A critical-state model capable of describing the experimentally observed secondary or fishtail peak in magnetization data for bulk high-$T_c$ superconductors is introduced. As suggested by a recent understanding of the fishtail effect, the field dependence of the critical current density is taken as a sum of two terms; one giving rise to a low-field magnetization peak and another being responsible for the fishtail peak. The model, which extends the Kim model by adding a Lorentzian term in $J_c\mathrm{}\left(B\right),$ allows analytical treatment. Expressions for internal flux-density profiles as well as the various branches of the magnetization loop are presented. It is shown that measured magnetization loops of ${\mathrm{NdBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ samples showing a very pronounced fishtail peak are well fitted by this model. Using our procedure, $J_c\mathrm{}\left(B\right)\mathrm{}$ can be determined without invoking the Bean model (with a constant $J_c$), and thus avoiding an inconsistency in the analysis.

• Received 14 January 1997

DOI:https://doi.org/10.1103/PhysRevB.56.11273