“…In practice, the local field on magnetic vortex can be generated by, for example, the dipolar field from an adjacent magnetic layer 21,32 or the neighboring magnetic element in a patterned nanostructure, 33-37 the stray field from a magnetic tip, 7,15 or point contact, 38 and the Oersted field from an electrode. [9][10][11]20,39,40 Spin-polarized current induced torque in nanostructure can also act like a local field on vortex.…”