Comparison of different approaches to modelling the fishtail shape in RE-123 bulk superconductors

We analyze and compare properties of different models proposed so far for modelling the shapes of F(B) and J(B) curves measured in RE-Ba₂Cu₃O_7-δ (RE-123, RE = rare earth) samples. The formulas following from the discussed models allow for a direct fit of experimental data in various representations. The models divide in two categories, according to the pinning potential used, namely the power-law and the logarithmic potential. We show that none of the pinning regimes proposed for low-T_c superconductors accounts for the fishtail effect (FE) observed in high-T_c materials. The conventional expressions allow a good fit of high-T_c experimental data, however, the resulting fitting parameters are much higher than those predicted by the theory. The logarithmic pinning potential justified in high-T_c materials by both magnetic and transport experiments leads to F(B) and J(B) functions that decay exponentially at high fields. The fit of experiments on a wide range of RE-123 samples, using only one free parameter, is nearly perfect. The role of free parameters is discussed in all the models.