Nonmonotonic relaxation of Campbell penetration depth from creep-enhanced vortex pinning

We study the effects of flux creep on the linear AC response of the vortex lattice in a low-pinning Ca_3Ir_4Sn_13 superconductor by measuring the Campbell penetration depth, λ_ 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 depth. This effect cannot be detected in conventional magnetic relaxation measurements but is revealed by our observation of a nonmonotonic time evolution of λ_ C(T,H,t), which directly probes the average curvature of the occupied pinning centers. The time evolution of λ_ C(T,H,t) was measured at different temperatures in samples with different densities of pinning centers produced by electron irradiation. The λ_ C(T,H,t) is hysteretic with a zero-field-cool warmed (ZFCW) state that exhibits a noticeable nonmonotonic relaxation but shows a monotonic change in the field-cooled (FC) state. The curves, measured at different temperatures, can be collapsed together when plotted on a logarithmic time scale t → Tln(t/t_0), quantitatively corroborating the proposed picture of vortex creep based on the strong pinning theory.