Campbell response in type II superconductors under strong pinning conditions

Measuring the $ac$ magnetic response of a type II superconductor provides valuable information on the pinning landscape (pinscape) of the material. We use strong pinning theory to derive a microscopic expression for the Campbell length $\lambda_{\rm \scriptscriptstyle C}$, the penetration depth of the $ac$ signal. We show that $\lambda_{\rm \scriptscriptstyle C}$ is determined by the jump in the pinning force, in contrast to the critical current $j_c$ which involves the jump in pinning energy. We demonstrate that the Campbell lengths generically differ for zero-field-cooled and field-cooled samples and predict that hysteretic behavior can appear in the latter situation. We compare our findings with new experimental data and show the potential of this technique in providing information on the material's pinscape.