Third harmonics of the AC magnetic susceptibility: a method for the study of flux dynamics in high temperature superconductors

The temperature dependence of the 1st and 3rd harmonics (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi^{\prime ,\prime\prime}_{1,3}$\end{document}) of the AC magnetic susceptibility has been measured on melt grown YBCO samples for different frequencies and amplitudes of the AC magnetic field and intensity of a contemporaneously applied DC field. With the help of critical state models and of numerical simulations [22], we have devised a novel method, based on the combined analysis of the 1st and the 3rd harmonics (specifically on the comparison between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi"_1$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi'_3$\end{document}), that allows to distinguish different temperature ranges dominated by the different dissipative magnetic flux regimes. In particular, we identified three principal “zones” in the temperature dependence of the real part of the 3rd harmonic: the “zone 1”, in the temperature range below the peak of the imaginary part of the 1st harmonic, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T_{p}(\chi"_1)$\end{document}, and the “zone 2”, characterized by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi'_3$\end{document} negative values in a temperature region just above \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T_{p}(\chi"_1)$\end{document}, both dominated by the creep regime; the zone 3, just below Tc, in which we revealed the presence of Thermally Assisted Flux Flow (TAFF). By the identification of these “zones”, an estimation of the value of the pinning potential can be obtained.