Phenomenological model for history effects and metastability in weakly pinned superconductors

We present a phenomenological model to describe features in the hysteretic magnetic response of weak pinning superconductors across the peak effect region. It accounts for the experimentally observed history dependent behavior of critical current density and the metastability of the vortex state prior to and across the peak effect region of superconducting systems such as ${\mathrm{NbSe}}_2,$ ${\mathrm{CeRu}}_2,$ and ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7.$ Moreover, this model reduces to Bean’s critical state model as a limiting case.