Domain structure in ultrathin ferroelectric films: Analysis with a free energy model

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Y. Yacoby and Y. Girshberg
Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel

E. A. Stern
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA

R. Clarke
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120, USA

Received 29 May 2006; published 22 September 2006

Experimentshave shown that the transition temperature of 4–75-unit-cell-thick PbTiO₃ filmsgrown on an insulating SrTiO₃ substrate range between 550 and980 K. At high temperatures (below T_c), the films are ina 180° stripe domain state, polarized perpendicular to the surface,and transform at about room temperature to a single macroscopicdomain. This transition is curious because the strong depolarizing fieldis expected to quench the spontaneous polarization. Indeed, a 10-unit-cell-thickBaTiO₃ film grown on the same substrate was found toremain in the paraelectric state even at room temperature. Tounderstand these phenomena, we present a free energy model basedon the bulk perovskite ferroelectricity model that we have previouslydeveloped. The model takes into account two interacting order parameters,the average spontaneous local off-center displacements (pseudospins) and the condensedsoft mode. The model shows that at high temperatures thePbTiO₃ films should be in the stripe domain state andpredicts in reasonable quantitative agreement with experiment the stripe periodas a function of temperature and film thickness. It furtherpredicts that at about room temperature the films would transforminto a single domain state with vanishing electrical polarization butwith large ionic displacements. Finally, the model explains why theproperties of PbTiO₃ and BaTiO₃ are so different from eachother.

URL:	http://link.aps.org/doi/10.1103/PhysRevB.74.104113
DOI:	10.1103/PhysRevB.74.104113
PACS:	77.84.-s; 68.55.-a; 77.55.+f 77.84.-s Dielectric, piezoelectric, ferroelectric, and antiferroelectric materials 68.55.-a Thin film structure and morphology 77.55.+f Dielectric thin films YEAR: 2006
KEYWORDS:	lead compounds, barium compounds, ferroelectric thin films, electric domains, dielectric polarisation, free energy, ferroelectricity, soft modes

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