Phase coherence in the hysteretic magnetic behavior of parallel Josephson-junction arrays

We report on the hysteretic field-dependent critical currents of large inductance arrays with up to ten ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ grain-boundary junctions in parallel. A peak in the critical current, roughly equal to its initial zero-field value, is observed after each reversal of the field sweep. This behavior indicates that the junction phases become equal modulo 2π (self-organized phase coherence) as the system relaxes away from the critical state. The primary features can be modeled using a Frenkel-Kontorova model generalized to include global interactions due to mutual inductance.