  Nano-magnetic systems of artificially shaped ferromagnetic islands, recently
became a popular subject due to their current and potential applications in
spintronics, magneto-photonics and superconductivity. When the island size is
close to the exchange length of magnetic material (around 15 nm), its magnetic
structure becomes markedly different. It determines both static and dynamic
magnetic properties of elements, but strongly depends on their shape and size.
Here we map this dependence for circular cylindrical islands of a few exchange
lengths in size. We outline the region of metastability of "C"-type magnetic
states, proving that they are indeed genuine and not a result of pinning on
particle imperfections. A way to create the smallest particles with guaranteed
magnetic vortex state at zero field becomes evident. It is expected that the
map will help focus the efforts in planning of experiments and devices.
