The contribution of the intergrain currents to the low field hysteresis cycle of granular superconductors and the connection with the micro- and macrostructures

Abstract

Abstract Granular superconductors exhibit a low field hysteresis cycle ( H H c1,g , the first critical field of the grains) which is related to the weak link network and to the macroscopic shape of the sample. We report measurements and calculations of the relationship between the low field cycle, the magnetic critical current density J wl,mag of the weak links, the radius R of the sample, the average radius r g of the grains and the normal state resistivity ϱ of the weak link network. It is found that the intergrain current J wl,mag is related to the low H cycle by a relation of the form 15( M + − M − )/( Rf ( x )), with f ( x )=2〈 λ L / r g 〉 in most experimental conditions. The ratio 2〈λ L / r g 〉 is related to the slopes of the low field magnetization cycle M ( H ) in the linear and reversible region and in the irreversible region curve in the linear and reversible regions. We show that for thick samples ( R ⪢ R 0 ≈50 μm typically) J wl,mag varies approximately as 1/( Rr g ), whereas for thin samples ( R ≤ R 0 ) it approaches a maximum limit inversely proportional to the resistivity ϱ of the Josephson junctions.