Distinct correlation effect in magnetization relaxation from the Bean critical state in type-II superconductors

Abstract

The magnetization relaxation in type-II superconductors is modelled by a thermally assisted two-dimensional sandpile model. The model reveals a distinct correlation effect, or the effect of flux avalanche in the initial stage of relaxation from the Bean critical state. The effective energy U eff( J) ≡ − kT ln|d J/d| where J is the current density, is n in this regime although the activation energy U( J) assumed beforehand is linear. The extracted scaling exponent α ≈ 0.5 (noticeably robust against different temperatures), which characterizes the current density dependence of the linear size of the avalanche cluster with l ≈ (1 − J J c0 ) −α , is in rough agreement with the theoretical estimation. As the system is driven away from the Bean critical state, flux avalanche plays less and less a role since the linear size of the characteristic avalanche cluster meets the distance between the pinning centers, and the usual logarithmic decay of the Anderson-Kim model is recovered. It is argued from further analysis that the scaling behavior together with the exponent α = 0.5 is a univeral feature of the present model, irrespectively of the linear or nonlinear details of the U( J) function, or equivalently the underlying pinning mechanism. The relevance of our results is also discussed.