  Vertically stacked exchange coupled magnetic heterostructures of cylindrical
geometry can host complex noncolinear magnetization patterns. By tuning the
interlayer exchange coupling between a layer accommodating magnetic vortex
state and an out-of-plane magnetized layer, one can efficiently realize new
topological chiral textures such as cone state vortices and circular stripe
domains. We study how the number of circular stripes can be controlled by both
the interlayer exchange coupling and the sample geometrical parameters. By
varying geometrical parameters, a continuous phase transition between the
homogeneous state, cone state vortex, circular stripe domains, and the
imprinted vortex takes place, which is analysed by full scale micromagnetic
simulations. The analytical description provides an intuitive pictures of the
magnetization textures in each of these phases. The possibility to realize
switching between different states allows for engineering magnetic textures
with possible applications in spintronic devices.
