The Pinning Force and the Flux Velocity in the Mixed-State Hall Effect

Abstract

Using the single flux motion model of Wang, Dong, and Ting (WDT) and taking into account both the pinning and thermal fluctuation, we perform a numerical study to investigate the dependence between the average pinning force F-p and the flux velocity vL in different temperature regions in the mixed-state of high-Tc superconductors. The numerical simulation shows that there does not exist a unified scaling relation between F-p and vL in the whole flux flow temperature region, but F-p and vL keep a linear dependence in the lower temperature region of the negative Hall effect. The variations of the magnetic field or the pinning concentration do not change this linear relation. Employing this linear relation and WDT's theory, we naturally give the scaling law of ρxy ∝ ρβxx with β ≈︂ 2. We also make a power fit for the data of F-p and vL in the high-temperature region of both the negative and the whole positive Hall effect. Finally, we obtain F-p ∼ v—νL with ν ≈︂ 1.5 to 2.0 for different magnetic fields and pinning concentrations.