发表机构
Graduate School of Science, Hokkaido University（北海道大学理学研究科）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对非相对论共线磁体，完成了所有非磁性点群与共线自旋点群的活性轨道、自旋多极分类，建立了多极与物理响应的对应关系，为相关磁性现象研究提供统一框架。
AI 中文摘要
多极矩为描述电子自由度及其相关物理响应提供了统一的对称语言。尽管活性多极已针对晶体学点群和磁点群进行了系统分类，但在自然描述无自旋轨道耦合的磁性系统的自旋点群中，其分类仍未被探索。本工作中，我们针对所有32个非磁性点群和122个共线自旋点群，提出了活性轨道多极与自旋多极的完整分类。通过独立处理轨道与自旋自由度，我们确定了与非磁性和共线磁性有序相关的对称允许多极，并通过对应自旋点群间的比较阐明了其层级关系。所得分类提供了一个基于对称的数据库，可区分活性多极的结构与磁贡献，并直接识别微观有序参数，包括负责d波、g波和i波反常铁磁性的参数。此外，通过在同一框架内分类响应张量，我们建立了活性多极与对称允许物理响应之间的对应关系。该对应关系系统地区分了无自旋轨道耦合时存在的非相对论响应与需要相对论效应的响应，为理解和预测磁性材料中与自旋相关的电磁及输运现象提供了统一框架。
英文摘要
Multipole moments provide a unified symmetry language for describing electronic degrees of freedom and their associated physical responses. Although active multipoles have been systematically classified for crystallographic and magnetic point groups, their classification in spin point groups, which naturally describe magnetic systems in the absence of spin-orbit coupling, has remained unexplored. In this work, we present a complete classification of active orbital and spin multipoles for all 32 nonmagnetic and 122 collinear spin point groups. Treating orbital and spin degrees of freedom independently, we identify the symmetry-allowed multipoles associated with nonmagnetic and collinear magnetic orderings and clarify their hierarchy through comparisons among the corresponding spin point groups. The resulting classification provides a symmetry-based database that distinguishes structural and magnetic contributions to active multipoles and directly identifies microscopic order parameters, including those responsible for $d$-, $g$-, and $i$-wave altermagnetism. Furthermore, by classifying response tensors within the same framework, we establish a correspondence between active multipoles and symmetry-allowed physical responses. This correspondence systematically distinguishes nonrelativistic responses that survive without spin-orbit coupling from those requiring relativistic effects, providing a unified framework for understanding and predicting spin-dependent electromagnetic and transport phenomena in magnetic materials.
Comments200 pages, 1 figure, 173 tables
