Microwave transmission and harmonic generation in granular high-Tcsuperconducting films: Evidence for viscous flux motion and weak links

We have studied the microwave transmission τ through thin superconducting films of Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O in the presence of a dc magnetic field ${\mathrm{H}}_0$ and an alternating magnetic field, ${\mathrm{H}}_1$cos2π${\mathrm{f}}_0$t. The alternating field generates many harmonics due to the nonlinear response of the complex resistivity. The microwave transmission with ${\mathbf{H}}_0$ in the plane of the film depends on the orientation Φ of ${\mathbf{H}}_0$ with respect to the microwave electric field. We found experimentally that the field-dependent part of the transmission behaves like δ${\mathrm{\tau }}_{\mathrm{f}}$∝|${\mathrm{H}}_0$sinΦ|. This indicates a macroscopic Lorentz force and strongly suggests that the complex resistivity in the magnetic field is dominated by a viscous-flux-motion dissipation mechanism. We demonstrate a simple model for the harmonic generation based on viscous fluxon motion. A comparison of the experiment with the model allows an estimate of the viscosity coefficient η for the fluxons in the direction of the c axis to be η=( 2–4)×${10}^{\mathrm{-}9}$ cgs units for Y-Ba-Cu-O film at T=70 K. Theoretical models suggest that the magnitude of η is appropriate to weakly pinned Abrikosov fluxons. The dc transport properties of superconducting films containing internal Josephson junctions are strongly affected by microwave irradiation and serve, therefore, as a diagnostic tool to detect the presence of “weak links.” Higher-order harmonics can be generated in all types of studied films independent of the presence or absence of weak links. However, in the presence of weak links, the onset temperature for the harmonic generation ${\mathrm{T}}_{\mathrm{c}}^{\prime }$ is lower than the onset temperature for the change in the microwave transmission, ${\mathrm{T}}_{\mathrm{c}}$. A simple model based on the granularity of the film can explain these observations.