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

摘要

The high-frequency permeability of Mn_(80)Ir_(20) (at. percent)/Fe_(89)Si_(11) (at. percent) 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 DELTA f_r/f_r of the exchange-biased Fe-Si film was larger than that of a single Fe-Si film with uniaxial magnetic anisotropy. This is where f_r is the ferromagnetic resonance (FMR) frequency and DELTA f_r is the frequency bandwidth of the FMR half line-width, i.e., where DELTA f_r/f_r 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 DELTA f_r/f_r. 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 mu erg/cm and its standard deviation sigma_A was 0.83 mu erg/cm, the calculated results agreed with those from experiments.