Modulated microwave surface impedance of superconducting films

We present details of an experimental method to measure the field modulated surface resistance (dR,/dH) of superconducting films accurately, which enables both field and temperature sweep experiments and is particularly useful for low-field or near T, measurements. The complex surface impedance Z,(H,T) =R,(H,T) + iX,(H, T) can also be simultaneously measured. This technique utilizes specially built circuitry to lock the microwave source to the cavity and keep the input power of the cavity constant, even as the resonant frequency or Q value of the cavity changes with changing temperature or applied field. With the above circuitry, we were able to measure (dR,/dH) directly rather than (dP/dH) as in some modulated microwave absorption measurements. With the high accuracy offered by the modulation technique and the high Q of the cavity, important information about the magnetic-field response of superconducting films, such as dynamics of vortices and low-field properties of weak links can be obtained. The technique can also be employed to measure any possible spontaneously induced internal fields in two-dimensional high-l”, superconductors.