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Frequency-dependent hysteresis for two-dimensional magnetic islands with uniaxial anisotropy is studied with a nearest-neighbor spin-one Ising model in the Bethe–Peierls approximation. A characteristic frequency for magnetization reversal is identified that depends on the island morphology only through the ratio θ/p of the coverage to the mean island perimeter roughness as measured by the density of unsaturated near-neighbor bonds. As a result, dissimilar hysteresis is predicted for large versus small and compact versus fractal islands.

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