Dependence of the ferromagnetic resonance modes on the coupling strength in exchange-coupled trilayer structures

The dependence of the dispersion relation and the magnetization on the exchange coupling strength was calculated for a system consisting of two ferromagnetic layers exchange-coupled through a nonmagnetic spacer layer. The magnetic layers are characterized by both uniaxial and cubic magnetocrystalline anisotropies. A minimization procedure was developed which allows the resonance modes to be obtained for any magnetic field orientation and strength, as well as for any exchange coupling strength. If the antiparallel coupled film is unsaturated at resonance, the dispersion relation for both acoustic and optic modes could be rather complex, especially when the field is applied in the plane of the film.