Magnetization process of the vortex state in soft magnetic thin square platelets

An analysis of the magnetization process in magnetically ultra-soft thin film elements is presented for the case of square platelets, which show a vortex ground state and have a very low thickness. The analysis is based on micromagnetic calculations for systems with 1 μm edge length, 8–20 nm thickness and for material parameters similar to permalloy, but with negligible magnetic anisotropy. For the case of a field applied along the diagonal of the square platelet the evolution of magnetization, critical fields for the expulsion of the vortex and the leading energy terms have been determined from the numerical simulations. We show that a phase theory approximation, by using the position of the vortex as the only variable for the evolution of the vortex pattern, semi-quantitatively describes the main features of the reversible magnetization process and the stability limit. An effective demagnetization factor for the vortex pattern of the squares is determined from the numerical results. This effective parameter enables a quantitative description of the main properties of the vortex state and its magnetization process. Deviations of this phase-theory approximation from the numerical calculations are traced back to the evolution of inhomogeneous internal magnetization states, in particular wide walls that change their profiles under the applied field.