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. 
R. Prozorov, R. W. Giannetta, N. Kameda, T. Tamegai, J. A. Schlueter,   P. Fournier