  Perovskite SrRuO$_3$ is a prototypical itinerant ferromagnet which allows
interface engineering of its electronic and magnetic properties. We report
synthesis and investigation of atomically flat artificial multilayers of
SrRuO$_3$ with the spin-orbit semimetal SrIrO$_3$ in combination with
band-structure calculations with a Hubbard $U$ term and topological analysis.
They reveal an electronic reconstruction and emergence of flat Ru-4d$_{xz}$
bands near the interface, ferromagnetic interlayer coupling and negative
Berry-curvature contribution to the anomalous Hall effect. We analyze the Hall
effect and magnetoresistance measurements as a function of the field angle from
out of plane towards in-plane orientation (either parallel or perpendicular to
the current direction) by a two-channel model. The magnetic easy direction is
tilted by about $20^\circ$ from the sample normal for low magnetic fields,
rotating towards the out-of-plane direction by increasing fields. Fully
strained epitaxial growth enables a strong anisotropy of magnetoresistance. An
additional Hall effect contribution, not accounted for by the two-channel model
is compatible with stable skyrmions only up to a critical angle of roughly
$45^\circ$ from the sample normal. Within about $20^\circ$ from the thin film
plane an additional peak-like contribution to the Hall effect suggests the
formation of a non-trivial spin structure.
