ANGULAR-DEPENDENCE OF FERROMAGNETIC-RESONANCE IN EXCHANGE-COUPLED CO RU/CO TRILAYER STRUCTURES/

The angular dependence of the dispersion relation is calculated for a system consisting of two ferromagnetic layers exchange coupled through a nonmagnetic spacer layer. Special attention has been focused on the resonance behavior in the unsaturated state of an antiparallel couple d system. The variation of both the acoustic mode and the optic mode w ith the external-field orientation is significantly modified from that in a noncoupled system and can be used to accurately evaluate the int erlayer exchange-coupling strength A(theta12) as a function of the ang le between the magnetization vectors in the two magnetic layers. Based on the exchange-coupled resonance theory, the angular dependence of f erromagnetic resonance (FMR) measurements has been performed on severa l series of symmetrical and asymmetrical Co/Ru/Co structures at X-band and K-band frequencies with the temperature ranging from 10 to 300 K. Only the bilinear exchange-coupling coefficient A12 was observed in t hese systems. The biquadratic contribution is more than two orders of magnitude smaller than A12. For the symmetrical Co(32 angstrom)/Ru(tRu )/CO(32 angstrom) series, oscillatory interlayer exchange coupling was observed as a function of the Ru thickness t(Ru). The oscillation per iod (approximately 12 angstrom) and phase do not vary with temperature . However, the oscillation amplitude is significantly enhanced at low temperatures, following roughly the relationship A12 is-proportional-t o (T/T0)/sinh(T/T0) predicted by the theoretical models. For the asymm etrical Co(32 angstrom)/Ru(t(Ru))/CO(t2) structures, variation of the exchange coupling strength as a function of t2 has also been observed for several series within which t(Ru) is constant. The variation lengt h DELTAt2 between maximum and minimum coupling strength is rather larg e (about 10 angstrom) and consistent from series to series.