Ground state of finite arrays of magnetic dots in the presence of an external magnetic field

The ground state of an array of magnetic particles (magnetic dots), which are ordered in a square 2D lattice and whose magnetic moment is perpendicular to the lattice plane, in the presence of an external magnetic field has been analyzed. Such a model is applicable for sufficiently small dots with perpendicular anisotropy that are in a single-domain state and for dots in a strongly inhomogeneous vortex state whose magnetic moment is determined by the vortex core. For the magnetic field perpendicular to the system plane, the entire set of the states has been analyzed from the chessboard antiferromagnetic order of magnetic moments in low fields to the saturated state of the system with the parallel orientations of the magnetic moments of all dots in strong fields. In the presence of the border, the destruction of the chessboard order first occurs at the edges of the system, then near the extended sections of the surface, and finally expands over the entire interior of the array. The critical field at which this simplest state is destroyed is much more weakly than the value characteristic of the ideal infinite system. In contrast to this scenario, the destruction of the saturated state with decreasing field always begins far from the borders. Despite such different behaviors, the magnetic structure in the intermediate range of fields that is obtained with both increasing and decreasing field for finite arrays strongly differs from that characteristic of the ideal infinite system. The role of simple stacking faults of the magnetic dot lattice (such as single vacancies or their clusters) in the remagnetization of the system has been analyzed. The presence of such faults is shown to give rise to the appearance of local destructions of the chessboard antiferromagnetic order at fields that are much weaker than those for an ideal lattice.