Dipole-dipole interactions in a square planar array of sub-micron magnetic disks (magnetic dots) have been studied theoretically. 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 formulae for the dipolar energy and anhysteretic magnetization curve are presented.I.

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An approximate expression (Kaczer and Tomas 1972) for the energy of cylindrical 180° domain walls in uniaxial ferromagnetic material predicts that long cylindrical reverse domains aligned in the easy direction should be metastable against collapse to zero radius. It is shown here by a scaling argument, without approximation, that these domains are unstable in a uniaxial continuum.