  The proposal that very small N\'eel skyrmions can form in SrRuO$_3$/SrIrO$_3$
epitaxial bilayers and that the electric field-effect can be used to manipulate
these skyrmions in gated devices strongly stimulated the recent research of
SrRuO$_3$ heterostructures. A strong interfacial Dzyaloshinskii-Moriya
interaction, combined with the breaking of inversion symmetry, was considered
as the driving force for the formation of skyrmions in SrRuO$_3$/SrIrO$_3$
bilayers. Here, we investigated nominally symmetric heterostructures in which
an ultrathin ferromagnetic SrRuO$_3$ layer is sandwiched between large
spin-orbit coupling SrIrO$_3$ layers, for which the conditions are not
favorable for the emergence of a net interfacial Dzyaloshinskii-Moriya
interaction. Previously the formation of skyrmions in the asymmetric
SrRuO$_3$/SrIrO$_3$ bilayers was inferred from anomalous Hall resistance loops
showing humplike features that resembled topological Hall effect contributions.
Symmetric SrIrO$_3$/SrRuO$_3$/SrIrO$_3$ trilayers do not show hump anomalies in
the Hall loops. However, the anomalous Hall resistance loops of symmetric
multilayers, in which the trilayer is stacked several times, do exhibit the
humplike structures, similar to the asymmetric SrRuO$_3$/SrIrO$_3$ bilayers.
The origin of the Hall effect loop anomalies likely resides in unavoidable
differences in the electronic and magnetic properties of the individual
SrRuO$_3$ layers rather than in the formation of skyrmions.
