称允许的磁性构型进行分类，但本身并不建立与母晶格振动的直接、模式分辨的对应关系。在此，我们为所有32个晶体学点群构建了一个由行列式诱导的普适赝标量扭转，从而在母振动与磁有序之间建立了精确的表示到几何的对应关系。在顺磁灰色群$G\times\Theta_{\mathcal{T}}$中，空间扭转决定对称定义的磁几何，而时间反演奇偶性独立指定磁特性。每个母声子不可约表示$\Gamma$映射到$\Gamma_{\mathrm{mag}}=\Gamma\otimes\Gamma_{\mathrm{ps}}$，保持重数，并在共同笛卡尔实现下产生投影恒等式$P_{\mathrm{mag},mn}^{(\Gamma\otimes\Gamma_{\mathrm{ps}})}=P_{\mathrm{ph},mn}^{(\Gamma)}$。这确立了模板原理：母振动模式提供实空间模板，其对称强制的节点流形被精确继承。应用于单层$\mathrm{Cd}_2\mathrm{N}_3$，该框架从母$A_{2u}$扇区识别出亚铁磁基态，经第一性原理计算证实，同时识别出团簇磁八极子和反铁磁流形。它还提供了筛选对称允许的线性磁响应的先验母群判据。
英文摘要
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.
