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Over 60 years ago, Charles Kittel predicted that quadrant domains should spontaneously form in small ferromagnetic platelets. He expected that the direction of magnetization within each quadrant should lie parallel to the platelet surface, minimizing demagnetizing fields, and that magnetic moments should be configured into an overall closed loop, or flux-closure arrangement. Although now a ubiquitous observation in ferromagnets, obvious flux-closure patterns have been somewhat elusive in ferroelectric materials. This is despite the analogous behaviour between these two ferroic subgroups and the recent prediction of dipole closure states by atomistic simulations research. Here we show Piezoresponse Force Microscopy images of mesoscopic dipole closure patterns in free-standing, single-crystal lamellae of BaTiO3. Formation of these patterns is a dynamical process resulting from system relaxation after the BaTiO3 has been poled with a uniform electric field. The flux-closure states are composed of shape conserving 90° stripe domains which minimize disclination stresses.
Bibliographical noteThe authors acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) and the National Science Foundation (NSF) for funding under the Materials World Network (MWN) scheme (NSF Grant No.: DMR-1007943; EPSRC Grant No.: EP/H047093/1), and The Leverhulme Trust for international network funding (F/00 203/V). R.G.P.McQ., L.J.McG. and J.M.G. acknowledge support from the Department of Employment and Learning (DEL). R.G.P.McQ. acknowledges support from the Dunville Studentship scheme. P.S. and A.G. acknowledge support from the NSF under Grant No. MRSEC DMR-0820521.
ASJC Scopus subject areas
- Biochemistry, Genetics and Molecular Biology(all)
- Physics and Astronomy(all)