Excess conductivity and magnetoresistance analysis for (BSF)_x/(Bi, Pb)-2223 composite

This study examined the impact of adding hard ferrite Ba_0.5Sr_0.5Fe₁₂O₁₉ (BSF) nanoparticles to the Bi_1.8Pb_0.4Sr₂Ca₂Cu_3.2O_10+δ (Bi, Pb)-2223) superconductor phase. The investigation specifically focused on evaluating the critical current density, fluctuation-induced conductivity, and magnetoresistance of nano-(BSF)_x/(Bi, Pb)-2223 composite, where 0.00 ≤ x ≤ 0.20 wt.%. The results revealed that the critical current density, J_c, increased with the addition of nano-(BSF) up to x = 0.04 wt.%, reaching a value of 441.20 A/cm². The Aslamazov and Larkin (A–L) approach has been evaluated the fluctuation-induced conductivity. Several superconducting parameters, including coherence length ζ_c(0), effective layer thickness d, penetration depth λ_pd(0), and Fermi energy \({E}_{F}\) $E_F$ showed improvement as the concentration of nano-(BSF) increased up to x = 0.04 wt.%. In addition to Ginzburg–Landau critical parameters, such as the thermodynamic critical field B_c(0), lower critical magnetic field B_c1(0), upper critical magnetic field B_c2(0), and critical current density J_c(0) demonstrated an increase up to x = 0.04 wt.%, followed by a decrease for higher concentrations. The magnetoresistance measurements were performed at various applied DC magnetic fields, with values ranging from 0.29 to 4.44 kG, and were analyzed using the thermally activated flux creep (TAFC) and Ambegaokar–Halperin (AH) models. The calculated flux pinning energy (U) increased with the addition of nano-(BSF) up to x = 0.04 wt.% and then decreased for x > 0.04 wt.%. Furthermore, the transition width (ΔT), was observed to increase as the applied magnetic field values increased. Moreover, the addition of nano-(BSF) increased the field-independent critical current density, J_c,0(0), up to x = 0.04 wt.%, after which it decreased for higher concentrations.