Time scales of the flux creep in superconductors

We have studied both theoretically and experimentally flux-creep dynamics in superconductors. A theoretical analysis of nonlinear flux diffusion shows that the relaxation of the electric field proves to be similar for different models of thermally activated flux creep, whereas the long-time decay of the magnetic moment M(t) can be essentially model dependent. A proposed scaling analysis indicates that the short-time decay of M(t) in the subcritical region jjc is universal and consists of two stages. The initial nonlogarithmic stage is due to a transient redistribution of magnetic flux over the sample cross section, the duration of this stage τ₀ being entirely determined by macroscopic quantities, such as sample sizes, flux creep rate M₁(T,B)=dM/d lnt, and magnetic ramp rate Ḃ \.ₑ=dB/dt. The second stage corresponds to the approximately logarithmic relaxation M(t)=Mc-M₁ln(t/t₀), with t₀ being a macroscopic time constant that also depends on sample sizes, M₁(T,B), and the voltage criterion Ec at which the critical current density jc is defined.We consider different models of flux dynamics with nonlinear flux-creep-activation barriers U(j) and obtain explicit formulas for τ₀ and t₀ for the exponential V-I curve and the vortex-glass model. We have also performed an experimental study of magnetic relaxation in grain-oriented YBa₂{Cu}₃O₇ in which the time constant τ₀ has been measured directly at different temperatures 4.2 KT88 K, magnetic fields 0B8 T, and ramp rates 5 {μ}T/sḂ \.ₑ10 mT/s. We have observed the inverse dependence of τ₀ upon Ḃ \.ₑ, with τ₀ ranging from 1 s to 10³ s and reaching 5000 s at Ḃ \.ₑ=5 {μ}T/s, B=6 T, and T=20 K. It is shown that, in accordance with our model, the dependences of τ₀ upon T and B coincide with those for the flux-creep rate M₁(T,B)=dM/d lnt measured on the logarithmic stage of the flux creep. We have also measured the dependences of the initial magnetic moment M(0) on T, B, and Ḃ \.ₑ. Manifestations of the obtained results in magnetic and relaxation measurements on high-Tc superconductors are discussed.