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 $J_1$ and biquadratic $J_2$ 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 ${(H}_{\mathrm{sat}})$ and critical ${(H}_{\mathrm{crit}})$ fields, the resonant frequency, and the mode intensity are discussed as functions of $J_1,$ $J_2,$ and δ. For a given positive $J_1,$ an additional $J_2{(J}_2<0)$ will lead to an increase (a decrease) of the optical (acoustic) mode intensity. For fixed $J_1<0,$ and if the magnetizations are parallel $(H>\mathrm{}{H}_{\mathrm{sat}})$ only the acoustic mode will appear with constant mode position and intensity for all $J_2$ values, making it difficult to detect any additional biquadratic coupling. On the other hand, and for the same parameters, if the magnetizations are antiparallel $(H<\mathrm{}{H}_{\mathrm{crit}}),$ then two modes are predicted; as $|J_2|$ increases the intensity of the acoustic (optical) mode will increase (decrease), while the resonant frequency of both modes decrease.

• Received 18 July 2001

DOI:https://doi.org/10.1103/PhysRevB.65.104422