AI 中文总结
该研究在手性反铁磁体Mn₃Sn中发现了原子内磁八极矩（AMO），证实其与团簇磁八极矩（CMO）存在耦合，揭示了其对自旋分裂等性质的作用及操控CMO的新途径。
AI 中文摘要
我们证明，Mn₃Sn除了已被充分证实的团簇磁八极矩（CMO）O之外，还具有有限的原子内磁八极矩（AMO）o。与团簇尺度的CMO不同，AMO是位点局域化的磁多极矩，与各向异性的原子内自旋密度相关。对称性分析表明，CMO和AMO在同一表示下变换，允许存在形式为-g·O·o的双线性相互作用。我们通过第一性原理计算证实了有限AMO密度的存在，并表明AMO在非共线磁结构的旋转下与CMO协同变换，为二者之间的耦合提供了微观证据。我们进一步证明，磁带分裂可通过投影AMO算子来描述，在实际的Mn₃Sn中存在依赖于流形的有效八极交换系数。AMO的存在具有三个重要意义：第一，我们表明Mn₃Sn的非相对论自旋分裂可通过投影AMO算子描述，具有依赖于流形的有效八极交换系数，确立了AMO作为自旋分裂的微观算子的地位；第二，从磁八极矩的角度，AMO揭示了Mn₃Sn与d波交替磁体之间的密切联系；第三，O·o耦合提出了一种利用AMO电流操控CMO的新途径，为控制Mn₃Sn中的多极序开辟了方向。
英文摘要
We demonstrate that Mn$_3$Sn hosts finite intra-atomic magnetic octupoles (AMOs) $\mathbf{o}$ in addition to the well-established cluster magnetic octupole (CMO) $\mathbf{O}$. In contrast to the cluster-scale CMO, the AMO is a site-localized magnetic multipole associated with the anisotropic intra-atomic spin density. Symmetry analysis shows that the CMO and AMO transform in the same representation, allowing a bilinear interaction of the form $-g\,\mathbf{O}\cdot\mathbf{o}$. Using first-principles calculations, we confirm the presence of finite AMO densities and show that the AMO transforms concomitantly with the CMO under rotations of the noncollinear magnetic structure, providing microscopic evidence for the coupling between them. We further show that the magnetic band splitting can be represented by projected AMO operators, with manifold-dependent effective octupolar exchange coefficients in realistic Mn$_3$Sn. The presence of AMOs has three important implications. First, we show that the nonrelativistic spin splitting of Mn$_3$Sn can be described in terms of projected AMO operators, with manifold-dependent effective octupolar exchange coefficients, establishing the AMO as a microscopic operator underlying the spin splitting. Second, the AMO reveals a close connection between Mn$_3$Sn and $d$-wave altermagnets from the magnetic-octupole perspective. Third, the $\mathbf{O}\cdot\mathbf{o}$ coupling suggests a new route to manipulate the CMO using AMO currents, opening a direction for controlling the multipolar order in Mn$_3$Sn.
