Geometry induced phase transitions in magnetic spherical shell

Highlights: • Ground states in magnetic spherical shells form two out-of-surface vortices. • Depending on geometrical parameters onion and whirligig states can be distinguished. • A continuous phase transition takes place between onion and whirligig ground states. • The magnetization state of infinitely small spherical shell is never homogeneous. - Abstract: Equilibrium magnetization states in spherical shells of a magnetically soft ferromagnet form two out-of-surface vortices with codirectionally magnetized vortex cores at the sphere poles: (i) a whirligig state with the in-surface magnetization oriented along parallels is typical for thick shells; (ii) a three dimensional onion state with the in-surface meridional direction of the magnetization is realized in thin shells. The geometry of spherical shell prohibits an existence of spatially homogeneous magnetization distribution, even in the case of small sample radii. By varying geometrical parameters a continuous phase transition between the whirligig and onion states takes place. The detailed analytical description of the phase diagram is well confirmed by micromagnetic simulations.