We investigate the magnetization dynamics in synthetic antiferromagnetic (SyAFM) Fe/[Co/Cu](10)/Co/Pt multilayers using the microwave rectifying effect. We observe two distinct resonant modes in the dynamics. Numerical simulations reveal that the resonant modes can be attributed to acoustic and optical modes, which are the characteristic resonant modes of antiferromagnetically coupled materials. It is found that the'linewidth of the optical mode is larger than that of the acoustic mode by a factor of 5. This broadening of the linewidth in the optical modes can be explained by the mutual spin pumping effect between the magnetizations precessing out of phase. (C) 2014 The Japan Society of Applied Physics