Ab initiostudy of ferroelectric domain walls inPbTiO3

Abstract

We have investigated the atomistic structure of the 180• and 90• domain boundaries in the ferroelectric perovskite compound PbTiO3 using a first-principles ultrasoft-pseudopotential approach. For each case we have computed the position, thickness and creation energy of the domain walls, and an estimate of the barrier height for their motion has been obtained. We find both kinds of domain walls to be very narrow with a similar width on the order of one to two lattice constants. The energy of the 90• domain wall is calculated to be 35 mJ/m 2 , about a factor of four lower than the energy of its 180• counterpart, and only a miniscule barrier for its motion is found. As a surprising feature we detected a small offset of 0.15-0.2 eV in the electrostatic potential across the 90• domain wall.

Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

“…Hence, the theory predicts that the 90º wall surface energy is on the order of one third of the 180º wall energy for barium titanate. This prediction is in qualitative accord with ab initio quantum mechanical computations on lead titanate that predict the 90º wall energy to be one fourth of the 180º wall energy, Meyer and Vanderbilt (2002) (we have been unable to find similar simulation results for 90º walls in barium titanate). For the continuum theory, the disparity between the two 90º wall energies is due to the differences in the internal fields generated within the wall and the slight differences in the polarization gradients for the two values of a 5 .…”

“…For a 5 = 368 E 0 P 0 7 this jump is ∆φ E 0 l 0 = −0.85 , and for a 5 = 0 the jump is ∆φ E 0 l 0 = 2.25 . This electric potential drop has been predicted by ab initio computations on lead titanate, Meyer and Vanderbilt (2002), and has a significant effect on the interaction of domain walls with charge defects, Xiao et al (2005). This feature of the domain wall solutions has interesting consequences for sharp interface model of domains which usually assume that the electric potential is continuous across a domain wall.…”

“…The theory falls into the class of phase-field or diffuse-interface modeling approaches (Cao and Cross, 1991;Nambu and Sagala, 1994;Hu and Chen, 1997;Cao, 2000, 2001;Li et al, 2001Li et al, , 2002and Zhang and Bhattacharya, 2005a,b), which has the potential to bridge atomistic calculations (Cohen and Krakauer, 1992;Meyer and Vanderbilt, 2002) and the larger scale phenomenological modeling approaches. In a departure from previous derivations of the phase-field equations, a set of micro-forces and governing balance laws are postulated and applied within the second law of thermodynamics to identify the appropriate material constitutive relationships, Gurtin, 1993, 1994;Gurtin, 1996).…”

Atomic-scale mechanisms of ferroelastic domain-wall-mediated ferroelectric switching

“…1a-d) show that the ferroelastic domain walls develop an electrical charge and are associated with significant strains despite lying on nominally charge and strain neutral {101} planes. In fact, an electrical potential step exists across a ferroelastic domain wall in bulk tetragonal PbTiO 3 according to firstprinciples calculations 25 and phase-field simulations 26 , indicating 90°domain walls may be inherently charged. In addition, the effect of the substrate constraint may lead to additional polarization charges at the domain wall because of different polarization magnitudes for the c-and a-domains in an epitaxial thin film (c refers to domains with the polarization oriented along the film normal and a refers to those with the polarization oriented in-plane).…”

Novel high-temperature ferroelectric domain morphology in PbTiO3 ultrathin films

“…The P y component (perpendicular to both the domain wall and surface normals), has a maximum value within unit cells constituting the domain walls (cell stacks (i), (ii), (vi) and (vii) in Figure 4a) and reduces sharply for cells further from the domain wall, reorientating along the c-axis at the centre of the film away from surface effects. The polar rotations at the surface layers act to change the anisotropy, forcing the domain walls to be more characteristic of magnetic Bloch-Néel walls than the distinctly Ising form in bulk [41]. Evidence for the existence of mixed Ising and Bloch-Néel character domain walls in ferroelectrics has recently been proposed in PbTiO 3 and LiNbO 3 from ab initio calculations [42].…”