In oxide heterostructures, different materials are integrated into a single artificial crystal, resulting in a breaking of inversion-symmetry across the heterointerfaces. A notable example is the interface between polar and non-polar materials, where valence discontinuities lead to otherwise inaccessible charge and spin states. This approach paved the way to the discovery of numerous unconventional properties absent in the bulk constituents. However, control of the geometric structure of the electronic wavefunctions in correlated oxides remains an open challenge. Here, we create heterostructures consisting of ultrathin SrRuO$_3$, an itinerant ferromagnet hosting momentum-space sources of Berry curvature, and LaAlO$_3$, a polar wide-bandgap insulator. Transmission electron microscopy reveals an atomically sharp LaO/RuO$_2$/SrO interface configuration, leading to excess charge being pinned near the LaAlO$_3$/SrRuO$_3$ interface. We demonstrate through magneto-optical characterization, theoretical calculations and transport measurements that the real-space charge reconstruction modifies the momentum-space Berry curvature in SrRuO$_3$, driving a reorganization of the topological charges in the band structure. Our results illustrate how the topological and magnetic features of oxides can be manipulated by engineering charge discontinuities at oxide interfaces.
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