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 YBa₂{Cu}₃O_7-δ sample.