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Title: Quantification of flexoelectricity in PbTiO 3/SrTiO 3 superlattice polar vortices using machine learning and phase-field modeling

Abstract

Flexoelectricity refers to electric polarization generated by heterogeneous mechanical strains, namely strain gradients, in materials of arbitrary crystal symmetries. Despite more than 50 years of work on this effect, an accurate identification of its coupling strength remains an experimental challenge for most materials, which impedes its wide recognition. Here, we show the presence of flexoelectricity in the recently discovered polar vortices in PbTiO 3 /SrTiO 3 superlattices based on a combination of machine-learning analysis of the atomic-scale electron microscopy imaging data and phenomenological phase-field modeling. By scrutinizing the influence of flexocoupling on the global vortex structure, we match theory and experiment using computer vision methodologies to determine the flexoelectric coefficients for PbTiO 3 and SrTiO 3. Here, our findings highlight the inherent, nontrivial role of flexoelectricity in the generation of emergent complex polarization morphologies and demonstrate a viable approach to delineating this effect, conducive to the deeper exploration of both topics.

Authors:
ORCiD logo [1];  [2];  [3]; ORCiD logo [3];  [1]; ORCiD logo [3];  [4]; ORCiD logo [5];  [3]; ORCiD logo [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Science (CNMS), Inst. for Functional Imaging of Materials and Center for Nanophase Materials Science
  2. Univ. of California, Berkeley, CA (United States). Dept. of Materials Science and Engineering; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Materials Science & Technology Division
  3. Univ. of California, Berkeley, CA (United States). Dept. of Materials Science and Engineering
  4. Univ. of California, Berkeley, CA (United States). Dept. of Physics
  5. Univ. of California, Berkeley, CA (United States). Dept. of Materials Science and Engineering; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Sciences Division
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1419453
Grant/Contract Number:  
AC02-05CH11231; SC0012375; GBMF5307; W911NF-14-1-0104
Resource Type:
Accepted Manuscript
Journal Name:
Nature Communications
Additional Journal Information:
Journal Volume: 8; Journal Issue: 1; Journal ID: ISSN 2041-1723
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Structural properties; Ferroelectrics and multiferroics; Coarse-grained models

Citation Formats

Li, Q., Nelson, C. T., Hsu, S. -L., Damodaran, A. R., Li, L. -L., Yadav, A. K., McCarter, M., Martin, L. W., Ramesh, R., and Kalinin, S. V. Quantification of flexoelectricity in PbTiO3/SrTiO3 superlattice polar vortices using machine learning and phase-field modeling. United States: N. p., 2017. Web. doi:10.1038/s41467-017-01733-8.
Li, Q., Nelson, C. T., Hsu, S. -L., Damodaran, A. R., Li, L. -L., Yadav, A. K., McCarter, M., Martin, L. W., Ramesh, R., & Kalinin, S. V. Quantification of flexoelectricity in PbTiO3/SrTiO3 superlattice polar vortices using machine learning and phase-field modeling. United States. doi:10.1038/s41467-017-01733-8.
Li, Q., Nelson, C. T., Hsu, S. -L., Damodaran, A. R., Li, L. -L., Yadav, A. K., McCarter, M., Martin, L. W., Ramesh, R., and Kalinin, S. V. Mon . "Quantification of flexoelectricity in PbTiO3/SrTiO3 superlattice polar vortices using machine learning and phase-field modeling". United States. doi:10.1038/s41467-017-01733-8. https://www.osti.gov/servlets/purl/1419453.
@article{osti_1419453,
title = {Quantification of flexoelectricity in PbTiO3/SrTiO3 superlattice polar vortices using machine learning and phase-field modeling},
author = {Li, Q. and Nelson, C. T. and Hsu, S. -L. and Damodaran, A. R. and Li, L. -L. and Yadav, A. K. and McCarter, M. and Martin, L. W. and Ramesh, R. and Kalinin, S. V.},
abstractNote = {Flexoelectricity refers to electric polarization generated by heterogeneous mechanical strains, namely strain gradients, in materials of arbitrary crystal symmetries. Despite more than 50 years of work on this effect, an accurate identification of its coupling strength remains an experimental challenge for most materials, which impedes its wide recognition. Here, we show the presence of flexoelectricity in the recently discovered polar vortices in PbTiO3 /SrTiO3 superlattices based on a combination of machine-learning analysis of the atomic-scale electron microscopy imaging data and phenomenological phase-field modeling. By scrutinizing the influence of flexocoupling on the global vortex structure, we match theory and experiment using computer vision methodologies to determine the flexoelectric coefficients for PbTiO3 and SrTiO3. Here, our findings highlight the inherent, nontrivial role of flexoelectricity in the generation of emergent complex polarization morphologies and demonstrate a viable approach to delineating this effect, conducive to the deeper exploration of both topics.},
doi = {10.1038/s41467-017-01733-8},
journal = {Nature Communications},
number = 1,
volume = 8,
place = {United States},
year = {2017},
month = {11}
}

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Works referenced in this record:

Spontaneous Vortex Nanodomain Arrays at Ferroelectric Heterointerfaces
journal, February 2011

  • Nelson, Christopher T.; Winchester, Benjamin; Zhang, Yi
  • Nano Letters, Vol. 11, Issue 2
  • DOI: 10.1021/nl1041808

Phase-Field Modeling of Domain Structure Energetics and Evolution in Ferroelectric Thin Films
journal, April 2010

  • Kontsos, Antonios; Landis, Chad M.
  • Journal of Applied Mechanics, Vol. 77, Issue 4
  • DOI: 10.1115/1.4000925

Observation of Nanoscale 180 ° Stripe Domains in Ferroelectric P b T i O 3 Thin Films
journal, July 2002


Finite-temperature flexoelectricity in ferroelectric thin films from first principles
journal, March 2012


Flexoelectric Effect in Solids
journal, July 2013


Observation of polar vortices in oxide superlattices
journal, January 2016

  • Yadav, A. K.; Nelson, C. T.; Hsu, S. L.
  • Nature, Vol. 530, Issue 7589
  • DOI: 10.1038/nature16463

Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning
journal, February 2007


Mechanical Writing of Ferroelectric Polarization
journal, April 2012


Atomic-scale evolution of modulated phases at the ferroelectric–antiferroelectric morphotropic phase boundary controlled by flexoelectric interaction
journal, January 2012

  • Borisevich, A. Y.; Eliseev, E. A.; Morozovska, A. N.
  • Nature Communications, Vol. 3, Issue 1
  • DOI: 10.1038/ncomms1778

Flexoelectricity and ferroelectric domain wall structures: Phase-field modeling and DFT calculations
journal, May 2014


Coupling of electrical and mechanical switching in nanoscale ferroelectrics
journal, November 2015

  • Cao, Ye; Li, Qian; Chen, Long-Qing
  • Applied Physics Letters, Vol. 107, Issue 20
  • DOI: 10.1063/1.4935977

Thin-film ferroelectric materials and their applications
journal, November 2016


Enhanced electromechanical response of ferroelectrics due to charged domain walls
journal, January 2012

  • Sluka, Tomas; Tagantsev, Alexander K.; Damjanovic, Dragan
  • Nature Communications, Vol. 3, Issue 1
  • DOI: 10.1038/ncomms1751

Flexoelectric rotation of polarization in ferroelectric thin films
journal, October 2011

  • Catalan, G.; Lubk, A.; Vlooswijk, A. H. G.
  • Nature Materials, Vol. 10, Issue 12
  • DOI: 10.1038/nmat3141

Big–deep–smart data in imaging for guiding materials design
journal, September 2015

  • Kalinin, Sergei V.; Sumpter, Bobby G.; Archibald, Richard K.
  • Nature Materials, Vol. 14, Issue 10
  • DOI: 10.1038/nmat4395

Clustering by Passing Messages Between Data Points
journal, February 2007


Strain-Gradient-Induced Polarization in SrTiO 3 Single Crystals
journal, October 2007


Fundamentals of flexoelectricity in solids
journal, October 2013


Breaking of macroscopic centric symmetry in paraelectric phases of ferroelectric materials and implications for flexoelectricity
journal, November 2014

  • Biancoli, Alberto; Fancher, Chris M.; Jones, Jacob L.
  • Nature Materials, Vol. 14, Issue 2
  • DOI: 10.1038/nmat4139

Nanoscale mechanical switching of ferroelectric polarization via flexoelectricity
journal, January 2015

  • Gu, Yijia; Hong, Zijian; Britson, Jason
  • Applied Physics Letters, Vol. 106, Issue 2
  • DOI: 10.1063/1.4905837

First-principles theory and calculation of flexoelectricity
journal, November 2013


Image Quality Assessment: From Error Visibility to Structural Similarity
journal, April 2004

  • Wang, Z.; Bovik, A. C.; Sheikh, H. R.
  • IEEE Transactions on Image Processing, Vol. 13, Issue 4
  • DOI: 10.1109/TIP.2003.819861

Neutron-Scattering Study of Soft Modes in Cubic BaTi O 3
journal, July 1971


Enhanced flexoelectric-like response in oxide semiconductors
journal, September 2016

  • Narvaez, Jackeline; Vasquez-Sancho, Fabian; Catalan, Gustau
  • Nature, Vol. 538, Issue 7624
  • DOI: 10.1038/nature19761

Flexocoupling impact on the generalized susceptibility and soft phonon modes in the ordered phase of ferroics
journal, September 2015

  • Morozovska, Anna N.; Vysochanskii, Yulian M.; Varenyk, Oleksandr V.
  • Physical Review B, Vol. 92, Issue 9
  • DOI: 10.1103/PhysRevB.92.094308

In Situ Observation of Oxygen Vacancy Dynamics and Ordering in the Epitaxial LaCoO 3 System
journal, June 2017


Observation of a periodic array of flux-closure quadrants in strained ferroelectric PbTiO3 films
journal, April 2015


Unified ab initio formulation of flexoelectricity and strain-gradient elasticity
journal, June 2016


Dielectric model of point charge defects in insulating paraelectric perovskites
journal, November 2011

  • Buniatian, V.; Martirosyan, N.; Vorobiev, A.
  • Journal of Applied Physics, Vol. 110, Issue 9
  • DOI: 10.1063/1.3660376

Piezoelectricity and flexoelectricity in crystalline dielectrics
journal, October 1986


Phase-Field Method of Phase Transitions/Domain Structures in Ferroelectric Thin Films: A Review
journal, June 2008


Giant Flexoelectric Effect in Ferroelectric Epitaxial Thin Films
journal, July 2011


Enhancement of the anisotropic photocurrent in ferroelectric oxides by strain gradients
journal, August 2015

  • Chu, Kanghyun; Jang, Byung-Kweon; Sung, Ji Ho
  • Nature Nanotechnology, Vol. 10, Issue 11
  • DOI: 10.1038/nnano.2015.191

Influence of flexoelectric coupling on domain patterns in ferroelectrics
journal, May 2014


First-principles theory of frozen-ion flexoelectricity
journal, November 2011


Effect of substrate constraint on the stability and evolution of ferroelectric domain structures in thin films
journal, January 2002


A modified Landau–Devonshire thermodynamic potential for strontium titanate
journal, June 2010

  • Sheng, G.; Li, Y. L.; Zhang, J. X.
  • Applied Physics Letters, Vol. 96, Issue 23
  • DOI: 10.1063/1.3442915

The origin of antiferroelectricity in PbZrO3
journal, July 2013

  • Tagantsev, A. K.; Vaideeswaran, K.; Vakhrushev, S. B.
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms3229

Stability of Polar Vortex Lattice in Ferroelectric Superlattices
journal, March 2017


    Works referencing / citing this record:

    Flexoelectricity in ferroelectric materials
    journal, September 2019


    Flexoelectricity in ferroelectric materials
    journal, September 2019