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.
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