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Magnetic viscosity and the phenomenon of the sweep-rate dependence of the coercivity are important for the characterization of magnetic recording media. The activation volume of magnetization reversal or switching volume is directly related to medium noise. The magnetic viscosity behavior of annealed Fe/Pt multilayers was studied and the switching volumes were obtained by both measurements of the sweep-rate dependence of coercivity and time dependence of magnetization. It is found that samples with larger coercivities have smaller switching volumes, and an estimate of the magnetic grain diameter is about 9 nm. The coercivity mechanisms are also discussed.