Cavity perturbation by superconducting films in microwave magnetic and electric fields

Cavity perturbation by superconducting films is treated in an unified way for the sample positions in both magnetic and electric microwave fields. The role of demagnetizing and depolarizing effects in the boundary conditions of the fields is analyzed. The general solutions for the complex frequency shift are specified for the samples having slab geometry and the field being parallel to the plane of the sample. For electromagnetically thick samples, the shifts for samples placed in the magnetic and electric fields are found to have the same magnitude and temperature dependence, while for thin films dramatic differences are obtained. The magnitude of the shift is reduced in the magnetic and increased by orders of magnitude in the electric field. A remarkable feature in the temperature dependence of the real frequency shift in the electric field is obtained. Experiments are performed on an ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ thin film, and all the predictions of the theory are confirmed. It is also shown that microwave cavity perturbation and ac susceptibility measurements in a dc magnetic field can be covered by the same theory. Their profoundly different temperature dependence can be accounted for by their different frequencies.