Surface impedance of YBa₂Cu₃O_7-x thin film grain boundary Josephson junctions: Evaluation of the I_{cR n} product

The temperature and the dc magnetic field dependence of the effective surface impedance Z_s of epitaxial YBa₂Cu₃O _7-x thin films on [001] tilt SrTiO₃ bicrystals with tilt angles of 36.8°and 24°have been investigated at 87 GHz. The effects of the grain boundaries become increasingly important with decreasing characteristic voltage I_cRn and increasing unit areal normal resistance R_nA. The boundaries can consistently be described with a resistively shunted Josephson transmission line model taking into account the effect of finite film thickness. Thermal or magnetic loading of the junction leads to additional losses, whereas the effective microwave penetration depth exhibits a specific extremal behavior. From the magnetic response of Z_s at 4.2 K, the junction lower critical fields as well as the values of I_cRn and R_nA can be deduced. The data agree well with dc transport measurements.