  Equilibrium magnetization states in thin spherical shells of a magnetically
soft ferromagnet are determined by the competition between two interactions:
(i) The local exchange interaction favours the more homogeneous onion state
with magnetization oriented in meridian directions; such a state is realized in
relatively small particles. (ii) The nonlocal magnetostatic interaction prefers
the double-vortex configuration with the magnetization oriented in the
parallels directions, since it minimizes the volume magnetostatic charges.
These sates are topologically equivalent, in contrast to the same-name states
of magnetic nanoring. As a consequence, a continuous (the second order) phase
transition between the vortex and onion states takes place. The detailed
analytical description of the phase diagram is well confirmed by micromagnetic
simulations.
