  Scalar spin chirality is expected to induce a finite contribution to the Hall
response at low temperatures. We study this spin-chirality-driven Hall effect,
known as the topological Hall effect, at the manganite side of the interface
between La$_{1-x}$Sr$_{x}$MnO$_{3}$ and SrIrO$_3$. The ferromagnetic
double-exchange hopping at the manganite layer, in conjunction with the
Dzyaloshinskii-Moriya (DM) interaction which arises at the interface due to
broken inversion symmetry and strong spin-orbit coupling from the iridate
layer, could produce a skyrmion-crystal (SkX) phase in the presence of an
external magnetic field. Using the Monte Carlo technique and a two-orbital
spin-fermion model for manganites, supplemented by an in-plane DM interaction,
we obtain phase diagrams which reveal at low temperatures a clear SkX phase and
also a low-field spin-spiral phase. Increasing temperature, a skyrmion-gas
phase, precursor of the SkX phase upon cooling, was identified. The topological
Hall effect primarily appears in the SkX phase, as observed before in oxide
heterostructures. We conclude that the manganite-iridate superlattices provide
another useful platform to explore a plethora of unconventional magnetic and
transport properties.
