Micromagnetic modeling of spin-wave dynamics in exchange-biased permalloy disks

The magnetization dynamics in exchange-biased 12 nm thick micron-sized permalloy disks have been studied using micromagnetic modeling. The magnetization in the permalloy and in the adjacent antiferromagnetic layer are set in a vortex configuration, and the disk is equilibrated in an applied field, which is then released. The behavior of the magnetization has been modeled as a function of both exchange bias strength and applied field, in both the time and frequency domains. We show that the exchange bias increases the curvature of the effective potential confining the vortex and that the gyrotropic frequency of the vortex core motion increases linearly with exchange bias. The eigenmodes of the spin waves to which the field couples are either azimuthal (for an in-plane field) or circularly symmetric (for a perpendicular field), with several orders of modes being visible. For the cicularly symmetric modes, the increase in frequency with exchange bias is in good agreement with an analytical model.