Creep effects on the Campbell response in type II superconductors

TL;DR

This paper investigates how thermal fluctuations affect the Campbell response in type II superconductors, revealing nonmonotonic relaxation behaviors and hysteresis, and proposes a method to spectroscopically analyze defect pinning potentials.

Contribution

It introduces a detailed theoretical analysis of creep effects on the Campbell length, showing nontrivial relaxation dynamics and hysteresis in different experimental protocols.

Findings

Campbell length exhibits nonmonotonic decay during ZFC relaxation.

Hysteretic effects observed in field cooled experiments.

Campbell length relaxation depends on temperature and waiting time.

Abstract

Applying the strong pinning formalism to the mixed state of a type II superconductor, we study the effect of thermal fluctuations (or creep) on the penetration of an ac magnetic field as quantified by the so-called Campbell length $\lambda_\textrm{C}$. Within strong pinning theory, vortices get pinned by individual defects, with the jumps in the pinning energy ($\Delta e_\mathrm{pin}$) and force ($\Delta f_\mathrm{pin}$) between bistable pinned and free states quantifying the pinning process. We find that the evolution of the Campbell length $\lambda_{\rm C}(t)$ as a function of time $t$ is the result of two competing effects, the change in the force jumps $\Delta f_\mathrm{pin}(t)$ and a change in the trapping area $S_\mathrm{trap}(t)$ of vortices; the latter describes the area around the defect where a nearby vortex gets and remains trapped. Contrary to naive expectation, we find that during the decay of the critical state in a zero-field cooled (ZFC) experiment, the Campbell length $\lambda_{\rm C}(t)$ is usually nonmonotonic, first decreasing with time $t$ and then increasing for long waiting times. Field cooled (FC) experiments exhibit hysteretic effects in $\lambda_\textrm{C}$; relaxation then turns out to be predominantly monotonic, but its magnitude and direction depends on the specific phase of the cooling--heating cycle. Furthermore, when approaching equilibrium, the Campbell length relaxes to a finite value, different from the persistent current which vanishes at long waiting times $t$, e.g., above the irreversibility line. Finally, measuring the Campbell length $\lambda_\textrm{C}(t)$ for different states, zero-field cooled, field cooled, and relaxed, as a function of different waiting times $t$ and temperatures $T,$ allows to "spectroscopyse" the pinning potential of the defects.