Nonequilibrium Campbell length: probing the vortex pinning potential

The $AC$ magnetic penetration depth $\lambda (T,H,j)$ was measured in presence of a macroscopic $DC$ (Bean) supercurrent, $j$. In single crystal BSCCO below approximately 28 K, $\lambda (T,H,j)$ exhibits thermal hysteresis. The irreversibility arises from a shift of the vortex position within its pinning well as $j$ changes. It is demonstrated that below a new irreversibility temperature, the nonequilibrium Campbell length depends upon the ratio $j/j_c$. $\lambda (T,H,j)$ {\it increases} with $j/j_c$ as expected for a non-parabolic potential well whose curvature {\it decreases} with the displacement. Qualitatively similar results are observed in other high-$T_{c}$ and conventional superconductors.