Low-dimensional ferroelectrics under different electrical and mechanical boundary conditions: Atomistic simulations

I. Ponomareva, I. I. Naumov, and L. Bellaiche

Phys. Rev. B 72, 214118 – Published 21 December 2005

Abstract

Ferroelectric nanodots and infinite wires of $Pb ({Zr}_{0.4} {Ti}_{0.6}) O_{3}$ alloy under different boundary conditions are investigated via Monte Carlo simulations using an atomistic first-principles-based effective Hamiltonian. These nanosystems all exhibit a spontaneous polarization that points along a nonperiodic direction, for situations close to short-circuit electrical boundary conditions and independently of the epitaxial strain. On the other hand, unusual dipole patterns arise in these systems when they are under open-like circuit conditions. The dependency of these patterns on the nanostructure’s dimensionality and strain is further revealed and explained.

Received 7 September 2005

DOI:https://doi.org/10.1103/PhysRevB.72.214118

Authors & Affiliations

I. Ponomareva^*, I. I. Naumov^†, and L. Bellaiche^‡

Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA

^*Electronic address: iponoma@uark.edu
^†Electronic address: inaumov@uark.edu
^‡Electronic address: laurent@uark.edu

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Vol. 72, Iss. 21 — 1 December 2005

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Images

Figure 1
Ground-state spontaneous polarization in freestanding dot (a) and wire (c) as a function of the screening coefficient $β$ . The $β$ dependency of the toroid moment of polarization in the freestanding nanodot is shown in (b). Right and left insets to both (a) and (b) show the projection of the dipole patterns on a chosen plane for perfect SC and OC conditions, respectively, in the corresponding nanostructure. (Note that these dipoles nearly lie in the plane shown in the insets; that is, there is only a slight difference between the dipole vectors and their displayed projections.) The infinite direction of the wire is along the $z$ -axis. The $x$ -, $y$ -, and $z$ -axes are chosen along the pseudocubic [100], [010], and [001] directions, respectively.Reuse & Permissions
Figure 2
Ground-state spontaneous polarization in dot (a) and wire (c), under a tensile strain $+ 2.65 %$ applied in the $(x, z)$ plane, as a function of the screening coefficient $β$ . The $β$ dependency of the toroid moment of polarization in the nanodot is shown in (b). Right and left insets to both (a) and (b) show the projection of the dipole patterns on a chosen plane for perfect SC and OC conditions, respectively, in the corresponding nanostructure. (Note that these dipoles nearly lie in the plane shown in the insets; that is, there is only a slight difference between the dipole vectors and their displayed projections.) The infinite direction of the wire is along the $z$ -axis. The $x$ -, $y$ -, and $z$ -axes are chosen along the pseudocubic [100], [010], and [001] directions, respectively.Reuse & Permissions
Figure 3
A cross section of another possible dipole pattern for a nanowire periodic along the $z$ direction, and under OC-like electrical boundary conditions and a tensile strain applied in the $(x, z)$ plane. The arrows show the projection of the dipole patterns on a chosen plane. (Note that these dipoles nearly lie in the plane shown in the insets; that is, there is only a slight difference between the dipole vectors and their displayed projections.) The $x$ -, $y$ -, and $z$ -axes are chosen along the pseudocubic [100], [010], and [001] directions, respectively.Reuse & Permissions
Figure 4
(Color online). Ground-state spontaneous polarization in dot (a) and wire (b), under a compressive strain $- 2.65 %$ in the $(x, z)$ plane, as a function of the screening coefficient $β$ . Right and left insets to both (a) and (b) show the projection of the dipole patterns on a chosen plane for perfect SC and OC conditions, respectively, in the corresponding nanostructure. (Note that these dipoles nearly lie in the plane shown in the insets; that is, there is only a slight difference between the dipole vectors and their displayed projections.) The infinite direction of the wire is along the $z$ -axis. The $x$ -, $y$ -, and $z$ -axes are chosen along the pseudocubic [100], [010], and [001] directions, respectively.Reuse & Permissions

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