Universal behavior of harmonic susceptibilities in type-II superconductors

Simple analytical expressions are derived for the harmonic susceptibilities in type-II superconductors, using a critical-state model with a general dependence of the critical current upon magnetic field. It is shown that the harmonic susceptibilities are determined by a single parameter, δ, which is a function of the full penetration field of the sample and the applied alternating field. This implies that measurements of harmonic susceptibilities as a function of any experimental variable, in any irreversible type-II superconductor, can be reduced to universal curves that describe the harmonic susceptibilities versus δ. In particular, the maximum values that can be attained by the harmonic susceptibilities are universal constants for irreversible type-II superconductors. Fitting of experimental data to the universal curves provides models for the dependence of the critical current density upon field and temperature. This is demonstrated using data of the third-harmonic response measured in a sintered YBa2Cu3O7-δ sample.