Harmonic generation by field modulation of the microwave complex impedance of high-T_c superconductors

The microwave transmission through thin superconducting films of BiSrCaCuO and YBaz.CuO was studied in the presence of an oscillating magnetic field, H₁ cos(2πf{hook}₀t), and a dc magnetic field, H₀. The oscillating field generates many even harmonics (kf{hook}₀, k=2, 4, 6,...) in the low frequency spectrum of the transmitted microwave for H₀=0. For H₀≠0 additional odd harmonics appear. We demonstrate the presence of irreversibilities in the harmonic signal and "memory" effect in the harmonic generation below a certain temperature, T_irr. The harmonic generation is explained by the non-linear response of the microwave transmission (through the non-linear response of the complex resistivity) to a periodic applied field. Following Portis et al., we show the dependence of the complex resistivity on the magnitude of the applied field and suggest a simple model. The model can account for (a) the harmonic generation, (b) the interesting oscillatory dependence of the even harmonic signal on H₀ and (c) the disappearance of all harmonics except the first harmonic for H₀≫H₁. The different onset temperatures for (a) the harmonic generation and (b) the change in the microwave transmittance may suggest two superconducting temperatures associated with the intergrain region, T_cJ, and the grains themselves, T_cg, as suggested by theoretical models for granular superconductors. For our BiSrCaCuO thin film we find T_cg=(102±2)K, and T_cJ=(92±3)K.