AI 中文总结
研究通过无自旋时间反演对称性扩展交替磁性分类到非中心对称晶体，给出二维磁性壁纸群和三维磁性空间群的交替磁序目录，揭示非对称对称性对实现新交替磁能带结构的关键作用。
AI 中文摘要
传统交替磁性具有补偿共线自旋排列和自旋分裂的特征，在相反动量处呈现相同自旋态。本工作采用非空间全局对称性\(S\)，即无自旋时间反演对称性，有效替代反演对称性以保持自旋态等效性，从而系统地将交替磁性分类扩展到所有可能的非中心对称晶体。通过分析必要的对称条件，给出了所有二维磁性壁纸群和三维磁性空间群的交替磁序完整目录，确定了17个交替磁性壁纸群（12个中心对称和5个非中心对称）以及422个交替磁性空间群（160个中心对称和262个非中心对称）。该目录将每个交替磁性壁纸和空间群分配到文献中建立的六种交替磁波类型之一，并展示其在布里渊区的独特自旋分布。非对称对称性通过出现沙漏色散进一步带来交替磁布里渊区的新模式，这源于两个对称保护简并流形之间的兼容性关系。在非中心对称交替磁性和沙漏色散出现中，无自旋时间反演对称性起关键作用。我们的工作扩展了交替磁性的对称目录，并揭示非对称对称性对于实现超越六种已建立波类型的交替磁能带结构至关重要，如四方布里渊区中的\(i\)波状自旋缠绕。
英文摘要
Conventional altermagnetism, characterized by compensated collinear spin alignment and spin splitting, exhibits identical spin states at opposite momenta. In this work, we employ a non-spatial global symmetry $S$, the spinless time-reversal symmetry, which effectively replaces inversion symmetry in preserving the spin-state equivalence; hence, we systematically extend the classification of altermagnetism to all possible non-centrosymmetric crystals. By analyzing the necessary symmetry conditions, we provide a complete catalog of altermagnetic orders for all 2D magnetic wallpaper groups and all 3D magnetic space groups, identifying 17 altermagnetic wallpaper groups (12 centrosymmetric and 5 non-centrosymmetric) and 422 altermagnetic space groups (160 centrosymmetric and 262 non-centrosymmetric). This catalog assigns each altermagnetic wallpaper and space group to one of the six altermagnetic wave types established in the literature and presents its distinct spin distribution in the Brillouin zone (BZ); notably, the low-energy wave-type description does not necessarily extend throughout the full BZ, since the spin-degenerate nodal lines and planes can be unpinned from the high-symmetry planes. Beyond the catalog, nonsymmorphic symmetries further bring new patterns of the altermagnetic BZs through the emergence of hourglass dispersions, which arise from the compatibility relations between two symmetry-protected degenerate manifolds: same-spin and opposite-spin degeneracies. In both the non-centrosymmetric altermagnetism and the emergence of the hourglass dispersion, the spinless time-reversal symmetry plays the key role. Our work extends the symmetry catalog of altermagnetism and reveals that nonsymmorphic symmetries are essential for realizing altermagnetic band structures beyond the six established wave types, such as an $i$-wave-like spin winding in a tetragonal BZ.
Comments30 pages, 7 figures
