Split-ring resonators for measuring microwave surface resistance of oxide superconductors

A cavity perturbation technique using split-ring resonators has been developed for measuring the surface resistance of metals in the frequency range 0.3-5.0 GHz. The system is designed particularly for measurements of films and crystals of high-T_c oxide superconductors. The small size of split-ring resonators in this frequency range makes them useful for measuring crystals with areas as small as 0.1 mm². The measurement geometry is favorable for the study of films because the sample screens its substrate from the microwave fields. The resonator temperature can be kept fixed at 4.2 or 1.2 K for sample temperatures as high as 120 K and this thermal isolation from the sample allows the use of a superconducting split-ring resonator. An unloaded Q of 1.2×10⁶ has been achieved with a superconducting resonator at 1.78 GHz and this makes it sensitive enough to detect surface resistances of the order of a few μΩ. This resonator has been used to measure the surface resistance (25 μΩ/⧠) of a 1-mm² crystal of Bi₂Sr₂CaCu₂O₈.