Order–Disorder Transitions in a Polar Vortex Lattice

Abstract

Order–disorder transitions are widely explored in various vortex structures in condensed matter physics, that is, in the type‐II superconductors and Bose–Einstein condensates. In this study, the ordering of the polar vortex phase in [Pb(Zr0.4Ti0.6)O3]n/(SrTiO3)n (PZT/STO) superlattices is investigated through phase‐field simulations. With a large tensile substrate strain, an antiorder vortex state (where the rotation direction of the vortex arrays in the neighboring ferroelectric layers are flipped) is discovered for short‐period PZT/STO superlattice. The driving force is the induced in‐plane polarization in the STO layers due to the large tensile epitaxial strain. Increasing the periodicity leads to antiorder to disorder transition, resulting from the high energy of the head‐to‐head/tail‐to‐tail domain structure in the STO layer. On the other hand, when the periodicity is kept constant in short‐period superlattices, the order–disorder–antiorder transition can be engineered by mediating the substrate strain, due to the competition between the induction of out‐of‐plane (due to interfacial depolarization effect) and in‐plane (due to strain) polarization in the STO layer. The 3D ordering of such polar vortices is still a topic of significant current interest and it is envisioned that this study will spur further interest toward the understanding of order–disorder transitions in ferroelectric topological structures.

Exchange‐Interaction‐Like Behavior in Ferroelectric Bilayers

“…The thickness of the SrTiO 3 spacer layer required to decouple the two adjoining ferroelectric layers is set by how the electric and elastic fields depend upon the polarization value of each ferroelectric layer, the magnitude of the ferroelectric proximity induced dipole–dipole interaction strength, [ 40 ] and the polarization due to substrate‐induced epitaxial strain. [ 41 ] This is consistent with what has been previously observed in the order‐disorder transition in superlattices exhibiting polar vortices [ 41 ] and in ferroelectric proximity effects in ferroelectric bilayers. [ 40 ] In essence, the electric and elastic fields in the SrTiO 3 layer decay with increasing distance, a distance that scales with the polarization of the adjoining ferroelectric layers and with the strain.…”

Interlayer Coupling Controlled Ordering and Phases in Polar Vortex Superlattices

“…These results help to explain previous observations in polar vortices 8,19,20 and polar skyrmions, 21,22 where the topological textures become more coherent with an increasing number of superlattice repetitions. Previously observed in polar sky- rmions, for example, there is a scaling of the dielectric response with the number of superlattice units.…”

Theoretical Understanding of Polar Topological Phase Transitions in Functional Oxide Heterostructures: A Review

“…[88] Besides the PTO/STO system, the polar vortex has also been discovered in other ferroelectric materials systems, including BiFeO 3 (BFO)-based superlattices, [154,155] BFO thin films, [132,156] BTO nanoparticles, [157] PVDF-based thin films, [158] and molecular ferroelectrics. [159] Moreover, polar antivortex, a structure with the opposite winding number as a polar vortex, has been discovered in the PTO/STO superlattice, [160,161] PZT/ STO superlattice, [162] as well as in the BFO thin films. [163,164] By carefully engineering of the film thicknesses, polar antivortex was successfully created and observed at atomic-scale within dielectric STO layer in PTO/STO superlattices (Figure 3d).…”