Campbell Penetration Depth of a Superconductor in the Critical State

The magnetic penetration depth $\lambda(T,H,j)$ was measured in the presence of a slowly relaxing supercurrent, $j$. In single crystal $\mathrm{Bi_2Sr_2CaCu_2O_8}$ below approximately 25 K, $\lambda(T,H,j)$ 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.