Ferromagnetic resonance frequency of a patterned synthetic antiferromagnet

We present a theoretical equation for the ferromagnetic resonance (FMR) frequency of a synthetic antiferromagnet (SAF) patterned into a sub-micrometer scale. As the pattern size decreases, both the FMR frequencies of the acoustic and the optic modes increase due to the increased dipolar coupling between two antiferromagnetically coupled ferromagnets. We verify the validity of the equation by comparing its solutions to the numerical results in the framework of the macrospin model. Using the theoretical equation, we investigate the effects of the geometric and the magnetic parameters of the SAF on the FMR frequencies of two modes.