Pattern analysis of magnetic stripe domains morphology and topological defects in the disordered state

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Abstract
A direct-space analysis of globally disordered (‘labyrinthine’) stripe domain patterns in thin ferrimagnetic garnet films is presented. A set of algorithms, designed to encode and analyse line patterns, serves to identify and correlate the positions of topological defects, and to delineate structural motifs in the pattern morphology. Despite the fact that labyrinthine patterns represent a metastable state, statistical analysis of morphological and certain geometrical features extracted via pattern analysis reveals that the labyrinthine state's structure is well defined and robust; it is composed of oblong polygonal regions of ‘smectic’ ordering of its constituent line segments. That is, there exists a well defined length scale in these globally disordered labyrinths over which the ordered lamellar state of minimal free energy is realized; this length scale corresponds to a characteristic size of the ordered regions (‘segment clusters’). Furthermore, local orientational correlations of adjacent segment clusters are well defined and discrete; the global azimuthal symmetry of the pattern is locally broken. These features are found to be independent of the choice of trajectory in the magnetic field-temperature phase diagram along which the labyrinthine state is approached, a remarkable observation given the distinct topological constraints associated with different trajectories. Our findings are discussed in the general contexts of defect-mediated melting and amorphous structure and suggest that the labyrinthine state may be viewed as a two-dimensional glass.