Temperature-, magnetic-field-, and power-dependent microwave resistance of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

We have measured the microwave resistance of sintered ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ at 9 GHz as a function of temperature, magnetic field, and microwave power. We observe a rapid change in slope with temperature about 1 K below the onset of the superconducting transition. There is a strong magnetic field dependence only below this slope-change temperature. This behavior is similar to that seen in low-frequency resistance measurements. We also observe an increase in microwave resistance with microwave power for temperatures below the superconducting onset temperature. We estimate that the microwave currents may be large enough to give such an effect due to weak-link structures in this material. We show that the power dependence is not due to bulk sample heating, but we cannot rule out self-heating on a microscopic scale.