In this Letter we address spin wave dynamics involved in fast and selective vortex core polarity reversal by rotating magnetic field bursts. In a first example we explain the origin of the delayed switching for excitations with short bursts of only one period duration as an interference effect between spin wave modes. Second, when the vortex core is initially no longer at rest but in gyrotropic motion, the magnetization dynamics become more complicated and the interaction of spin waves with the vortex core leads to a variety of nonlinear effects. Our analysis allows us to explain the experimentally observed switching diagram for simultaneous excitation of spin waves and gyrotropic mode.
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