Vortices in ferromagnetic elements with perpendicular anisotropy

We study equilibrium properties of disc-shaped ferromagnetic elements with perpendicular anisotropy and quality factor less than unity. A vortex is a static state for sufficiently thin particles. For thicker particles we find a continuous transition to a bidomain state which is stable for a range of particle diameters. This bidomain state is akin to a magnetic “bubble” where the magnetization is directed along the symmetry axis at the center of the disc and it is oppositely magnetized at the periphery. The magnetization profile of the bidomain state presents the same winding around the symmetry axis as the vortex. Its signature is its magnetostatic field which consists of two concentric regions of opposite sign above the particle top surface. Higher-order states of multiple concentric domains with alternating magnetization direction are also found for particles of sufficiently large lateral dimensions. Finally, we explain how these ideas apply to particles with a very small perpendicular anisotropy.