Permeability Measurement up to 30 GHz of a Magnetically Isotropic Thin Film Using a Short-Circuited Coaxial Line

In this study, the high frequency permeability (  ) and ferromagnetic resonance(FMR) phenomena of a thin film with a strong perpendicular magnetic anisotropy and in-plane magnetically isotropic properties was measured using the short-circuited coaxial line technique; the analyzed sample had a toroidal shape. A field method was used for the background correction, where a strong magnetic bias field was applied and removed. However, when using a short-circuited coaxial line, the  =1 condition cannot be achieved beyond a few ten GHz frequencies, whereas ferromagnetic resonance (denoted as FMR2) occurred because of the insufficient bias field. This resonance was compensated using the Landau-Lifshitz-Gilbert (LLG) equation, and the net  - f properties without the bias field (denoted as FMR1) up to 30 GHz successfully extracted. Finally, a good agreement between the experimental results and the calculations based on the assumption of a magnetic multi-domain structure in