Analytical approximations to the core radius and energy of magnetic vortex in thin ferromagnetic disks

The energy of magnetic vortex core and its equilibrium radius in thin circular cylinder were first presented by Usov and Peschany in 1994. Yet, the magnetostatic function, entering the energy expression, is hard to evaluate and approximate. Here, precise and explicit analytical approximations to this function (as well as equilibrium vortex core radius and energy) are derived in terms of elementary functions. Also, several simplifying approximations to the magnetic Hamiltonian and their impact on theoretical stability of magnetic vortex state are discussed. - Highlights: • Approximate expressions for the magnetic vortex equilibrium core radius. • Approximate expressions for the magnetic vortex equilibrium energy. • Exact formulas for the exchange energy of magnetic textures in complex variable. • Impact of approximations in Hamiltonian on magnetic vortex state is analyzed