Dynamic exchange via spin currents in acoustic and optical modes of   ferromagnetic resonance in spin-valve structures
  Two ferromagnetic layers magnetically decoupled by a thick normal metal spacer layer can be, nevertheless, dynamically coupled via spin currents emitted by the spin-pump and absorbed through the spin-torque effects at the neighboring interfaces. A decrease of damping in both layers due to a partial compensation of the angular momentum leakage in each layer was previously observed at the coincidence of the two ferromagnetic resonances. In case of non-zero magnetic coupling, such a dynamic exchange will depend on the mutual precession of the magnetic moments in the layers. A difference in the linewidth of the resonance peaks is expected for the acoustic and optical regimes of precession. However, the interlayer coupling hybridizes the resonance responses of the layers and therefore can also change their linewidths. The interplay between the two mechanisms has never been considered before. In the present work, the joint influence of the hybridization and non-local damping on the linewidth has been studied in weakly coupled NiFe/CoFe/Cu/CoFe/MnIr spin-valve multilayers. It has been found that the dynamic exchange by spin currents is different in the optical and acoustic modes, and this difference is dependent on the interlayer coupling strength. In contrast to the acoustic precession mode, the dynamic exchange in the optical mode works as an additional damping source. A simulation in the framework of the Landau-Lifshitz-Gilbert formalism for two ferromagnetic layers coupled magnetically and by spin currents has been done to separate the effects of the non-local damping from the resonance modes hybridization. In our samples both mechanisms bring about linewidth changes of the same order of magnitude, but lead to a distinctly different angular behavior. The obtained results are relevant for a broad class of coupled magnetic multilayers with ballistic regime of the spin transport. 
A.A. Timopheev, Yu.G. Pogorelov, S. Cardoso, P.P. Freitas, G.N.   Kakazei and N.A. Sobolev
cond-mat.mes-hall