Strong flux pinning in YBa₂Cu₃O7−δthin films due to nanometer-sized precipitates

The magnetic field angle dependence of the critical current density J c ( H ,θ) was measured in epitaxial YBa 2 Cu 3 O 7−δ (YBCO) thin films with strong flux pinning ( J c >25 GA m −2 at 77 K). The YBCO films were classified into two categories: (1) films that showed J c (θ) peaks around with the shape of a stratovolcano (i.e., like Mount Fuji) and (2) films that showed high, broad J c (θ) peaks centered at in addition to less prominent peaks. Transmission electron microscope observations revealed that the films in category 1 contained a high density of very small precipitates, most of which were less than 7 nm, and that the films in category 2 contained a high density of precipitates whose typical diameters ranged from 5 to 25 nm. The J c ( H ,θ) data were analyzed based on the angular-dependent coherence length ξ(θ) within an anisotropic Ginzburg–Landau approximation. The pinning of the films in category 1 can be described by a direct summation of the core pinning interaction that is due to small point defects whose diameters are less than 2ξ. The high, broad J c (θ) peaks centered at in the films in category 2 were due to a high density of larger precipitates, and they can also be explained by a similar analysis for spherical pinning centers whose diameters are larger than 2ξ.