Stability of Polar Vortex Lattice in Ferroelectric Superlattices

Zijian Hong; Anoop R. Damodaran; Fei Xue; Shang Lin Hsu; Jason Britson; Ajay K. Yadav; Christopher T. Nelson; Jian Jun Wang; James F. Scott; Lane W. Martin; Ramamoorthy Ramesh; Long Qing Chen

doi:10.1021/acs.nanolett.6b04875

Stability of Polar Vortex Lattice in Ferroelectric Superlattices

Zijian Hong, Anoop R. Damodaran, Fei Xue, Shang Lin Hsu, Jason Britson, Ajay K. Yadav, Christopher T. Nelson, Jian Jun Wang, James F. Scott, Lane W. Martin, Ramamoorthy Ramesh, Long Qing Chen

Research output: Contribution to journal › Article › peer-review

157 Scopus citations

Abstract

A novel mesoscale state comprising of an ordered polar vortex lattice has been demonstrated in ferroelectric superlattices of PbTiO₃/SrTiO₃. Here, we employ phase-field simulations, analytical theory, and experimental observations to evaluate thermodynamic conditions and geometric length scales that are critical for the formation of such exotic vortex states. We show that the stability of these vortex lattices involves an intimate competition between long-range electrostatic, long-range elastic, and short-range polarization gradient-related interactions leading to both an upper and a lower bound to the length scale at which these states can be observed. We found that the critical length is related to the intrinsic domain wall width, which could serve as a simple intuitive design rule for the discovery of novel ultrafine topological structures in ferroic systems.

Original language	English
Pages (from-to)	2246-2252
Number of pages	7
Journal	Nano Letters
Volume	17
Issue number	4
DOIs	https://doi.org/10.1021/acs.nanolett.6b04875
State	Published - Apr 12 2017
Externally published	Yes

Funding

The work is supported by U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award FG02-07ER46417 (L.-Q.C., F.X. and J.B.). Z.H. acknowledges the support by NSF-MRSEC Grant DMR-1420620 and NSF-MWN Grant DMR-1210588. A.R.D. acknowledges support from the Army Research Office under Grant W911NF-14-1-0104. L.W.M. acknowledges support from the National Science Foundation under Grant DMR-1451219. A.K.Y., C.T.N., and R.R. acknowledge support from the Office of Basic Energy Sciences, U.S. Department of Energy under contract no. DE-AC02-05CH11231. L.W.M. and R.R. acknowledge support from the Gordon and Betty Moore Foundations EPiQS Initiative, Grant GBMF5307.

Funders	Funder number
NSF-MRSEC	DMR-1420620
NSF-MWN	DMR-1210588
Office of Basic Energy Sciences
National Science Foundation	DMR-1451219, DE-AC02-05CH11231, 1451219, 1210588
U.S. Department of Energy
Army Research Office	W911NF-14-1-0104
Gordon and Betty Moore Foundation	GBMF5307
Division of Materials Sciences and Engineering	FG02-07ER46417

Keywords

Ferroelectric superlattices
geometric length scale
phase-field simulations
topological structures by design
ultrafine polar vortex

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10.1021/acs.nanolett.6b04875

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title = "Stability of Polar Vortex Lattice in Ferroelectric Superlattices",

abstract = "A novel mesoscale state comprising of an ordered polar vortex lattice has been demonstrated in ferroelectric superlattices of PbTiO3/SrTiO3. Here, we employ phase-field simulations, analytical theory, and experimental observations to evaluate thermodynamic conditions and geometric length scales that are critical for the formation of such exotic vortex states. We show that the stability of these vortex lattices involves an intimate competition between long-range electrostatic, long-range elastic, and short-range polarization gradient-related interactions leading to both an upper and a lower bound to the length scale at which these states can be observed. We found that the critical length is related to the intrinsic domain wall width, which could serve as a simple intuitive design rule for the discovery of novel ultrafine topological structures in ferroic systems.",

keywords = "Ferroelectric superlattices, geometric length scale, phase-field simulations, topological structures by design, ultrafine polar vortex",

author = "Zijian Hong and Damodaran, {Anoop R.} and Fei Xue and Hsu, {Shang Lin} and Jason Britson and Yadav, {Ajay K.} and Nelson, {Christopher T.} and Wang, {Jian Jun} and Scott, {James F.} and Martin, {Lane W.} and Ramamoorthy Ramesh and Chen, {Long Qing}",

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AU - Hong, Zijian

AU - Damodaran, Anoop R.

AU - Xue, Fei

AU - Hsu, Shang Lin

AU - Britson, Jason

AU - Yadav, Ajay K.

AU - Nelson, Christopher T.

AU - Wang, Jian Jun

AU - Scott, James F.

AU - Martin, Lane W.

AU - Ramesh, Ramamoorthy

AU - Chen, Long Qing

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AB - A novel mesoscale state comprising of an ordered polar vortex lattice has been demonstrated in ferroelectric superlattices of PbTiO3/SrTiO3. Here, we employ phase-field simulations, analytical theory, and experimental observations to evaluate thermodynamic conditions and geometric length scales that are critical for the formation of such exotic vortex states. We show that the stability of these vortex lattices involves an intimate competition between long-range electrostatic, long-range elastic, and short-range polarization gradient-related interactions leading to both an upper and a lower bound to the length scale at which these states can be observed. We found that the critical length is related to the intrinsic domain wall width, which could serve as a simple intuitive design rule for the discovery of novel ultrafine topological structures in ferroic systems.

KW - Ferroelectric superlattices

KW - geometric length scale

KW - phase-field simulations

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Stability of Polar Vortex Lattice in Ferroelectric Superlattices

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