Thin superconducting disk with field-dependent critical current: Magnetization and ac susceptibilities

Magnetization hysteresis loops and the ac susceptibility chi=chi'+i chi" of a superconducting thin disk are calculated in the critical-state model ass uming a field-dependent critical current density J(c)(B). The results are o btained by solving numerically the set of coupled integral equations for th e Bur and current distributions [Phys. Rev. B 60, 13 112 (1999)] for a disk placed in a perpendicular applied field B-a. From the magnetization curves the range of fields where the vertical width of the loop Delta M(B-a) rela tes directly to J(c)(B-a) is determined. The susceptibility is analyzed in the limits of small and large ac-field amplitudes B-am, and also as a param etric relation chi"(chi') Comparing our results with experimental data for chi"(chi') shows that by taking the B dependence of J(c) into account the a greement Improves dramatically, in particular at small \chi'\ (large field amplitudes). We show that the asymptotic behavior for large B-am changes fr om chi' proportional to B-am(-3/2) and chi" proportional to B-am(-1) for th e Bean model, to chi' proportional to B-am(-3) and chi" proportional to B-a m(-2) for J(c) decreasing with \B\ as \B\(-1) or faster. For small B-am the behavior can always be described by an effective Bean model with a renorma lized J(c). We also find that in the chi"(chi') plot the peak of chi" incre ases in magnitude and shifts towards chi' = 0 when J(c) decreases with \B\. This allows an easy experimental discrimination between a Bean model behav ior, one with J(c)(B), and one where flux creep is an ingredient.