  The penetration of magnetic flux fronts in the optimally-doped iron-based
superconductor Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_2$ ($x = 0.07 \pm 0.005$) is
studied by means of magneto-optical imaging and Bitter decoration. The
higher-order analysis of roughening and growth of the magnetic flux front
reveals anomalous scaling properties, indicative of non-Gaussian correlations
of the disorder potential. While higher-order spatial correlation functions
reveal multi-fractal behavior for the roughening, the usual Kardar-Parisi-Zhang
growth exponent is found. Both exponents are found to be independent of
temperature. The scaling behavior is manifestly different from that found for
other modes of flux penetration, such as that mediated by avalanches,
suggesting that multi-scaling is a powerful tool for the characterization of
roughened interfaces. We propose a scenario for vortex penetration based on
two-dimensional percolation and cluster aggregation for an inhomogeneously
disordered superconductor.
