  We investigated the structural and magnetic properties of bare SrRuO$_3$
(SRO) ultra-thin films and SrRuO$_3$/SrIrO$_3$/SrZrO$_3$ (SRO/SIO/SZO: RIZ)
trilayer heterostructures between 10 K and 80 K, by comparing macroscopic data
using magneto-optical Kerr effect (MOKE) and magneto-transport (anomalous Hall
effect: AHE), with nanoscale fingerprints when applying non-contact scanning
force microscopy (nc-SFM) and magnetic force microscopy (MFM). SRO and RIZ
ultra-thin films were epitaxially grown at 650C onto vicinal SrTiO$_3$ (100)
single-crystalline substrates to a nominal thickness of 4 and 4/2/2 unit cells
(uc), respectively. Our correlated analysis allows associating topographic
sample features of overgrown individual layers to their residual magnetization,
as is shown here to be relevant for interpreting the macroscopic AHE data.
Although the hump-like features in the AHE suggest a magnetically extured
skyrmion phase to exist around 55 K associated to the topological Hall effect
(THE), both our MOKE and MFM data cannot support this theory. In contrast, our
SFM/MFM local-scale analysis finds the local coercive field to be strongly
dependent on the effective layer thickness and stoichiometry in both the SRO
and RIZ samples, with huge impact on the local band-structure. In fact, it is
these variations that in turn mimic a potential THE through anomalies in the
AHE resistivity loops.
