  Diameter-modulated nanowires offer an important paradigm to design the
magnetization response of 3D magnetic nanostructures by engineering the domain
wall pinning. With the aim to understand its nature and to control the process,
we analyze the magnetization response in FeCo modulated polycrystalline
two-segment nanowires varying the minor diameter. Our modelling indicates a
very complex behavior with a strong dependence on the disorder distribution and
an important role of topologically non-trivial magnetization structures. We
demonstrate that modulated nanowires with a small diameter difference are
characterized by an increased coercive field in comparison to the straight ones
which is explained by a formation of topologically protected walls formed by
two 3D skyrmions with opposite chiralities. For a large diameter difference we
report the occurrence of a novel pinning type called here the "corkscrew": the
magnetization of the large diameter segment forms a skyrmion tube with a core
position in a helical modulation along the nanowire. This structure is pinned
at the constriction and in order to penetrate the narrow segments the
vortex/skyrmion core size should be reduced.
