Creep effects on the Campbell response in type II superconductors

• Published in: arXiv.org 2021-11
• Main Authors: Gaggioli, Filippo, Blatter, Gianni, Geshkenbein, Vadim B
• Format: Article
• Language: English
• Subjects: Defects; Pinning; Superconductors; Vortices
• ISSN: 2331-8422

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.