Enhanced stability and decreased size limit for magnetic vortex state in thin permalloy nanodisk by radial modulation of thickness

Magnetization reversal in thin cylindrical nanodisks with radius between 20 and 100 nm is investigated with particular emphasis to modulation of disk thickness. The nanodisk is kept 1 nm thin at the center, whereas it gradually thickens to 21 nm at the periphery. The thickness modulation stabilizes the vortex closure state as the ground state in nanodisk for radius as low as 20 nm. An onion state appears at remanence during in-plane magnetization reversal. Nudged elastic band method verifies that the vortex state is highly stable in all the nanodisks. In the nanodisk of 100 nm radius, the vortex state requires an energy of 2677 kT to transit into onion state where kT is thermal energy at room temperature. This stability however reduces with size of nanodisk and the smallest nanodisk of 20 nm radius has to surpass an energy barrier of 120 kT to topple over to onion state.