Effect of flux flow on microwave losses inYBa2Cu3O7−xsuperconducting films

Abstract

Microwave losses in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}x}$ (YBCO) films carrying overcritical currents were measured at several temperatures between 74 and 85 K, and found to be in good agreement with the predictions of the vortex dynamics model for the magnetic flux flow. For the measurements a 2.3-GHz microstrip resonator made of an epitaxial double-sided YBCO film on ${\mathrm{CeO}}_{2}$ buffered sapphire was equipped with a Cu coil, which is usually used for ac (1.1 kHz) inductive measurements of the critical current density ${J}_{C}.$ The ac current density induced in the film, ${J}_{\mathrm{ind}}$ controlled the vortex flow, while the microwave surface impedance ${(Z}_{S}{=R}_{S}{+iX}_{S})$ of the film was measured as a function of ${J}_{\mathrm{ind}}.$ Both ${R}_{S}$ and ${X}_{S}$ remained fairly constant for ${J}_{\mathrm{ind}}<{J}_{C},$ indicating a weak contribution of the thermally activated flux flow to the microwave loss. The loss revealed a sharp increase at ${J}_{\mathrm{ind}}\ensuremath{\approx}{J}_{C}.$ In the flux flow regime, ${J}_{\mathrm{ind}}>~{2J}_{C},$ both $\ensuremath{\Delta}{R}_{S}$ and $\ensuremath{\Delta}{X}_{S}$ were linear with ${J}_{\mathrm{ind}}.$ This behavior of the microwave losses agrees well with the dependence $\ensuremath{\Delta}{Z}_{S}={\ensuremath{\rho}}_{f}/2{\ensuremath{\lambda}}_{L}$ predicted by the vortex dynamics model $({\ensuremath{\lambda}}_{L}$ is the London penetration depth and ${\ensuremath{\rho}}_{f}$ is the complex flux flow resistivity of type-II superconductors). The ratio $\ensuremath{\Delta}{X}_{S}/\ensuremath{\Delta}{R}_{S}$ in the flux flow regime was independent of ${J}_{\mathrm{ind}}$ and increased with decreasing temperature from 2.7 at 85 K to 7.9 at 74 K, in agreement with the model.