Extraction of complex permeability on coplanar transmission line by measuring scattering parameters up to 20 GHz

The purpose of this study is to extract complex permeability of magnetic thin films such as CoZrNb and CoPdAlO from their complex scattering parameters measured for up to 20 GHz on a coplanar transmission line using a broad band automated technique. Only samples shorter than the half wavelength show continuous frequency profiles of complex permeability. The values of FMR frequencies for CoZrNb and CoPdAlO magnetic thin films loaded on coplanar waveguide (CPW) transmission lines are 4.2 and 7 GHz, respectively, which resulted from a shape anisotropy effect of magnetic field distributed only along a center line of CPW transmission line. By subtracting as-extracted initial permeability of CPW transmission line without a magnetic film from as-extracted initial permeability of a magnetic thin film loaded on a CPW line, normal shapes of complex permeability spectra for a magnetic film on a CPW line are obtained. The value of the initial permeability after subtraction is about 30 times lower than that of the initial permeability calculated by using LLG equation, showing a future need of absolute value calibration.