Magnetism and spin–orbit coupling are two quintessential ingredients underlying topological transport phenomena in itinerant ferromagnets. When spin-polarized bands support nodal points/lines with band degeneracy that can be lifted by spin–orbit coupling, the nodal structures become a source of Berry curvature, leading to a large anomalous Hall effect. However, two-dimensional systems can possess stable nodal structures only when proper crystalline symmetry exists. Here we show that two-dimensional spin-polarized band structures of perovskite oxides generally support symmetry-protected nodal lines and points that govern both the sign and the magnitude of the anomalous Hall effect. To demonstrate this, we performed angle-resolved photoemission studies of ultrathin films of SrRuO₃, a representative metallic ferromagnet with spin–orbit coupling. We show that the sign-changing anomalous Hall effect upon variation in the film thickness, magnetization and chemical potential can be well explained by theoretical models. Our work may facilitate new switchable devices based on ferromagnetic ultrathin films.

磁性和自旋轨道耦合是巡回铁磁体中拓扑传输现象的两个典型成分。当自旋极化带支持具有带简并性的节点/线时，可以通过自旋轨道耦合提升，节点结构成为贝里曲率的来源，导致大的反常霍尔效应。然而，只有当存在适当的晶体对称性时，二维系统才能拥有稳定的节点结构。在这里，我们表明钙钛矿氧化物的二维自旋极化能带结构通常支持对称保护的节点线和控制异常霍尔效应的符号和大小的点。_{为了证明这一点，我们对 SrRuO 3}的超薄膜进行了角分辨光电子发射研究，具有自旋轨道耦合的代表性金属铁磁体。我们表明，理论模型可以很好地解释薄膜厚度、磁化强度和化学势变化引起的变号反常霍尔效应。我们的工作可能会促进基于铁磁超薄膜的新型可切换设备。