Pinning of Elastic Vortex Bundle by Large Defect in High-Temperature Superconductors

We present a model of flux pinning in a superconductor with relatively large nonsuperconducting spherical particles. Minimizing the total energy of a pinned vortex bundle we deduce equations for pinning force and critical current density. The calculated field dependencies of both quantities are in a good agreement with the earlier reported empirical formula and numerous experimental data for RE-Ba-Cu-O melt-textured superconductors. Introduction The REBa2Cu3O7-δ (RE=rare earth, RE-123) superconductors with micron-size RE2BaCuO5 (RE211, secondary phase) particles are promising materials for applications due to flexibility in manipulation with their pinning properties [Muralidhar at al., 2001]. It has been experimentally proved that relatively large secondary phase particles contribute to flux pinning and enhance superconducting currents, especially in low magnetic fields. Vortex lattice interaction with large (volume) pins has been treated by many authors. Campbell, Evetts, and Dew-Hughes [Campbell at al., 1968] used direct summation of elementary pinning forces and found field-dependent critical current density Jc(B)∝ b(1-b) with b=B/Bc2. Dew Hughes studied the interaction of a rigid vortex lattice with different types of pins [Dew-Hughes, 1974]. For core pinning by large normal pins he deduced Jc(B)∝ b(1-b). Murakami et al. [Murakami at al., 1991, Fujimoto et al., 1992] suggested a model of flux pinning on large cubic pins for melt-textured materials doped by relatively large normal secondary phase particles. They introduced concept of surface pinning and obtained Jc(B)∝ b for it. All above cases indicated a strong pinning at low magnetic fields, in qualitative agreement with experiment. The quantitative comparison is in real samples complicated by presence of other types of pins. For example, after separation of the second peak effect contribution [M. Jirsa et al., 2001a] it was found that the low-field part of Jc(B) (central peak) decays with field much faster than the dependencies proposed in above models and fits well with the exponentially decaying function suggested e.g. by Kobayashi et al. [Kobayashi et al., 1995]. We should note here that in low magnetic fields the simple proportionality between irreversible magnetic moment and critical current density according to the extended Bean model [Chen at al., 1989] does not apply [Shantsev at al, 1999]. The “real” critical currents are even higher and decay with field even faster than the irreversible magnetic moment [Shantsev at al, 1999], which gives further support to the exponential J(B) dependence. In all the above models flux was supposed to be homogeneously trapped by normal inclusions over the whole sample. Under this assumption, a direct summation of elementary pinning forces consisted of multiplying the elementary pinning force by the defect concentration. Due to magnetic history and irregular distribution of pins and vortices in a real sample various inclusions can keep different numbers of vortices. In this work we treat the interaction of an elastic vortex lattice with defects that are large compared to vortex core size, ξ. Taking into account stochastic character of the vortex trapping by large inclusions, we calculate and discuss the associated pinning force. Model of pinning by large defects We will suppose a lattice of elastic vortices that can adapt to the structure of large normal defects of the mean radius R, randomly distributed over the sample. The vortices crossing a normal defect lose part of their condensation energy, proportional to the trapped volume πξ z1, WDS'05 Proceedings of Contributed Papers, Part III, 495–500, 2005. ISBN 80-86732-59-2 © MATFYZPRESS