Spontaneous magnetization in multi-junction superconducting π rings when the junctions’ critical currents are not equal

Abstract

We theoretically investigate the spontaneous magnetization in double-junction and multi-junction π rings when the junctions' superconducting critical currents are not equal. The analytical solutions for the relations between the total magnetic flux and the external magnetic flux x , the free energy f and the circulating current i, and the spontaneous magnetization conditions of the double-junction π rings are deduced. For the multi-junction π rings consisting of more than two junctions, mathematical computation is needed to analyse thex and f -i relations.In the conditions where the absolute critical current value of each junction is equal and there are hystereses on thex characteristic curve, the system has spontaneous magnetization solutions. However, the non-spontaneous magnetization state with zero circulating current is a metastable state with local minimum free energy; therefore, the multi-junction π ring system probably would not spontaneously magnetize.