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Magnetism and spin-orbit coupling (SOC) are two quintessential ingredientsunderlying novel topological transport phenomena in itinerant ferromagnets.When spin-polarized bands support nodal points/lines with band degeneracy thatcan be lifted by SOC, the nodal structures become a source of Berry curvature;this leads to a large anomalous Hall effect (AHE). Contrary tothree-dimensional systems that naturally host nodal points/lines,two-dimensional (2D) systems can possess stable nodal structures only whenproper crystalline symmetry exists. Here we show that 2D spin-polarized bandstructures of perovskite oxides generally support symmetry-protected nodallines and points that govern both the sign and the magnitude of the AHE. Todemonstrate this, we performed angle-resolved photoemission studies ofultrathin films of SrRuO$_3$, a representative metallic ferromagnet with SOC.We show that the sign-changing AHE upon variation in the film thickness,magnetization, and chemical potential can be well explained by theoreticalmodels. Our study is the first to directly characterize the topological bandstructure of 2D spin-polarized bands and the corresponding AHE, which couldfacilitate new switchable devices based on ferromagnetic ultrathin films.

Sign-tunable anomalous Hall effect induced by two-dimensional symmetry-protected nodal structures in ferromagnetic perovskite oxide thin films