The field dependence of the microwave vortex pinning parameters: Evidence for collective pinning effects and unconventional frictional damping

We have investigated the microwave surface impedance Z = R + iX of two high-quality HTS thin-film samples (YBCO and TI-2212) at 5 GHz in a dc magnetic field up to 1 T applied parallel to the crystallographic c-axis. From the changes of R and X in magnetic fields we have extracted the field dependence of the pinning parameters κ, η and f for 21 K ≤ T ≤ 55 K. For both samples we find that after a weak field dependence at low fields (<0.1 T), κ increases as B at higher fields. These results suggest that collective pinning influences the pinning parameter κ at microwave frequencies. The field behaviour of η (B) is found to be different between the two samples. Neither the Bardeen-Stephen model nor a d-wave approach can explain the field dependence of η. The depinning frequency f is always greater than the operating frequency at ∼5 GHz so that the vortices show pinned behaviour at the operating frequency.