  The FMR linewidth and its anisotropy in F$_1$/f/F$_2$/AF multilayers, where
spacer f has a low Curie point compared to the strongly ferromagnetic F$_1$ and
F$_2$, is investigated. The role of the interlayer exchange coupling in
magnetization relaxation is determined experimentally by varying the thickness
of the spacer. It is shown that stronger interlayer coupling via thinner
spacers enhances the microwave energy exchange between the outer ferromagnetic
layers, with the magnetization of F$_2$ exchange-dragged by the resonance
precession in F$_1$. A weaker mirror effect is also observed: the magnetization
of F$_1$ can be exchange-dragged by the precession in F$_2$, which leads to
anti-damping and narrower FMR linewidths. A theory is developed to model the
measured data, which allows separating various contributions to the magnetic
relaxation in the system. Key physical parameters, such as the interlayer
coupling constant, in-plane anisotropy of the FMR linewidth, dispersion of the
magnetic anisotropy fields are quantified. These results should be useful for
designing high-speed magnetic nanodevices based on thermally-assisted
switching.
