Experimental test of theories describing the magnetic ac susceptibility of differently shaped superconducting films: Rectangles, squares, disks, and rings patterned fromYBa2Cu3O7−δfilms

Abstract

The magnetic ac response of rectangles, squares, disks, and rings patterned from ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ films (typical thickness 200 nm) was determined as a function of temperature for the case of the exciting external magnetic ac field being directed perpendicular to the film plane. For this geometry strong demagnetizing effects are expected and corresponding theories describing the resulting real $({\ensuremath{\chi}}^{\ensuremath{'}})$ and imaginary $({\ensuremath{\chi}}^{\ensuremath{''}})$ parts of the magnetic susceptibility $\ensuremath{\chi}$ on the basis of critical state models have only recently been developed. Plotting ${\ensuremath{\chi}}^{\ensuremath{''}}$ versus ${\ensuremath{\chi}}^{\ensuremath{'}}$ turns out to be useful in order to test these theories with respect to different sample shapes without invoking a specific temperature dependence of the critical current density ${J}_{c}(T)$. In this way, the following results were found. The shape dependent differences of the susceptibility are only small (of the order of %) with the smallest difference between squares and disks as predicted by theory. The recent theories yield an improved description of the experimental $\ensuremath{\chi}$ data as compared to a conventional Bean model neglecting demagnetization effects. At temperatures just below the superconducting transition, however, these theories based on purely hysteretic losses fail to be quantitative. A systematic change of symmetry of the ${\ensuremath{\chi}}^{\ensuremath{''}}$ versus ${\ensuremath{\chi}}^{\ensuremath{'}}$ curves is observed if rings of decreasing widths are patterned from a disk. For a diameter to width ratio $D/wg20$ the experimental susceptibilities, including the temperature dependence of the third harmonic, approach the behavior as calculated for an ideal thin narrow ring. This result allows a quantitative determination of ${J}_{c}(T)$ on such rings as is demonstrated by additional dc magnetization measurements using a SQUID magnetometer.