Generation of Magnetic Flux by Single Grain Boundaries of ${{\mathrm{YBa}}_2{\mathrm{Cu}}_3{O}_{7-}}_{\mathit{x}}$

Using scanning SQUID microscopy, we have directly imaged spontaneously generated delocalized magnetic flux in 45° [001] tilt grain boundaries in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ films. Implications for the transport properties of the grain boundaries are discussed. A model based on a $d_{x^2{-y}^2}$-wave symmetry component of the superconducting order parameter and on grain-boundary faceting is consistent with the results of our experiments.