Order–Disorder Transitions in a Polar Vortex Lattice

Linming Zhou, Cheng Dai, Peter Meisenheimer, Sujit Das, Yongjun Wu, Fernando Gómez-Ortiz, Pablo García-Fernández, Yuhui Huang, Javier Junquera, Long Qing Chen, Ramamoorthy Ramesh, Zijian Hong

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7 Scopus citations


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.

Original languageEnglish (US)
Article number2111392
JournalAdvanced Functional Materials
Issue number22
StatePublished - May 25 2022

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • General Chemistry
  • General Materials Science
  • Electrochemistry
  • Biomaterials


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