Exponential dependence of the vortex pinning potential on current density in high- Tc superconductors

We investigated the dependence of the vortex pinning potential on current density Ueff (J) in Tl2 Ba2 Ca Cu2 Oy, Tl2 Ba2 Ca2 Cu3 Oy, and Y Ba2 Cu3 Oy thin films and single crystals, measured by us and other research groups. In all these cases Ueff (J) was calculated from the magnetic relaxation data using Maley's procedure [Phys. Rev. B 42, 2639 (1990)]. We explored the exponential dependence of Ueff (J), first introduced by Thompson [Phys. Rev. B 44, 456 (1991).] to explain long-term nonlogarithmic magnetic relaxations in high-temperature superconductors (HTSC), as an alternative to power-law and logarithmic forms of Ueff (J). The results revealed that for J larger than approximately 0.4 Jc, the energy barrier can be expressed in the following form: Ueff (J) =a Ico (1-T/T*) 3/2 exp (-bJ/Jco), where the constant b is the same for all samples investigated. This result is independent of the anisotropy (the interplanar coupling). The experimental results were analyzed taking into account the spatial dependence of the pinning potential, proposed by Qin [J. Appl. Phys. 77, 2618 (1995)]. We suggested that the exponential form of Ueff (J) could represent vortex pinning and motion in the a-b planes due to a nanoscopic variation of the order parameter, in agreement with the growing experimental evidence for the presence of nanostructures, stripes (filaments) in HTSC.