Despite recent efforts to advance spintronics devices and quantum information technology using materials with non-trivial topological properties, three key challenges are still unresolved^{1,2,3,4,5,6,7,8,9}. First, the identification of topological band degeneracies that are generically rather than accidentally located at the Fermi level. Second, the ability to easily control such topological degeneracies. And third, the identification of generic topological degeneracies in large, multisheeted Fermi surfaces. By combining de Haas–van Alphen spectroscopy with density functional theory and band-topology calculations, here we show that the non-symmorphic symmetries^{10,11,12,13,14,15,16,17} in chiral, ferromagnetic manganese silicide (MnSi) generate nodal planes (NPs)^11,12, which enforce topological protectorates (TPs) with substantial Berry curvatures at the intersection of the NPs with the Fermi surface (FS) regardless of the complexity of the FS. We predict that these TPs will be accompanied by sizeable Fermi arcs subject to the direction of the magnetization. Deriving the symmetry conditions underlying topological NPs, we show that the 1,651 magnetic space groups comprise 7 grey groups and 26 black-and-white groups with topological NPs, including the space group of ferromagnetic MnSi. Thus, the identification of symmetry-enforced TPs, which can be controlled with a magnetic field, on the FS of MnSi suggests the existence of similar properties—amenable for technological exploitation—in a large number of materials.

尽管最近努力使用具有重要拓扑特性的材料来推进自旋电子器件和量子信息技术，但三个关键挑战仍未解决^{1,2,3,4,5,6,7,8,9} 。首先，识别一般而非偶然位于费米能级的拓扑能带简并性。其次，能够轻松控制这种拓扑简并性。第三，识别大型多片费米表面中的一般拓扑简并性。通过将德哈斯-范阿尔芬光谱与密度泛函理论和能带拓扑计算相结合，我们在这里证明了手性铁磁硅化锰（MnSi）中的非对称性^{10,11,12,13,14,15,16,17} ）生成节点平面（NP） ^11,12 ，无论 FS 的复杂性如何，它都会在 NP 与费米面（FS）的相交处强制实施具有大量贝里曲率的拓扑保护区（TP）。我们预测这些TP将伴随着受磁化方向影响的相当大的费米弧。推导了拓扑纳米粒子的对称条件，我们发现 1,651 个磁性空间群包括 7 个灰色群和 26 个具有拓扑纳米粒子的黑白群，其中包括铁磁 MnSi 空间群。因此，在 MnSi 的 FS 上识别出可以用磁场控制的对称强化 TP，表明在大量材料中存在类似的特性（适合技术开发）。