Creep-enhanced vortex pinning revealed through nonmonotonic relaxation of the Campbell length

TL;DR

This study reveals how flux creep affects the vortex lattice's linear AC response in a superconductor, showing nonmonotonic relaxation of the Campbell length due to re-trapping of vortices in deeper pinning wells, which is linked to strong pinning theory.

Contribution

It demonstrates nonmonotonic relaxation of the Campbell length caused by flux creep, revealing the average curvature of pinning centers through time-resolved measurements.

Findings

Nonmonotonic evolution of Campbell length observed.

Flux creep driven by temperature and pinning density.

Hysteresis depends on vortex density distribution.

Abstract

We study the effects of flux creep on the linear AC response of the vortex lattice in single crystals Ca$_3$Ir$_4$Sn$_{13}$ by measuring the Campbell penetration depth, $\lambda_{\rm \scriptscriptstyle C}(T,H,t)$. Thermal fluctuations release vortices from shallow pinning sites, only for them to become re-trapped by deeper potential wells, causing an initial increase of the effective Labusch parameter, which is proportional to the pinning well curvature. This effect cannot be detected in conventional magnetic relaxation measurements but is revealed by our observation of a nonmonotonic time evolution of $\lambda_{\rm \scriptscriptstyle C}(T,H,t)$, which directly probes the average curvature of the occupied pinning centers. The time evolution of $\lambda_{\rm \scriptscriptstyle C}(T,H,t)$ was measured at different temperatures in samples with different densities of pinning centers produced by electron irradiation. The curves can be collapsed together when plotted on a logarithmic time scale $t \to T\ln{(t/t_0)}$ confirming that the time evolution is driven by flux creep. The $\lambda_{\rm \scriptscriptstyle C}(T,H,t)$ is hysteretic with a noticeable nonmonotonic relaxation in the presence of a vortex density gradient (after zero-field cooling), but is monotonic after field cooling, where the vortex density is uniform. This result quantitatively corroborates the novel picture of vortex creep based on the strong pinning theory.