Microwave properties of thin films in linear and nonlinear regime in a dc magnetic field

We report an experimental and theoretical study of the linear and nonlinear microwave impedance of thin (Formula presented) films in a dc magnetic field of different orientations. The measurements were done using the parallel-plate resonator technique at 5.7 GHz, (Formula presented) and for (Formula presented) We demonstrate that the contributions to the microwave response from nonlinearity and from the dc magnetic field are almost additive for our films (excluding very low microwave power). The increase of microwave current simply leads to a parallel shift of the dc magnetic field dependences of the surface impedance. This result shows that widely discussed nonlinear mechanisms related to vortices produced by the dc field are not relevant for our experimental conditions. The theoretical analysis of other nonlinear mechanisms points out that the most probable source of nonlinearity is vortices produced by microwave currents in weak links. A qualitative description of the experimentally observed nonlinear microwave response is provided by the critical-state Bean model, which was modified for thin films.