I_c hysteresis in polycrystalline high T_c superconductors: Double-valued I_c curves with identically magnetized grains, final fields and temperature: An effect of edge return fields

In the analysis of I_c hysteresis phenomena, many researchers have assumed that the return field H_r(H_a,T) obeys a linear relationship, H_r = CM_g(H_a,T) where C is a parameter of the specimen which may depend on T, and M_g is the magnetization of the grains. Kwasnitza and Widmer [IEEE Trans. Magn. 27 (1991) 1202] measured both I_c and M_g at a chosen temperature after various magnetic field cycles terminating at the same chosen final field H_f. They found I_c to be an intricate double-valued function of M_g and that the two different curves traced by I _c versus M_g changed their structure as a function of H_f. We show that these results indicate unambiguously that the configurations of the induced currents circulating along the periphery of the grains exert the main influence on H_r. We apply simple models to calculate the return field along the edges of grains in the form of thin ribbons and thin disks containing two concentric zones of countercirculating induced persistent currents of density J_cg independent of H, and the magnetic moments they generate. Then exploiting critical state expressions for I_c and the Evetts-Glowacki superposition concept we reproduce all the observations of Kwasnitza and Widmer, and make predictions on the evolution of the double-valued curves of I_c(H_f) versus M _g(H_f) as a function of H_f over a wide range extending from zero to high fields.