A two dimensional analytical model for the study of ferromagnetic resonance responses of single and multilayer films

Abstract

An advanced analytical formulation to model the response of coplanar and stripline based broadband ferromagnetic resonance (FMR) for single and multilayer ferromagnetic films is presented. Several numerical examples are provided implementing the formulation. The model accounts for exchange interactions as well as exchange boundary conditions at the film surfaces and the film interfaces (in the case of multilayer films). The solutions to the Landau-Lifshitz equation and relevant Maxwell's equations are conducted in Fourier space and are transformed back to real space as required to ensure computational efficiency and to avoid length scale incompatibility due to the experiment geometry. This work presents several numerical examples pertaining to the effect of waveguide geometry and microwave eddy current shielding on the shape of coplanar and stripline FMR responses of single-layer ferromagnetic films. Additionally, the effect of microwave eddy current shielding and distance (dielectric spacer thickness) of the film from the transducer on the stripline FMR responses, dynamic magnetization, magnetic field strength, and precession angle for multilayer film samples is discussed.