Calculation of rf magnetic permeability of nearly ferroelectric superconductors in a parallel field

The complex rf magnetic permeability μ˜=μ′-jμ″ of nearly ferroelectric superconductors in the Meissner-like response is theoretically investigated based on the electrodynamics of the nearly ferroelectric superconductors. The complex rf magnetic permeability is calculated and analyzed for a superconducting slab in a parallel applied magnetic field. It is found that the peak of the loss curve (curve of imaginary part, μ″) occurs at some critical thickness, which is frequency-dependent, decreasing as the frequency is increased. In addition, the magnitude in peak is strongly depressed as the frequency is increased. This critical thickness is also dependent on the damping factor appearing in the dielectric function, increasing with decreasing the damping coefficient. As for the frequency-dependent μ″ we find that it increases with increasing the frequency, showing a strong dispersion in the imaginary part of the complex permeability.