How to Retrieve More Information on Magnetic Films From Microwave Permeability Measurements

The microwave permeability of soft thin films is a useful quantity for the design of fast, high-frequency systems. A number of setups now provide reliable permeability measurements. It is quite common to determine the saturation magnetization from the permeability measurements by using either a generalization of Snoek's law, or a curve fit with the Landau-Lifschitz model. This is a good way of verifying the consistency of the microwave measurements, since the saturation magnetization can be obtained by other means. However, in certain cases the permeability spectra reveal some features that cannot be accounted for by the uniform Landau-Lifschitz model, due to skin effect, heterogeneities, spinwave excitations, etc. The present article demonstrates that a better way to obtain reliable saturation magnetization values from permeability spectra is to use quantities based on the integral of the imaginary part of the measured permeability. Such quantities can also be used to determine the standard deviation of the magnetization orientation within the sample. These theoretical results are illustrated on CoZr thin films of various thicknesses, as well as on samples with a large built-in dispersion of the magnetization orientation.