发表机构
Sungkyunkwan University（成均馆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明交变磁体的自旋劈裂源于磁轨道及其配体的各向异性排列，而非对称性；通过三斜Mn氧化物实验和形式论证，指出对称性仅组织或禁止劈裂，并统一了交变磁体与补偿铁磁体，将搜索导向轨道排列。
AI 中文摘要
共线交变磁体的自旋劈裂通常归因于连接相反自旋子晶格的晶体对称性——即相对于传统反铁磁体的平移或反演，这里采用的是旋转或镜面对称。我们表明，这种对称性组织劈裂但不产生劈裂；其起源是磁轨道及其配体的各向异性排列，而这种排列本身也决定了对称性。两个结果确立了这一点。一种三斜（$P1$）\\(\ce{Mn}\\)氧化物，是一种完全补偿的铁磁体，其两个不等价子晶格之间没有任何对称性关联，却在整个布里渊区内发生自旋劈裂；将相同的配体逐原子重新定位，以恢复连接两个金属位点的反演中心，劈裂便缩减至残余的两个数量级以下，因此劈裂源于排列而非对称性。我们在形式上表明，对称性只能反转或禁止已经存在的劈裂：它无法在排列使子晶格电子上等同的情况下创造劈裂，也无法在底层轨道本身不具有各向异性可供排列的情况下产生劈裂。通过操作分辨的对称性层级来组织分析，并将晶体类别视为单一轴线，强制性的节面在正交、单斜和三斜晶类中从两个降到一再到零，而排列产生的劈裂则持续到基底。因此，交变磁体和完全补偿铁磁体是同一轴线的两端——同一劈裂，在一端由对称性组织，在另一端则无组织——而对补偿自旋劈裂磁体的搜索是对轨道排列的搜索，而非对对称性标签的搜索。
英文摘要
The spin splitting of collinear altermagnets is usually attributed to the crystal symmetry relating the opposite-spin sublattices --- a rotation or mirror in place of the translation or inversion of a conventional antiferromagnet. We show that this symmetry organizes the splitting but does not produce it; its origin is the anisotropic arrangement of the magnetic orbitals and their ligands, which also fixes the symmetry itself. Two results establish this. A triclinic ($P1$) \ce{Mn} oxide, a fully compensated ferrimagnet whose two inequivalent sublattices are related by no symmetry, is spin split throughout the Brillouin zone; repositioning the same ligands, atom for atom, to restore an inversion centre relating the two metal sites collapses the splitting to a residual two orders of magnitude smaller, so the splitting follows from the arrangement rather than the symmetry. Symmetry, we show formally, can only ever reverse or forbid a splitting that already exists: it cannot create one between sublattices an arrangement has left electronically identical, nor where the underlying orbitals carry no anisotropy to arrange in the first place. Organizing the analysis through an operation-resolved symmetry hierarchy and reading the crystal classes as a single axis, the enforced nodal planes fall from two to one to zero across the orthorhombic, monoclinic, and triclinic classes while the arrangement-generated splitting persists to the base. The altermagnet and the fully compensated ferrimagnet are thus the two ends of one axis --- the same splitting, organized by symmetry at one end and unorganized at the other --- and the search for compensated spin-split magnets is a search over orbital arrangements rather than symmetry labels.
Comments43 pages,6 figures
