Magnetization ground states and phase diagrams for a nano-sized Co   hollow sphere : an onion-type magnetization state
  The magnetization ground states (MGSs) for a nanosized Co hollow sphere, with the outer radius, R < 50 nm, have been studied numerically by micromagnetic simulation using object oriented micromagnetic framework (OOMMF). In addition to the originally known single domain and vortex-curling states, a three dimensional "onion" state with a corresponding analytical expression is proposed and confirmed as one of the ground states. Two phase diagrams, one for a single crystalline and the other for a polycrystalline nanosphere, are obtained for the three MGSs. The result reveals that the magnetic anisotropy has a significant effect on the phase line in the diagrams. The finite temperature effect and the blocking properties of the nanosphere for the magnetization reversal are discussed. 
Desheng Kong, Siming Wang, and Chinping Chen