Evolution of disorder in two-dimensional stripe patterns: ‘‘Smectic’’ instabilities and disclination unbinding

Abstract

A combination of video polarization microscopy and extensive digital line pattern analysis has been invoked to examine in quantitative detail the transformation of a lamellar into a "labyrinthine" magneticstripe domain pattern. The evolution of disorder is found to be mediated by a sequence of transverse, "smectic" instabilities culminating in the generation of disclination dipoles. Their subsequent continuous "unbinding" facilitates the formation of a globally isotropic nonequilibrium pattern adopting the topology of a binary tree and displaying a well-defined morphology with a motif in the form of oblong, polygonal clusters of linear-stripe segments. PACS numbers: 6!.70.-r, 05.70.Fh, 64.70.-p, 75.70.Kw Uniaxially modulated states abound in both two-and three-dimensional condensed-matter systems. Widely studied examples include the following: the ubiquitous lamellar or smectic phases of liquid crystals [1], surfactants [2], and block copolymers [3]; linear arrays of domain walls or discommensurations stabilized by competing periodicities such as those of rare-gas atomic and simple molecular adsorbate layers and the crystalline substrates on which they are deposited [4], as well as those of intercalates and their graphite host [5]; steps decorating reconstructed surfaces of certain semiconductors [6] and metals [7]; and stripe domain phases in ferrofluids [8], Langmuir monolayers [9], and thin magnetic garnet films [10], favored by the competition between a local attractive interaction, manifesting itself in the form of a domain-wall energy, and a repulsive electrostatic or magnetostatic interaction of long range [11]. The latter class of materials, long the subject of a substantial and ongoing effort to realize a variety of devices [12], has recently received renewed attention focusing on dynamic as well as structural aspects of their characteristic "stripe" and "bubble" phases [11]. Topological considerations play an essential role, whether they pertain to the cellular network of coarsening bubble domains [13], to the melting of bubble lattices [14], to the sequence of domain-wall bifurcations in thick garnet films [15], or to the constraints governing a complex variety of disordered, nonequilibrium stripe patterns [16].In this Letter we investigate the evolution of disorder in the two-dimensional lamellar ground state of magneticstripe domains transforming the initial ordered pattern into a globally isotropic "labyrinthine" pattern [16][17][18]. We show that this process is mediated by a sequence of transverse instabilities bearing a close resemblance to those of smectic liquid crystals subjected to compressive or dilative stress [19], and culminating in the formation and subsequent "unbinding" of disclination dipoles. The emerging nonequilibrium labyrinthine patterns exhibit a characteristic density of disclination defects, symmetrically distributed between the two components of magnetization and imparting on each the topology of a binary tree. This network of disclinations delineates a welldefined local stru...

Monte Carlo approach for studying microphases applied to the axial next-nearest-neighbor Ising and the Ising-Coulomb models

“…5 Periodic lamellae, cylinders, clusters, etc., are thus similarly found in block copolymers, [6][7][8] oil-water surfactant mixtures, 9,10 charged colloidal suspensions, 11 and numerous magnetic materials. 12,13 Microphase formation has also been hypothesized to play a role in biological membrane organization 14 and in the formation of stripes in certain superconductors, [15][16][17][18][19][20] although the microscopic interpretation is still debated. The spontaneous nature of microphase organization allows for these mesoscale periodic textures to find technological success as thermoplastic elastomers 6 and nanostructure templates.…”

Critical Phenomena in Hydrodynamics

“…This instability eventually leads to the formation of a glo bally isotropic and disordered state via an unbinding of disclination dipoles [26]. We have not yet investigated the generation of labyrinthine patterns in RBC, but a similar scenario can be expected.…”

Temperature‐induced changes of domain structures in ultrathin magnetic films

“…Temperature-dependent intrinsic magnetic parameters of ultrathin films may cause many interesting phenomena in the thermal evolution of domain structures (DS): i) nontrivial temperature changes of the DS period; ii) domain-shape instabilities and temperature-induced transitions between domain structures [1][2][3]; iii) so-called inverse melting of DSs (processes where a more symmetric domain phase is found at lower temperatures than at higher temperatures -the inverse phase sequence) [4]. A possibility of such transitions is determined by lowering of the potential barriers separating different magnetization states as the film temperature increases approaching either the Curie point or the temperature of the reorientation phase transition where the effective first anisotropy constant vanishes [5].…”