Theoretical study of resonance modes of coupled thin films in the rigid layer model

Abstract

An investigation of the ferromagnetic resonance (FMR) modes is done for a two coupled ferromagnetic film system in the framework of the rigid layer model. In this case, one of the layers (the driver layer) has a strong in-plane anisotropy compared to the coupling strength and to in-plane anisotropy of the other layer (the sensor). The curves of dispersion relation, the resonant frequency f, and the mode intensity I vs applied field H are discussed as a function of the bilinear ${J}_{1}$ and biquadratic ${J}_{2}$ coupling terms, and of the angle \ensuremath{\delta} between the in-plane uniaxial anisotropy easy axis directions in the two layers. Depending on the coupling strength and \ensuremath{\delta} values and the anisotropy of the sensor layer, as the applied field is increased, the sensor layer magnetization may smoothly rotate or suddenly switch from the antiparallel configuration to the saturated state. In the latter case, a discontinuity is observed in the mode position as well as in the FMR intensity. The discontinuities are more important for the optical than for the acoustic modes. Moreover, the coupling strengths ${(J}_{1}{,J}_{2})$ affect the mode intensity but, practically, not the position of the acoustic mode; while for the optical mode, the effect of these parameters on the f vs H and I vs H curves is more apparent. Also, for all \ensuremath{\delta} angles (other than 0 and 90\ifmmode^\circ\else\textdegree\fi{}), no effect of \ensuremath{\delta} is observed on the position and intensity of the high-frequency mode but \ensuremath{\delta} does affect the lower-frequency mode position.