Micromagnetic modeling of the magnetization dynamics in a circularly exchange-biased and exchange-coupled ferromagnetic multilayer

The magnetization dynamics of a magnetically coupled multilayer structure have been studied by analytical and numerical methods. The simulated multilayer is disk-shaped and consists of a circularly exchange-biased ferromagnetic permalloy (Py) layer coupled to an unbiased Py layer, each in a magnetic vortex configuration, separated by a thin nonmagnetic spacer. The sign and strength of the interlayer exchange coupling was varied, leading to either parallel or antiparallel vortex chiralities in the two Py layers. The magnetization dynamics after the application of an external magnetic field pulse normal to the plane of the disks were investigated. Both analytical and numerical models show two branches of frequency response of circularly symmetric eigenmodes for both parallel and antiparallel configurations. However, the upper branch mode in the antiparallel configuration is severely damped in the numerical simulations due to coupling with short-wavelength spin waves. The frequency of the modes can be tuned independently with interlayer exchange coupling strength and exchange-bias strength. The good agreement between the mode frequencies obtained from the analytical and numerical models confirms that the main driving forces for the eigenmodes are the magnetostatic field from the radial motion of the magnetization, and also the interlayer exchange coupling field. In addition, the vortex cores, which are neglected in the analytical model, are found to play no significant role in the dynamic response.