Josephson vortices with fractional flux quanta at YBa₂Cu₃O_7-x grain boundaries

We report numerical simulations of magnetic flux patterns in asymmetric 45° [001]-tilt grain boundaries in YBa₂Cu₃O_7-x superconducting films. The grain boundaries are treated as Josephson junctions with a critical current density j_c(x) alternating rapidly along the junctions with a typical length scale which is much less than Josephson penetration depth. We demonstrate the existence of Josephson vortices with fractional flux quanta for both periodic and random j_c(x). A method is proposed to extract these "fractional" vortices from experimental flux patterns.