Hysteresis of Finite Arrays of Magnetic nano Dots

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Hysteresis curves for finite arrays of N× N ferromagnetic nano dots subject to the dipole-dipole interaction are investigated for N=2... 13. Spin arrangements up to N=6 are presented, which indicate the onset of bulk-like behavior associated with odd (N=5) and even (N=6) systems. The effect of field misalignment on the hysteresis loops is also studied for N=3... 6. The area Aₙ of the hysteresis loop is studied as a function of N. We find that Aₙ-A∞ approximately scales as N-3/2 for N odd and as N⁻² for N even.