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

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