@article{cca17c6f60b94e2bbcdd424bb443e551,

title = "Surface effect on domain wall width in ferroelectrics",

abstract = "We study the effect of the depolarization field on a domain wall structure near the surface of a ferroelectric. Since in real situation bound and screening charges form an electric double layer, the breaking of this layer by the domain wall induces stray depolarization field, which in turn changes the domain wall structure. Power law decay of the stray field results in the power law of polarization saturation near the surface, as compared to exponential saturation in the bulk. Obtained results predict that the surface broadening of ferroelectric domain walls appeared near Curie temperature as well as describe domain wall depth profile in weak ferroelectrics. We qualitatively describe extra-broad domain walls near LiNbO3 and LiTaO3 surfaces observed experimentally at room temperature, which probably originate at high temperatures but did not fully relax their width with temperature decrease allowing for lattice pinning and defect centers. Thus results have broad implication for fundamental issues such as maximal information storage density in ferroelectric data storage, domain wall pinning mechanisms at surfaces and interfaces, and nucleation dynamics.",

author = "Eliseev, {Eugene A.} and Morozovska, {Anna N.} and Kalinin, {Sergei V.} and Yulan Li and Jie Shen and Glinchuk, {Maya D.} and Chen, {Long Qing} and Venkatraman Gopalan",

note = "Funding Information: Research was partially (E.A.E. and M.D.G.) supported by the Science and Technology Center in Ukraine, Project No. 3306. The research is supported in part (S.V.K.) by the Division of Scientific User Facilities, DOE BES. V.G. wishes to gratefully acknowledge financial support from the National Science Foundation Grant Nos. DMR-0602986, 0512165, 0507146, and 0213623, and CNMS at Oak Ridge National Laboratory. L.Q. and Y.L. are supported by DOE under Grant No. DE-FG02-07ER46417 and Los Alamos National Laboratory. Research also sponsored by Ministry of Science and Education of Ukrainian (Grant No. UU30/004) and National Science Foundation (Materials World Network, DMR-0908718). FIG. 1. 180°-domain wall structure near the film surface. The double electric layer is formed due to either the physical dead layer (a) or intrinsic surface effect leading to diminished polarization at interface (b). Discontinuity of the double electric layer of screening and bound changes results in an additional stray depolarization field. FIG. 2. Normalized domain wall profile P 3 ( x , z ) / P S calculated for different values of distances from the surface z / R ⊥ = 1 , 2 , 5 , 10 , 20 , ∞ (curves 1, 2, 3, 4, 5, 6) and dead layer thickness H / R ⊥ = 1 , 3 [panels (a) and (b), respectively]. FIG. 3. Normalized domain wall profile P 3 ( x , z ) / P S ( T ) calculated at fixed temperature T for R z = R ⊥ and extrapolation length λ = 0.5 R ⊥ . (a) Profile in linear scale and (b) half-profile in log-linear scale. Solid, dashed, and dotted curves correspond to different distances z / R ⊥ = 0 , 5 , ∞ from the surface of thick film ( L ⪢ R z ) . FIG. 4. Domain wall profiles at different temperatures T / T C = 0 , 0.6 , 0.8 [panels (a)–(c), respectively]. Curves 1–3 correspond to different distances z / R ⊥ ( T = 0 ) = 1 , 10 , ∞ from the surface of thick film ( L ⪢ R z ) . (d) Domain wall half width w ( z ) / R ⊥ ( T = 0 ) (at level 0.76) as the function of depth z at different temperature values, specified near the curves. R z = R ⊥ , extrapolation length λ = 2 R ⊥ ( T = 0 ) . FIG. 5. Domain structure near the surface of LiTaO 3 (a), (b) and LiNbO 3 (c), (d) films calculated numerically by using phase field method for R z = R ⊥ [(a) and (b)] and R z = 1.5 R ⊥ [(c) and (d)], extrapolation length λ = 0.5 R ⊥ [(a) and (c)] λ = − 2 R ⊥ [(b) and (d)] and different distances from the surface z = 0 , 0.5 R ⊥ , 5 R ⊥ , and 20 R ⊥ . FIG. 6. [(a) and (b)] Thickness of domain wall w / 2 R ⊥ at level 0.76 as a function of depth z from the surface at R z = R ⊥ , extrapolation length λ = 0.5 R ⊥ (a), and λ = R ⊥ (b) for material parameters of PbZr 0.5 Ti 0.5 O 3 . (c) Thickness of domain wall at level 0.76 as a function of its depth from the surface of LiTaO 3 . Squares are experimental data from Refs. 17 and 18 for 500 nm thick stoichiometric LiTaO 3 (SLT), and triangles correspond to 50 nm thick congruent LiTaO 3 (CLT). Solid curves are analytical calculations for fitting parameters R ⊥ = 1.3 nm , R z = 1.6 nm , different extrapolation lengths λ 1 ( 0 ) = 0.1 nm , and ( λ 2 ( h ) value appeared not important), for SLT; while R ⊥ = 0.7 nm , R z = 1.4 nm and λ 1 ( 0 ) = 0.1 nm , λ 2 ( h ) ⪢ 30 nm for CLT. Corresponding dotted curves are numerical calculations by phase field modeling for the same fitting parameters. ",

year = "2009",

doi = "10.1063/1.3236644",

language = "English (US)",

volume = "106",

journal = "Journal of Applied Physics",

issn = "0021-8979",

publisher = "American Institute of Physics Publising LLC",

number = "8",

}