  Geometric phases in condensed matter play a central role in topological
transport phenomena such as the quantum, spin and anomalous Hall effect (AHE).
In contrast to the quantum Hall effect - which is characterized by a
topological invariant and robust against perturbations - the AHE depends on the
Berry curvature of occupied bands at the Fermi level and is therefore highly
sensitive to subtle changes in the band structure. A unique platform for its
manipulation is provided by transition metal oxide heterostructures, where
engineering of emergent electrodynamics becomes possible at atomically sharp
interfaces. We demonstrate that the Berry curvature and its corresponding
vector potential can be manipulated by interface engineering of the correlated
itinerant ferromagnet SrRuO$_3$ (SRO). Measurements of the AHE reveal the
presence of two interface-tunable spin-polarized conduction channels. Using
theoretical calculations, we show that the tunability of the AHE at SRO
interfaces arises from the competition between two topologically non-trivial
bands. Our results demonstrate how reconstructions at oxide interfaces can be
used to control emergent electrodynamics on a nanometer-scale, opening new
routes towards spintronics and topological electronics.
