Thermal hysteresis of the Campbell response as a probe for bulk pinning landscape spectroscopy

Abstract

In type-II superconductors, the macroscopic response of vortex matter to an external perturbation depends on the local interaction of flux lines with the pinning landscape (pinscape). The (Campbell) penetration depth $\lambda_{\mathrm{\scriptscriptstyle C}}$ of an $ac$ field perturbation is often associated with a phenomenological pinning curvature. However, this basic approach is unable to capture thermal hysteresis effects observed in a variety of superconductors. The recently developed framework of strong-pinning theory has established a quantitative relationship between the microscopic pinscape and macroscopic observables. Specifically, it identifies history-dependent vortex arrangements as the primary source for thermal hysteresis in the Campbell response. In this work, we show that this interpretation is well suited to capture the experimental results of the clean superconductor $\mathrm{Nb}\mathrm{Se}_{2}$; as observed through Campbell response (linear $ac$ susceptibility) and small-angle neutron scattering measurements. Furthermore, we exploit the hysteretic Campbell response upon thermal cycling to extract the temperature dependence of microscopic pinning parameters from bulk measurements; specifically the pinning force and pinning length. This spectroscopic tool may stimulate further pinscape characterization in other superconducting systems.