Ferromagnetic resonance frequency increase and resonance line broadening of a ferromagnetic Fe―Co―Hf―N film with in-plane uniaxial anisotropy by high-frequency field perturbation

Soft ferromagnetic Fe-Co-Hf-N films, produced by reactive r.f. magnetron sputtering, are useful to study the ferromagnetic resonance (FMR) by means of frequency domain permeability measurements up to the GHz range. Films with the composition Fe33Co43Hf10N14 exhibit a saturation polarisation Js of around 1.35 T. They are consequently considered as being uniformly magnetised due to an in-plane uniaxial anisotropy of approximately μ0Hu=4.5 m T after annealing them, e.g., at 400 °C in a static magnetic field for 1 h. Being exposed to a high-frequency field, the precession of magnetic moments leads to a marked frequency-dependent permeability with a sharp Lorentzian shaped imaginary part at around 2.33 GHz (natural resonance peak), which is in a very good agreement with the modified Landau―Lifschitz―Gilbert (LLG) differential equation. A slightly increased FMR frequency and a clear increase in the resonance line broadening due to an increase of the exciting high-frequency power (1-25.1 mW), considered as an additional perturbation of the precessing system of magnetic moments, could be discovered. By solving the homogenous LLG differential equation with respect to the in-plane uniaxial anisotropy, it was revealed that the high-frequency field perturbation impacts the resonance peak position fFMR and resonance line broadening ΔfFMR characterised by a completed damping parameter α=αeff+Δα. Adapted from this result, the increase in fFMR and decrease in lifetime of the excited level of magnetic moments associated with ΔfFMR, similar to a spin-½ particle in a static magnetic field, was theoretically elaborated as well as compared with experimental data.