Ground states of an array of magnetic dots with Ising-type anisotropy and subject to a normal magnetic field

Dipole-dipole interactions in a square planar array of submicron magnetic particles (magnetic dots) with their moments perpendicular to the plane of the array have been studied theoretically. The proposed theory is related to single-domain uniaxial particles and to disk-shaped dots in the vortex state. Under a normal magnetic field the ground state of the array undergoes many structural transitions between the limiting chessboard antiferromagnetic state at zero field and the ferromagnet at a threshold field. At intermediate fields, numerous ferrimagnetic states having mean magnetic moments between zero and that of the ferromagnetic state are favorable energetically. The structures and energies of a selection of states are calculated and plotted, as are the fields required to optimally reverse the magnetic moment of a single dot within them. Approximate formulas for the dipolar energy and anhysteretic magnetization curve are presented.