Controllable Thickness Inhomogeneity and Berry Curvature Engineering of Anomalous Hall Effect in SrRuO₃ Ultrathin Films

In quantum matters hosting electron-electron correlation and spin-orbit coupling, spatial inhomogeneities, arising from competing ground states, can be essential for understanding exotic topological properties. A prominent example is Hall anomalies observed in SrRuO₃ films, which were interpreted in terms of either magnetic skyrmion-induced topological Hall effect or inhomogeneous anomalous Hall effect (AHE). To clarify this ambiguity, we systematically investigated the evolution of AHE with controllable inhomogeneities in SrRuO₃ film thickness (tSRO). By exploiting the step-flow growth of SrRuO₃ films, we induced a microscopically ordered stripe pattern with one-unit-cell differences in tSRO. The associated spatial distribution of momentum-space Berry curvatures enables a two-channel AHE with hump-like Hall anomalies, which can be continuously engineered according to non-integer tSRO. We further microscopically characterized the stripe-like ferromagnetic domains and two-step magnetic switching behavior in the inhomogeneous SrRuO₃ film. These unique features can be utilized to identify the two-channel AHE model and understand its microscopic origin.