A Symmetry Microscope for Disordered Materials

We use position-resolved coherent speckle patterns in concert with rotational x-ray autocorrelation analysis to uncover ``hidden'' ordering at specific length scales in labyrinthine magnetic domains. Central to this measurement is understanding how finite-size effects influence the statistics of rotational cross-correlations. To this end, we present numerical simulations of domain configurations whose speckle patterns display rotational ordering similar to experimental candidates, and examine how the real-space structure of ordered and disordered domains differs. In a scanning measurement, we observe what appears to be an island of ordering in an otherwise disordered perpendicular magnetic thin film.