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Presented here are micromagnetic simulations of the behavior of single phase media and exchange spring media for data storage devices under the influence of a microwave field. A reduction of the switching field by about a factor of two can be found in both single phase and exchange spring media when the microwave field reaches an amplitude of 12% of the remanent coercivity without microwave assist. It is shown here that the switching time for exchange spring media is less than that for single phase media due to the influence of soft upper layer which helps in reversing the magnetization along the opposite direction. The optimum microwave frequency that leads to the most effective reduction of the switching field depends on the angle of the applied field. At higher field angle the frequency band for successful microwave assist becomes smaller. In exchange spring media the frequency that leads to a maximum switching field reduction is smaller than in single phase media.