Ferromagneticlike Closure Domains in Ferroelectric Ultrathin Films: First-Principles Simulations

Pablo Aguado-Puente and Javier Junquera

Phys. Rev. Lett. 100, 177601 – Published 29 April 2008

Abstract

We simulate from first principles the energetic, structural, and electronic properties of ferroelectric domains in ultrathin ${SrRuO}_{3} / {BaTiO}_{3} / {SrRuO}_{3}$ ferroelectric capacitors in short circuit. The domains are stabilized down to two unit cells at zero temperature, adopting the form of a domain of closure, common in ferromagnetic thin films. The domains are closed by the in-plane relaxation of the atoms in the first SrO layer of the electrode, which behaves more like SrO in highly polarizable ${SrTiO}_{3}$ than in metallic ${SrRuO}_{3}$ . Even if small, these lateral displacements are very important to stabilize the domains and might provide some hints to explain why some systems break into domains while others remain in a monodomain configuration. An analysis of the electrostatic potential reveals preferential points of pinning for charged defects at the ferroelectric-electrode interface, possibly playing a major role in film fatigue.

Received 8 October 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.177601

Authors & Affiliations

Pablo Aguado-Puente and Javier Junquera

CITIMAC, Universidad de Cantabria, Avenida de los Castros s/n, E-39005 Santander, Spain

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Vol. 100, Iss. 17 — 2 May 2008

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Images

Figure 1
Difference in energy between polydomain and paraelectric phases as a function of (a) the domain period $N_{x}$ for a ferroelectric thin film two unit cells thick ( $m = 2$ ) and (b) the thickness of the ferroelectric film for a capacitor with $N_{x} = 4$ . The energy of the paraelectric phase (dotted line) is taken as a reference. First-principles results for both Ba-centered (circles, solid line) and Ti-centered (squares, dashed) domain walls are shown. In (a), differences in energies between local minima of the polydomain phase are represented by error bars. Inset: Structure of the ferroelectric capacitor considered. $N_{x}$ is the stripe period, and $m$ is the thickness of the ferroelectric thin film, in number of unit cells of the ferroelectric perovskite oxide. In (b), the result for the most stable monodomain configuration is also shown (triangle). Solid symbols correspond to constrained relaxations where no in-plane displacements are allowed.Reuse & Permissions
Figure 2
Schematic representation of the atomic relaxations in patterns of domains of closure with a domain period of (a) $N_{x} = 4$ and (b) $N_{x} = 6$ . Balls, representing atoms, are located at the positions of the reference paraelectric phase. Atomic displacements for the polydomain configuration after relaxation are represented by arrows, whose magnitude can be gauged with respect to the displacements in the bulk tetragonal phase of ${BaTiO}_{3}$ at the scale on the left. Dotted lines indicate the position of the domain wall. Only Ba-centered domains are shown. Similar results are obtained for Ti-centered domains. (For an enlarged figure, see 31.)Reuse & Permissions
Figure 3
Measurement of the polarization in the ferroelectric layer as a function of position along the [100] direction of the capacitor. (a) Definition of the average change in distance $Δ$ between Ti and apical O in a chain along [001] for an interface with $m = 2$ . In every case, the atomic positions correspond to the lowest energy structure. A positive value of $Δ$ means a polarization pointing upward. (b) Profile of the normalized averaged change in distance along $z$ as a function of the position of the chain for a Ba-centered interface of domain period $N_{x} = 4$ . The chains are numbered as indicated in Fig. 2. Results are shown for $m = 2$ (circles, dashed line) and $m = 4$ (squares, dotted-dashed line). Dotted lines represent the position of the domain walls.Reuse & Permissions
Figure 4
Map of the nanosmoothed electrostatic potential in a two-unit-cell-thick ferroelectric capacitor with a stripe period of (a) $N_{x} = 4$ and (b) $N_{x} = 6$ . The arrows represent the atomic displacements with respect to the paraelectric phase as in Fig. 2. Only the displacements of the cations are shown for simplicity. Solid lines are a schematic representation of the domains of closure, while dashed lines mark the position of the ${BaTiO}_{3} / {SrRuO}_{3}$ interface.Reuse & Permissions

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