Vortex pinning and modulated microwave absorption in thin HTSC films

We present the results of the experimental and theoretical investigation of the modulated microwave absorptions (MMWA) in the Bi2Sr2CaCu2O8 thin film with columnar defects. The dependence of the MMWA hysteresis loop on the applied magnetic field and the modulation amplitude was studied. It is found that the hysteresis has unusual properties, in particular (i) the amplitude falls down when the magnetic field increases whereas the critical current density is nearly constant; (ii) the hysteresis changes the sign when the modulation amplitude increases. These features can be explained if one takes into account that in thin superconducting films (d ≤ λ) each vortex interacts with a limited number of pinning centers with a different coordination (gradient). We develop the theoretical model of the MMWA hysteresis in a thin superconductor with regard to these peculiarities. Five possible types of pinning centers are considered. It is shown that the vortices pinned on the centers of different type can make opposite contributions to MMWA. Good agreement between calculated theoretical curves and experimental data has been obtained