Magnetization reversal due to vortex nucleation, displacement, and annihilation in submicron ferromagnetic dot arrays

Magnetization processes are analytically described for the arrays of soft ferromagnetic polycrystalline circular dots with submicron dimensions, wherein the magnetization reversal accompanied by nucleation, displacement, and annihilation of magnetic vortices. Magnetostatic, exchange, and Zeeman energies are taken into account for the analysis. The magnetic state of each dot in an applied magnetic field is treated as an off-centered rigid vortex structure; i.e., the vortex keeps its spin distribution while being displaced. This rigid vortex model yields analytical expressions for the size-dependent initial susceptibility, the vortex nucleation, and the annihilation fields. The interdot magnetostatic interaction plays an important role in the magnetization reversal for the arrays when the interdot distance is smaller than the disk radius, where the initial susceptibility increases and both the nucleation and annihilation fields decrease. The analytical predictions are compared to the micromagnetic calculations, and limitations of the model are discussed.