  We have studied the influence of the patterning procedure on the critical
current density of high-$T_c$ YBa$_2$Cu$_3$O$_{7-\delta}$ thin rings using the
nonlinear ac susceptibility method. At no applied dc magnetic field we have
found that laser ablation degrades strongly the critical current density
whereas ion beam etching has only a weak influence on it. From the measurements
at different frequencies and dc magnetic fields we analyzed the influence of
flux creep and obtained the field dependence of the flux creep exponent. Our
data reconfirm the recently observed scaling relation for the nonlinear
susceptibility response of type-II superconductors.
