Hysteresis curves are investigated for finite arrays of $N\times N$ ferromagnetic nanodots subject to the dipole-dipole interaction ($N=2,\dots$,13). Spin arrangements up to $N=6$ are presented, which indicate the onset of bulklike behavior associated with odd $\left(N=5\right)$ and even $\left(N=6\right)$ systems. The effect of field misalignment on the hysteresis loops is also studied for $N=3,\dots$,6. The area $A_N$ of the hysteresis loop is studied as a function of $N$. $A_N-A_{\infty }$ approximately scales as $N^{-\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ for $N$ odd and as $N^{-2}$ for $N$ even.

• Received 20 October 2003

DOI:https://doi.org/10.1103/PhysRevB.70.174404