Ferromagnetic Resonance Simulation of Mn-Ir/Fe-Si Exchange-Coupled Film on Basis of LLG Equation Taking Exchange-Stiffness Dispersion Model into Account

The high-frequency permeability of Mn80Ir20 (at.%)/Fe89Si11 (at.%) exchange-coupled films for microwave applications was evaluated. For this purpose, a micromagnetic simulator based on the LLG equation was introduced. When the complex permeability of exchange-coupled and non-exchange-coupled films with the same Fe-Si thickness of 100 nm was compared in the experimental results, parameter Δfr/fr of the exchange-biased Fe-Si film was larger than that of a single Fe-Si film with uniaxial magnetic anisotropy. This is where fr is the ferromagnetic resonance (FMR) frequency and Δfr is the frequency bandwidth of the FMR half line-width, i.e., where Δfr/fr corresponds to the inverse of the FMR Q factor. An exchange-stiffness dispersion model was introduced into the LLG simulation to investigate the behavior of FMR in the exchange-biased film. We found that the exchange-stiffness dispersion in Fe-Si gives rise to a distribution of exchange bias in the thickness direction, and that such spatial distribution increases parameter Δfr/fr. The authors consider that the exchange-stiffness in polycrystalline Fe-Si film is not constant and has a Gaussian distribution, because distributed exchange-stiffness occurs with lattice defects and/or grain boundaries. When average stiffness constant A was 1.7 μerg/cm and its standard deviation σA was 0.83 μerg/cm, the calculated results agreed with those from experiments.