Finite - temperature atomic structure of 180 ◦ ferroelectric domain walls in PbTiO 3

In this letter we obtain the finite-temperature structure of 180◦ domain walls in PbTiO3 using a quasi-harmonic–lattice dynamics approach. We obtain the temperature dependence of the atomic structure of domain walls from 0K up to room temperature. We also show that both Pb-centered and Ti-centered 180◦ domain walls are thicker at room temperature; domain wall thickness at T = 300K is about three times larger than that of T = 0K. Our calculations show that Ti-centered domain walls have a lower free energy than Pb-centered domain walls and hence are more likely to be seen at finite temperatures. Copyright c © EPLA, 2010 Introduction. – Ferroelectric perovskites have been the focus of intense research in recent years because of their potential applications in high-strain actuators, high-density storage devices, etc. [1]. It is known that macroscopic properties of ferroelectrics strongly depend on domain walls, which are extended two-dimensional defects. Any fundamental understanding of ferroelectricity in perovskites requires a detailed understanding of domain walls in the nanoscale (see [2] and references therein). Theoretical studies of domain walls have revealed many of their interesting features. From both theoretical calculations and experimental works, it has been observed that the thickness of domain walls can vary from thin walls, which consist of only a few atomic spaces to thick walls, which are in the order of a few micrometers. There have been studies using ab inito calculations [3–5] and anaharmonic-lattice statics calculations [6] suggesting that ferroelectric domain walls are atomically sharp. Hlinka and Marton [7] analyzed 90 domain walls in BaTiO3like crystals in the framework of the phenomenological Ginzburg-Landau-Devonshire (GLD) model and obtained a domain wall thickness of 3.6 nm at room temperature. Chrosch and Salje [8] measured the domain wall thickness in LaAlO3 in the temperature range 295–900K by X-ray diffraction. They observed that the domain wall thickness increases from about 20 Å to 200 Å and that the variation of domain wall thickness with temperature is linear at low temperatures. Using scanning probe microscopy, (a)E-mail: [email protected] Iwata et al. [9] found complex 180 domain walls with thicknesses 1–2μm in PZN-20% PT. Lehnen et al. [10] investigated 180 domain walls in PbTiO3 using electrostatic force microscopy (EFM) and piezoelectric force microscopy (PFM) and observed thick 180 domain walls at room temperature with thickness of about 5μm. Shilo et al. [11] studied the structure of 90 domain walls in PbTiO3 by measuring the surface profile close to emerging domain walls and then fitting it to the soliton-type solution of GLD theory. Using this technique they observed that the domain wall thickness is about 1.5 nm but with a wide scatter. They suggested that the presence of point defects within the domain wall is responsible for such variations. Lee et al. [12] provided a model to investigate the effect of point defects on the domain wall thickness. See also [13] for a similar study. Domain walls have been studied using different techniques in the atomic scale at T = 0K. However, one would be interested to know how different the structure and thickness of a 180 domain wall at room temperature are compared to those at T = 0K. In this letter, we study the structure of Pband Ti-centered 180 domain walls in PbTiO3 as a function of temperature in some detail. We first start with the static configuration of domain walls and iteratively optimize the free energy for a small temperature, e.g. T1 = 5K. The optimized structure at T1 will be the reference configuration for a higher temperature T2 = T1+ΔT . Continuing in this way we optimize the structure of the domain wall up to T = 300K. This temperature range is where quantum effects are