Nanoscale Toroidal Ferroelectricity in Perovskite Oxides.

M. G. STACHIOTTI; M. SEPLIARSKY

Bordeaux

Conferencia; 12th European Meeting on Ferroelectricity (EMF12).; 2011

&lt;!-- @page { margin: 2cm } P { margin-bottom: 0.21cm } --&gt; We applied a first-principles-based atomistic model to investigate the formation of dipolar structures in isolated stress-free PbTiO3 nanoparticles. The studies were carried performing molecular dynamics simulation in rectangular nanodots under ideal open-circuit boundary conditions, with Nx×Ny×Nz numbers of Ti atoms along the pseudocubic directions. We found that size-induced topological transformations, which are driven by the aspect ratio of the nanostructure, change the topology of the polarization field producing a rich variety of polar configurations. In cubic nanodots (Nx=Ny=Nz=N) with N ≥ 7 individual dipoles rotate from cell to cell forming a vortex-like pattern with toroidal moment g along <111> axes. This state transforms into another one-vortex state but with g parallel to the <001> direction when nanoparticles are elongated along z. On the other side, more complex configurations are observed when the lateral sizes of the nanoparticles are increased. Of a particular interest is the formation a four-vortex state with cores aligned along a closed path. The vortex structure forms a ring-shaped torus, and a ferroelectric bubble is developed as a strong resultant polarization concentrated through the center of the ring, directed perpendicular to the plane of the ring. This state is in agreement with the one suggested by Gorbatsevich and Kopaev [1], and differs to those obtained by Naumov et al. [2] Figure 1 shows the Pz map (a) and a polarization pattern (b) for a 22×22×10 nanodot, where the bubble is perfectly formed. The polarization map displays a core domain state where the center of the nanodot is polarized up while the outer region polarizes down. The profiles show that a bell-shaped ferroelectric bubble is formed, having a strong electric polarization aligned along the z axis, which is confined at the center of the torus. The bubble is stabilized in flat rectangular PbTiO3 nanodots with aspect ratio ~ 2.5, being the 8x8x3 unit cells nanoparticle the smallest one (Fig. 1 (c)). In addition, Figure 1(d) indicates that the ferroelectric bubbles have a strong thermal stability. While the Curie temperature for the 8×8×3 nanodot is ~ 200K, the remaining bubbles are all stable at room temperature. Moreover, the 22×22×10 and 28×28×14 nanodots have Curie temperatures even higher than the bulk. For an even greater increase in the lateral size of the nanodots, a multi-bubble state bridges the gap between 0D nanodots and 2D ultra-thin films. Finally, we obtained that a ferroelectric bubble state can be stabilized also in a flat stress-free isolated nanodisk with similar aspect ratio. Our results are thus interesting not only in terms of a fundamental knowledge of structural ordering in low-dimensional systems but also by their practical implications.