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Early stages of magnetization relaxation in superconductors

Magnetic flux dynamics in type-II superconductors is studied within the model of a viscous nonlinear diffusion of vortices for various sample geometries. We find that time dependence of magnetic moment relaxation after the field is switched off can be accurately approximated by $m(t)\propto 1-\sqrt{t/\tildeτ}$ in the narrow initial time interval and by $m(t)\propto (1+t/τ)^{-1}$ at later times before the flux creep sets in. The characteristic times $\tildeτ$ and $τ$ are proportional to the viscous drag coefficient $η$. Quantitative agreement with available experimental data is obtained for both conventional and high-temperature superconductors with $η$ exceeding by many orders of magnitude the Bardeen-Stephen coefficient for free vortices. Huge enhancement of the drag, as well as its exponential temperature dependence, indicates a strong influence of pinning centers on the flux diffusion. Notwithstanding complexity of the vortex motion in the presence of pinning and thermal agitation, we argue that the initial relaxation of magnetization can still be considered as a viscous flux flow with an effective drag coefficient.