Frequency dependence of harmonic susceptibilities in high-temperature superconductors

The ac response of a superconducting slab immersed in an ac magnetic field together with a dc bias magnetic field has been investigated by numerically solving the flux creep equation, for the situation where the flux creep activation barrier U depends explicitly on current density j as U(j)=U₀/μ[(j_c/j)^μ-1]. The fundamental and harmonic ac susceptibilities of the superconducting slab as a function of temperature for different frequencies have been derived in a unified picture. The critical state model breaks down in explaining the frequency dependence of the fundamental and harmonic ac susceptibilities, however, our calculations, which take the relaxation effect into account, reproduce all the features exhibited by experiments.