Vortex structures in planar lattices of magnetic dipoles in the presence of exchange coupling

Vortex equilibrium states of planar square lattices of magnetic dipoles in the presence of the exchange interaction have been studied. It has been shown that the vortex equilibrium configurations differ in the position of the vortex center and, correspondingly, in the magnitude and direction of the total magnetic moment of the system. In the case of the position of the vortex center in the center of the array, the total magnetic moment of the system is zero. The vortex center moves in the direction perpendicular to the field under the action of the external planar magnetic field on the system. Thus, the transitions between different equilibrium vortex configurations are implemented and the magnetic moment of the system of dipoles is controlled.