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The magnetic hysteresis and its area for two-dimensional nanomagnets with precessional magnetization reversal, driven by ac magnetic field of frequency f and amplitude H-0, are investigated by numerically solving the Landau-Lifshitz-Gilbert equation. Irregular hysteresis loops are observed when f is low and H-0 is high, indicating the significant contribution of nonadiabatic precession to the magnetization reversal. The frequency dispersion of hysteresis area A(f) shows the double-peaked pattern with the low-f peak caused by the precessional magnetization reversal and the high-f peak originating from the quasichaotic oscillations of the spin precession. The power-law scaling behavior of the hysteresis dispersion, i.e., A proportional to H(0)(lambda)f(beta) with exponents lambda=0.60 and beta=0.50, is observed in the low-f range limit. We present the one-parameter dynamic scaling on the low-f hysteresis dispersions over a broad range of H-0, demonstrating the scalability of the hysteresis dispersion and thus the existence of the unique characteristic time for magnetization reversal process in nanomagnets, given the field amplitude H-0.

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