Probing the pinning landscape in type-II superconductors via Campbell penetration depth

TL;DR

This paper derives a microscopic expression for the Campbell penetration depth in type-II superconductors, linking vortex pinning landscape properties to measurable magnetic response, and compares theoretical predictions with experimental data.

Contribution

It introduces a microscopic theory for the Campbell penetration depth based on strong pinning theory, explaining its dependence on vortex state preparation and hysteresis.

Findings

Derived a microscopic expression for $\lambda_C$

Explained hysteretic behavior of $\lambda_C$

Compared models with experimental results

Abstract

Type-II superconductors owe their magnetic and transport properties to vortex pinning, the immobilization of flux quanta through material inhomogeneities or defects. Characterizing the potential energy landscape for vortices, the pinning landscape (or short, pinscape), is of great technological importance. Besides measurement of the critical current density $j_c$ and of creep rates $S$, the $ac$ magnetic response provides valuable information on the pinscape which is different from that obtained through $j_c$ or $S$, with the Campbell penetration depth $\lambda_{\rm \scriptscriptstyle C}$ defining a characteristic quantity well accessible in an experiment. Here, we derive a microscopic expression for the Campbell penetration depth $\lambda_{\rm \scriptscriptstyle C}$ using strong pinning theory. Our results explain the dependence of $\lambda_{\rm \scriptscriptstyle C}$ on the state preparation of the vortex system and the appearance of hysteretic response. Analyzing different pinning models, metallic or insulating inclusions as well as $\delta T_c$- and $\delta \ell$-pinning, we discuss the behavior of the Campbell length for different vortex state preparations within the phenomenological $H$-$T$ phase diagram and compare our results with recent experiments.