Geometry induced phase transitions in magnetic spherical shell
  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. 
Mykola I. Sloika, Denis D. Sheka, Volodymyr P. Kravchuk, Oleksandr V.   Pylypovskyi, Yuri Gaididei
cond-mat.mes-hall