  Herein, we study the spin-wave dispersion and dissipation in a ferromagnetic
insulator--normal metal--ferromagnetic insulator system. Long-range dynamic
coupling because of spin pumping and spin transfer lead to collective magnetic
excitations in the two thin-film ferromagnets. In addition, the dynamic dipolar
field contributes to the interlayer coupling. By solving the
Landau-Lifshitz-Gilbert-Slonczewski equation for macrospin excitations and the
exchange-dipole volume as well as surface spin waves, we compute the effect of
the dynamic coupling on the resonance frequencies and linewidths of the various
modes. The long-wavelength modes may couple acoustically or optically. In the
absence of spin-memory loss in the normal metal, the spin-pumping-induced
Gilbert damping enhancement of the acoustic mode vanishes, whereas the optical
mode acquires a significant Gilbert damping enhancement, comparable to that of
a system attached to a perfect spin sink. The dynamic coupling is reduced for
short-wavelength spin waves, and there is no synchronization. For intermediate
wavelengths, the coupling can be increased by the dipolar field such that the
modes in the two ferromagnetic insulators can couple despite possible small
frequency asymmetries. The surface waves induced by an easy-axis surface
anisotropy exhibit much greater Gilbert damping enhancement. These modes also
may acoustically or optically couple, but they are unaffected by thickness
asymmetries.
