Effect of biquadratic coupling and in-plane anisotropy on the resonance modes of a trilayer system

Ferromagnetic resonance modes are investigated for a trilayer system consisting of two ferromagnetic films interacting through a nonmagnetic interlayer. Included in the model are the bilinear J₁ and biquadratic J₂ couplings and in-plane uniaxial magnetocrystalline anisotropies with anisotropy axis directions in the two layers making a {δ} angle. An analytical expression for the mode intensity is derived. The saturation (Hₛₐₜ) and critical (Hcrit) fields, the resonant frequency, and the mode intensity are discussed as functions of J₁, J₂, and {δ}. For a given positive J₁, an additional J₂(J₂<0) will lead to an increase (a decrease) of the optical (acoustic) mode intensity. For fixed J₁<0, and if the magnetizations are parallel (H>Hₛₐₜ) only the acoustic mode will appear with constant mode position and intensity for all J₂ values, making it difficult to detect any additional biquadratic coupling. On the other hand, and for the same parameters, if the magnetizations are antiparallel (H<Hcrit), then two modes are predicted; as |J₂| increases the intensity of the acoustic (optical) mode will increase (decrease), while the resonant frequency of both modes decrease.