Abstract
Unusual domains with curved walls and failure to satisfy the Landau–Lifshitz-Kittel Law are modeled as folding catastrophes (saddle-node bifurcations). This description of ballistic motion in a viscous medium is based upon early work by Dawber et al 2003 Appl. Phys. Lett. 82 436. It suggests that ferroelectric films can exhibit folds or vortex patterns but not both.
Highlights
Room-temperature studies of magnetic switching of ferroelectric domains and electric switching of magnetic domains were reported [1] in the single-phase but complicated perovskite oxide Pb[Fe1/2Ta1/2]1−x[Ti1−-yZry]xO3 by Evans et al in 2013, a paper downloaded more than 10 000 times in two years
In addition to providing a potentially new kind of memory device, this work displayed some deep puzzles: (1) the magnetic and ferroelectric domains switched polarization/ magnetization under applied fields, they failed to satisfy the Landau–Lifshitz-Kittel Law [2] for domain widths versus film thickness; (2) the domain walls were not rectilinear but instead were highly curved, resembling grapefruit sections; (3) the polarization switching with magnetic fields H fatigued quickly, whereas ferroelectric domain switching with E was indefinitely repetitive
This work shows that the smooth round domains exhibited in TEM by focusedion beam (FIB) single nano-crystals of lead iron-tantalate zirconate-titanate can be described as fold bifurcations, and suggests a shear strain term having velocity dx/dt = a–cx2 and dy/dt = −y; these are compatible with recent data
Summary
Room-temperature studies of magnetic switching of ferroelectric domains and electric switching of magnetic domains were reported [1] in the single-phase but complicated perovskite oxide Pb[Fe1/2Ta1/2]1−x[Ti1−-yZry]xO3 by Evans et al in 2013, a paper downloaded more than 10 000 times in two years. In addition to providing a potentially new kind of memory device, this work displayed some deep puzzles: (1) the magnetic and ferroelectric domains switched polarization/ magnetization under applied fields, they failed to satisfy the Landau–Lifshitz-Kittel Law [2] for domain widths versus film thickness; (2) the domain walls were not rectilinear but instead were highly curved, resembling grapefruit sections; (3) the polarization switching with magnetic fields H fatigued quickly (a few cycles), whereas ferroelectric domain switching with E was indefinitely repetitive These observations are reviewed in terms of the theory of folding catastrophes. Wrinkles are generally smooth and sinusoidal and energetically favored only where the substrate modulus is that of the overlapping film, whereas folds are more abrupt and occur for film/substrate modulus ratios nearer unity
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