Interactions of domain walls are analyzed with relevance to formation of stationary bubbles (bound state of two domain walls) and bound states of many domains in one-dimensional systems. We investigate the domain structures in ferromagnets which are described with the Landau-Lifshitz equation as well as the domains in critical systems described with the Ginzburg-Landau equation. Supplementing previous author studies on the creation of hard bubbles [formed by one Bloch domain wall and one Néel (Ising) domain wall] in the presence of an external (magnetic) field, the soft bubbles consisting of two Bloch domain walls or two Néel (Ising) domain walls are studied in detail. The interactions of two domain walls of the same kind are studied in the framework of a perturbation calculus.
Interaction of domain walls in ferromagnetic stripes is studied with relevance to the formation of stable complexes of many domains. Two domain wall system is described with the Landau-Lifshitz-Gilbert equation including regimes of narrow and wide stripes which correspond the presence of transverse and vortex domain walls. The domain walls of both kinds are characterized with their chiralities (the direction of the magnetization rotation in the stripe plane) and polarities (the magnetization orientation in the center of a vortex and/or halfvortices), hence, their interactions are analyzed with dependence on these properties. In particular, pairs of the domain walls of opposite or like chiralities and polarities are investigated as well as pairs of opposite (like) chiralities and of like (opposite) polarities. Conditions of the creation of stationary bubbles built of two interacting domain walls are formulated with relevance to the situations of presence and absence of the external magnetic field.
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