Vortex states in a PbTiO$_3$ ferroelectric cylinder

Abstract

The past decade's discovery of topological excitations in nanoscale ferroelectrics has turned the prevailing view that the polar ground state in these materials is uniform. However, the systematic understanding of the topological polar structures in ferroelectrics is still on track.Here we study stable vortex-like textures of polarization in the nanocylinders of ferroelectric PbTiO 3 , arising due to the competition of the elastic and electrostatic interactions. Using the phase-field numerical modeling and analytical calculations, we show that the orientation of the vortex core with respect to the cylinder axis is tuned by the geometrical parameters and temperature of the system. A SupplementaryInformation 11 A.1 Computational techniques 11 A.2 Structure of an isotropic vortex 13 A.3 Energy parameters 15 A.4 Critical temperatures 15 References 17

Phase Diagram of a Strained Ferroelectric Nanowire

“…The two-dimensional and quasi-two-dimensional ferroelectric thin films and superlattices harboring a variety of topological excitations such as soft domains [6], vortices [7], skyrmions [8], and merons [9] are now understood reasonably well. At the same time, cognizance surrounding the properties of topological excitations in their lowerdimensional relatives, zero-dimensional nanodots, is much less extensive, although similar excitations-vortices [10][11][12][13][14], skyrmions [15,16], and hopfions [17]-have been predicted. Furthermore, while the fabrication methods of one-dimensional nanorods, nanotubes, and nanowires have achieved considerable progress [18][19][20][21][22][23], the topological dynamics in these one-dimensional nanostructures remain even more puzzling.…”