Investigation of Magnetic Coupling by Ferromagnetic Resonance

Abstract

Ferromagnetic Resonance (FMR) is a powerful method for study the magnetic coupling in multilayers. In the present work, a trilayer system is assumed to be characterized by the bilinear J 1 , biquadratic J 2 coupling, and in-plane uniaxial magneto-crystalline anisotropies with anisotropy axis directions in the two layers making a δ angle. A detailed discussion of the effect of J 2 and δ on the mode characteristics (resonant frequency and the mode intensity) will be given. In certain situations, (for instance when J 1 < 0, and the magnetizations are parallel) 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. Also, it will be shown that, for small J 2 and δ values, the effect of the misalignment of the easy axes in the two layers, δ, on the FMR modes can be similar to that of J 2 , making it hard to distinguish the effect of δ from that of the biquadratic coupling strength J 2 from an FMR experiment. A relation establishing the equivalence between J 2 and δ in the small (J 2 , δ) region, is derived. Thus precautions have to be taken to avoid confusion which may lead to incorrect interpretations of the FMR experimental data and consequently to erroneous values of J 1 and J 2 . All these effects will be described and discussed.