Campbell Penetration Depth of a Superconductor in the Critical State

The magnetic penetration depth $\ensuremath{\lambda}(T,H,j)$ was measured in the presence of a slowly relaxing supercurrent j. In single crystal ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}$ below approximately 25 K, $\ensuremath{\lambda}(T,H,j)$ is strongly hysteretic. We propose that the irreversibility arises from a shift of the vortex position within its pinning well as j changes. The Campbell length depends upon the ratio ${j/j}_{c}$ where ${j}_{c}$ is the critical current defined through the Labusch parameter. Similar effects were observed in other cuprates and in an organic superconductor.