Three-dimensional imaging of vortex structure in a ferroelectric nanoparticle driven by an electric field

Karpov, D.; Liu, Z.; Rolo, T. dos Santos; Harder, R.; Balachandran, P. V.; Xue, D.; Lookman, T.; Fohtung, E.

doi:10.1038/s41467-017-00318-9

Title: Three-dimensional imaging of vortex structure in a ferroelectric nanoparticle driven by an electric field

Journal Article · 16 August 2017 · Nature Communications

DOI: https://doi.org/10.1038/s41467-017-00318-9 · OSTI ID:1624043

^[1]; Liu, Z. ^[2];

^[3]; Harder, R. ^[4]; Balachandran, P. V. ^[5];

^[6]; Lookman, T. ^[5];

^[7]

New Mexico State Univ., Las Cruces, NM (United States). Dept. of Physics; National Research Tomsk Polytechnic Univ., Tomsk (Russia). Dept. of General Physics, Physical-Technical Inst.; DOE/OSTI
Harbin Inst. of Technology (China). Condensed Matter Science and Technology Inst., School of Science; Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Karlsruhe Inst. of Technology (KIT) Garmisch-Partenkirchen (Germany). Inst. for Photon Science and Synchrotron Radiation
Argonne National Lab. (ANL), Argonne, IL (United States). Advanced Photon Source (APS)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Xi'an Jiaotong Univ., Xian (China). State Key Lab. for Mechanical Behavior of Materials
New Mexico State Univ., Las Cruces, NM (United States). Dept. of Physics; Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Topological defects of spontaneous polarization are extensively studied as templates for unique physical phenomena and in the design of reconfigurable electronic devices. Experimental investigations of the complex topologies of polarization have been limited to surface phenomena, which has restricted the probing of the dynamic volumetric domain morphology in operando. Here, we utilize Bragg coherent diffractive imaging of a single BaTiO₃ nanoparticle in a composite polymer/ferroelectric capacitor to study the behavior of a three-dimensional vortex formed due to competing interactions involving ferroelectric domains. Our investigation of the structural phase transitions under the influence of an external electric field shows a mobile vortex core exhibiting a reversible hysteretic transformation path. We also study the toroidal moment of the vortex under the action of the field. Our results open avenues for the study of the structure and evolution of polar vortices and other topological structures in operando in functional materials under cross field configurations.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States). Advanced Photon Source (APS)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); US Air Force Office of Scientific Research (AFOSR); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1624043

Journal Information:: Nature Communications, Journal Name: Nature Communications Journal Issue: 1 Vol. 8; ISSN 2041-1723

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (69)

Differential stress induced by thiol adsorption on facetted nanocrystals Watari, Moyu; McKendry, Rachel A.; Vögtli, Manuel Nature Materials, Vol. 10, Issue 11 https://doi.org/10.1038/nmat3124	journal	September 2011
Selective coherent x-ray diffractive imaging of displacement fields in (Ga,Mn)As/GaAs periodic wires Minkevich, A. A.; Fohtung, E.; Slobodskyy, T. Physical Review B, Vol. 84, Issue 5 https://doi.org/10.1103/PhysRevB.84.054113	journal	August 2011
Synthesis of Monodisperse Nanoparticles of Barium Titanate: Toward a Generalized Strategy of Oxide Nanoparticle Synthesis O'Brien, Stephen; Brus, Louis; Murray, Christopher B. Journal of the American Chemical Society, Vol. 123, Issue 48 https://doi.org/10.1021/ja011414a	journal	December 2001
Synthesis of Single-Crystalline Perovskite Nanorods Composed of Barium Titanate and Strontium Titanate Urban, Jeffrey J.; Yun, Wan Soo; Gu, Qian Journal of the American Chemical Society, Vol. 124, Issue 7, p. 1186-1187 https://doi.org/10.1021/ja017694b	journal	February 2002
Shapes and vorticities of superfluid helium nanodroplets Gomez, L. F.; Ferguson, K. R.; Cryan, J. P. Science, Vol. 345, Issue 6199 https://doi.org/10.1126/science.1252395	journal	August 2014
Unusual phase transitions in ferroelectric nanodisks and nanorods Naumov, Ivan I.; Bellaiche, L.; Fu, Huaxiang Nature, Vol. 432, Issue 7018 https://doi.org/10.1038/nature03107	journal	December 2004
Probing Strain in Bent Semiconductor Nanowires with Raman Spectroscopy Chen, Jianing; Conache, Gabriela; Pistol, Mats-Erik Nano Letters, Vol. 10, Issue 4 https://doi.org/10.1021/nl904040y	journal	April 2010
Electrically Conductive Epoxy Adhesives Sancaktar, Erol; Bai, Lan Polymers, Vol. 3, Issue 1 https://doi.org/10.3390/polym3010427	journal	February 2011
Surface effects and ferroelectric phase transitions in BaTiO 3 ultrathin films Tinte, S.; Stachiotti, M. G. Physical Review B, Vol. 64, Issue 23 https://doi.org/10.1103/PhysRevB.64.235403	journal	November 2001
Sol−Gel Synthesis of Free-Standing Ferroelectric Lead Zirconate Titanate Nanoparticles Liu, Chao; Zou, Bingsuo; Rondinone, Adam J. Journal of the American Chemical Society, Vol. 123, Issue 18, p. 4344-4345 https://doi.org/10.1021/ja001893y	journal	May 2001
Phase field simulations of stress controlling the vortex domain structures in ferroelectric nanosheets Chen, W. J.; Zheng, Yue; Wang, Biao Applied Physics Letters, Vol. 100, Issue 6 https://doi.org/10.1063/1.3681379	journal	February 2012
Ferroelectric tunnel junctions for information storage and processing Garcia, Vincent; Bibes, Manuel Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5289	journal	July 2014
Coherent X-ray diffraction imaging of strain at the nanoscale Robinson, Ian; Harder, Ross Nature Materials, Vol. 8, Issue 4 https://doi.org/10.1038/nmat2400	journal	April 2009
From Grain Boundaries to Single Defects: A Review of Coherent Methods for Materials Imaging in the X-ray Sciences Abbey, Brian JOM, Vol. 65, Issue 9 https://doi.org/10.1007/s11837-013-0702-4	journal	August 2013
Nanoshell tubes of ferroelectric lead zirconate titanate and barium titanate Luo, Yun; Szafraniak, Izabela; Zakharov, Nikolai D. Applied Physics Letters, Vol. 83, Issue 3 https://doi.org/10.1063/1.1592013	journal	July 2003
Domain evolution in epitaxial (001) Pb(Zr,Ti)O 3 ultrathin films under an electric field applied along the [111] direction Sichuga, D.; Bellaiche, L. Physical Review B, Vol. 85, Issue 21 https://doi.org/10.1103/PhysRevB.85.214111	journal	June 2012
Some implications of a theorem due to Shannon Sayre, D. Acta Crystallographica, Vol. 5, Issue 6 https://doi.org/10.1107/S0365110X52002276	journal	November 1952
Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects Miao, J.; Sayre, D.; Chapman, H. N. Journal of the Optical Society of America A, Vol. 15, Issue 6 https://doi.org/10.1364/JOSAA.15.001662	journal	January 1998
Ferroelectric Memories Scott, J. F.; Paz de Araujo, C. A. Science, Vol. 246, Issue 4936 https://doi.org/10.1126/science.246.4936.1400	journal	December 1989
Synthesis of Monodisperse Nanoparticles of Barium Titanate: Toward a Generalized Strategy of Oxide Nanoparticle Synthesis O'Brien, Stephen; Brus, Louis; Murray, Christopher B. Journal of the American Chemical Society, Vol. 123, Issue 48 https://doi.org/10.1021/ja011414a	journal	December 2001
Ferroelectric Properties of Individual Barium Titanate Nanowires Investigated by Scanned Probe Microscopy Yun, Wan Soo; Urban, Jeffrey J.; Gu, Qian Nano Letters, Vol. 2, Issue 5, p. 447-450 https://doi.org/10.1021/nl015702g	journal	May 2002
Direct structural determination in ultrathin ferroelectric films by analysis of synchrotron x-ray scattering measurements Fong, D. D.; Cionca, C.; Yacoby, Y. Physical Review B, Vol. 71, Issue 14 https://doi.org/10.1103/PhysRevB.71.144112	journal	April 2005
A phenomenological thermodynamic potential for BaTiO3 single crystals Li, Y. L.; Cross, L. E.; Chen, L. Q. Journal of Applied Physics, Vol. 98, Issue 6 https://doi.org/10.1063/1.2042528	journal	September 2005
Ab initio study of ferroelectricity in BaTiO 3 nanowires Pilania, G.; Alpay, S. P.; Ramprasad, R. Physical Review B, Vol. 80, Issue 1 https://doi.org/10.1103/PhysRevB.80.014113	journal	July 2009
Charge Density Wave Dislocation as Revealed by Coherent X-Ray Diffraction Le Bolloc’h, D.; Ravy, S.; Dumas, J. Physical Review Letters, Vol. 95, Issue 11 https://doi.org/10.1103/PhysRevLett.95.116401	journal	September 2005
Observation of polar vortices in oxide superlattices Yadav, A. K.; Nelson, C. T.; Hsu, S. L. Nature, Vol. 530, Issue 7589 https://doi.org/10.1038/nature16463	journal	January 2016
Ferroelectric order in individual nanometre-scale crystals Polking, Mark J.; Han, Myung-Geun; Yourdkhani, Amin Nature Materials, Vol. 11, Issue 8 https://doi.org/10.1038/nmat3371	journal	July 2012
The Physics of Ferroelectric Memories Auciello, Orlando; Scott, James F.; Ramesh, Ramamoorthy Physics Today, Vol. 51, Issue 7 https://doi.org/10.1063/1.882324	journal	July 1998
Ferroelectric Properties of Individual Barium Titanate Nanowires Investigated by Scanned Probe Microscopy Yun, Wan Soo; Urban, Jeffrey J.; Gu, Qian Nano Letters, Vol. 2, Issue 5, p. 447-450 https://doi.org/10.1021/nl015702g	journal	May 2002
Local, Nonvolatile Electronic Writing of Epitaxial Pb(Zr0.52Ti0.48)O3/SrRuO3 Heterostructures Ahn, C. H. Science, Vol. 276, Issue 5315 https://doi.org/10.1126/science.276.5315.1100	journal	May 1997
Phase field simulations of stress controlling the vortex domain structures in ferroelectric nanosheets Chen, W. J.; Zheng, Yue; Wang, Biao Applied Physics Letters, Vol. 100, Issue 6 https://doi.org/10.1063/1.3681379	journal	February 2012
Electrically Conductive Epoxy Adhesives Sancaktar, Erol; Bai, Lan Polymers, Vol. 3, Issue 1 https://doi.org/10.3390/polym3010427	journal	February 2011
Differential stress induced by thiol adsorption on facetted nanocrystals Watari, Moyu; McKendry, Rachel A.; Vögtli, Manuel Nature Materials, Vol. 10, Issue 11 https://doi.org/10.1038/nmat3124	journal	September 2011
Quantitative imaging of flux vortices in the type-II superconductor MgB 2 using cryo-Lorentz transmission electron microscopy Cottet, M. J. G.; Cantoni, M.; Mansart, B. Physical Review B, Vol. 88, Issue 1 https://doi.org/10.1103/PhysRevB.88.014505	journal	July 2013
Unusual phase transitions in ferroelectric nanodisks and nanorods Naumov, Ivan I.; Bellaiche, L.; Fu, Huaxiang Nature, Vol. 432, Issue 7018 https://doi.org/10.1038/nature03107	journal	December 2004
A ferroelectric memristor Chanthbouala, André; Garcia, Vincent; Cherifi, Ryan O. Nature Materials, Vol. 11, Issue 10 https://doi.org/10.1038/nmat3415	journal	September 2012
Nanoshell tubes of ferroelectric lead zirconate titanate and barium titanate Luo, Yun; Szafraniak, Izabela; Zakharov, Nikolai D. Applied Physics Letters, Vol. 83, Issue 3 https://doi.org/10.1063/1.1592013	journal	July 2003
Observation of polar vortices in oxide superlattices Yadav, A. K.; Nelson, C. T.; Hsu, S. L. Nature, Vol. 530, Issue 7589 https://doi.org/10.1038/nature16463	journal	January 2016
First-Principles Study of Piezoelectricity in PbTiO 3 Sághi-Szabó, Gotthard; Cohen, Ronald E.; Krakauer, Henry Physical Review Letters, Vol. 80, Issue 19 https://doi.org/10.1103/PhysRevLett.80.4321	journal	May 1998
In situ imaging of vortices in Bose-Einstein condensates Wilson, Kali E.; Newman, Zachary L.; Lowney, Joseph D. Physical Review A, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevA.91.023621	journal	February 2015
Local, Nonvolatile Electronic Writing of Epitaxial Pb(Zr0.52Ti0.48)O3/SrRuO3 Heterostructures Ahn, C. H. Science, Vol. 276, Issue 5315 https://doi.org/10.1126/science.276.5315.1100	journal	May 1997
Vortex-to-Polarization Phase Transformation Path in Ferroelectric Pb ( ZrTi ) O 3 Nanoparticles Naumov, Ivan; Fu, Huaxiang Physical Review Letters, Vol. 98, Issue 7 https://doi.org/10.1103/PhysRevLett.98.077603	journal	February 2007
Sol−Gel Synthesis of Free-Standing Ferroelectric Lead Zirconate Titanate Nanoparticles Liu, Chao; Zou, Bingsuo; Rondinone, Adam J. Journal of the American Chemical Society, Vol. 123, Issue 18, p. 4344-4345 https://doi.org/10.1021/ja001893y	journal	May 2001
Enhanced electric conductivity at ferroelectric vortex cores in BiFeO3 Balke, Nina; Winchester, Benjamin; Ren, Wei Nature Physics, Vol. 8, Issue 1 https://doi.org/10.1038/nphys2132	journal	November 2011
Surface-Initiated Polymerization from Barium Titanate Nanoparticles for Hybrid Dielectric Capacitors Paniagua, Sergio A.; Kim, Yunsang; Henry, Katherine ACS Applied Materials & Interfaces, Vol. 6, Issue 5 https://doi.org/10.1021/am4056276	journal	February 2014
Topological phase transformations and intrinsic size effects in ferroelectric nanoparticles Mangeri, John; Espinal, Yomery; Jokisaari, Andrea Nanoscale, Vol. 9, Issue 4 https://doi.org/10.1039/C6NR09111C	journal	January 2017
Unusual Phase Transitions in Ferroelectric Nanodisks and Nanorods Naumov, Ivan I.; Bellaiche, L.; Fu, Huaxiang ChemInform, Vol. 36, Issue 9 https://doi.org/10.1002/chin.200509003	journal	March 2005
Probing Strain in Bent Semiconductor Nanowires with Raman Spectroscopy Chen, Jianing; Conache, Gabriela; Pistol, Mats-Erik Nano Letters, Vol. 10, Issue 4 https://doi.org/10.1021/nl904040y	journal	April 2010
Topological defect dynamics in operando battery nanoparticles Ulvestad, A.; Singer, A.; Clark, J. N. Science, Vol. 348, Issue 6241 https://doi.org/10.1126/science.aaa1313	journal	June 2015
Surface-Initiated Polymerization from Barium Titanate Nanoparticles for Hybrid Dielectric Capacitors Paniagua, Sergio A.; Kim, Yunsang; Henry, Katherine ACS Applied Materials & Interfaces, Vol. 6, Issue 5 https://doi.org/10.1021/am4056276	journal	February 2014
Phase retrieval algorithms: a comparison Fienup, J. R. Applied Optics, Vol. 21, Issue 15 https://doi.org/10.1364/AO.21.002758	journal	January 1982
Multilevel Data Storage Memory Using Deterministic Polarization Control Lee, Daesu; Yang, Sang Mo; Kim, Tae Heon Advanced Materials, Vol. 24, Issue 3 https://doi.org/10.1002/adma.201103679	journal	December 2011
Electrical Conductive Adhesives with Nanotechnologies Li, Yi; Lu, Daniel; Wong, C. P. https://doi.org/10.1007/978-0-387-88783-8	book	January 2010
Ferroelectric order in individual nanometre-scale crystals Polking, Mark J.; Han, Myung-Geun; Yourdkhani, Amin Nature Materials, Vol. 11, Issue 8 https://doi.org/10.1038/nmat3371	journal	July 2012
Synthesis of Single-Crystalline Perovskite Nanorods Composed of Barium Titanate and Strontium Titanate Urban, Jeffrey J.; Yun, Wan Soo; Gu, Qian Journal of the American Chemical Society, Vol. 124, Issue 7, p. 1186-1187 https://doi.org/10.1021/ja017694b	journal	February 2002
Ferroelectric Switching Dynamics of Topological Vortex Domains in a Hexagonal Manganite Han, Myung-Geun; Zhu, Yimei; Wu, Lijun Advanced Materials, Vol. 25, Issue 17 https://doi.org/10.1002/adma.201204766	journal	March 2013
Phase retrieval algorithms: a comparison Fienup, J. R. Applied Optics, Vol. 21, Issue 15 https://doi.org/10.1364/ao.21.002758	journal	January 1982
Topological defect dynamics in operando battery nanoparticles Ulvestad, A.; Singer, A.; Clark, J. N. Science, Vol. 348, Issue 6241 https://doi.org/10.1126/science.aaa1313	journal	June 2015
Ferroelectric Memories Scott, J. F.; Paz de Araujo, C. A. Science, Vol. 246, Issue 4936 https://doi.org/10.1126/science.246.4936.1400	journal	December 1989
A phenomenological thermodynamic potential for BaTiO3 single crystals Li, Y. L.; Cross, L. E.; Chen, L. Q. Journal of Applied Physics, Vol. 98, Issue 6 https://doi.org/10.1063/1.2042528	journal	September 2005
The Physics of Ferroelectric Memories Auciello, Orlando; Scott, James F.; Ramesh, Ramamoorthy Physics Today, Vol. 51, Issue 7 https://doi.org/10.1063/1.882324	journal	July 1998
Charge Density Wave Dislocation as Revealed by Coherent X-Ray Diffraction Le Bolloc’h, D.; Ravy, S.; Dumas, J. Physical Review Letters, Vol. 95, Issue 11 https://doi.org/10.1103/physrevlett.95.116401	journal	September 2005
A ferroelectric memristor Chanthbouala, André; Garcia, Vincent; Cherifi, Ryan O. arXiv https://doi.org/10.48550/arxiv.1206.3397	text	January 2012
Quantitative phase contrast tomography using coherent synchrotron radiation Cloetens, Peter; Ludwig, Wolfgang; Boller, Elodie International Symposium on Optical Science and Technology, SPIE Proceedings https://doi.org/10.1117/12.452867	conference	January 2002
Quantitative phase contrast tomography using coherent synchrotron radiation Cloetens, Peter; Ludwig, Wolfgang; Boller, Elodie International Symposium on Optical Science and Technology, SPIE Proceedings https://doi.org/10.1117/12.452867	conference	January 2002
Ferroelectric switching dynamics of topological vortex domains in a hexagonal manganite Han, Myung-Geun; Zhu, Yimei; Wu, Lijun arXiv https://doi.org/10.48550/arxiv.1303.3593	preprint	January 2013
High-resolution ab initio three-dimensional x-ray diffraction microscopy Chapman, Henry N.; Barty, Anton; Marchesini, Stefano Journal of the Optical Society of America A, Vol. 23, Issue 5 https://doi.org/10.1364/JOSAA.23.001179	journal	January 2006
Enhanced electric conductivity at ferroelectric vortex cores in BiFeO3 Balke, Nina; Winchester, Benjamin; Ren, Wei Nature Physics, Vol. 8, Issue 1 https://doi.org/10.1038/nphys2132	journal	November 2011
From Grain Boundaries to Single Defects: A Review of Coherent Methods for Materials Imaging in the X-ray Sciences Abbey, Brian JOM, Vol. 65, Issue 9 https://doi.org/10.1007/s11837-013-0702-4	journal	August 2013

Cited By (16)

Spatially resolved steady-state negative capacitance Yadav, Ajay K.; Nguyen, Kayla X.; Hong, Zijian Nature, Vol. 565, Issue 7740 https://doi.org/10.1038/s41586-018-0855-y	journal	January 2019
Intrinsic and extrinsic effects on the electrotoroidic switching in a ferroelectric notched nanodot by a homogeneous electric field Dinh-Van, Hai; Lich, Le Van; Bui, Tinh Quoc Physical Chemistry Chemical Physics, Vol. 21, Issue 45 https://doi.org/10.1039/c9cp04676c	journal	January 2019
Characterization and control of vortex and antivortex domain defects in quadrilateral ferroelectric nanodots Ding, L. L.; Ji, Ye; Zhang, X. Y. Physical Review Materials, Vol. 3, Issue 10 https://doi.org/10.1103/physrevmaterials.3.104417	journal	October 2019
Investigation of AFM-based machining of ferroelectric thin films at the nanoscale Zhang, Fengyuan; Edwards, David; Deng, Xiong Journal of Applied Physics, Vol. 127, Issue 3 https://doi.org/10.1063/1.5133018	journal	January 2020
Rotational polarization nanotopologies in BaTiO3/SrTiO3 superlattices Estandia, Saul; Sanchez, Florencio; Chisholm, Matthew F. arXiv https://doi.org/10.48550/arxiv.1911.06075	text	January 2019
Boosting Photovoltaic Output of Ferroelectric Ceramics by Optoelectric Control of Domains Bai, Yang; Vats, Gaurav; Seidel, Jan Advanced Materials, Vol. 30, Issue 43 https://doi.org/10.1002/adma.201803821	journal	September 2018
Electromechanical control of polarization vortex ordering in an interacting ferroelectric-dielectric composite dimer Mangeri, John; Alpay, S. Pamir; Nakhmanson, Serge arXiv https://doi.org/10.48550/arxiv.1901.11433	text	January 2019
Nanoscale topological defects and improper ferroelectric domains in multiferroic barium hexaferrite nanocrystals Karpov, D.; Liu, Z.; Kumar, A. Physical Review B, Vol. 100, Issue 5 https://doi.org/10.1103/physrevb.100.054432	journal	August 2019
Size, shape, and orientation dependence of the field-induced behavior in ferroelectric nanoparticles Zhu, Daopei; Mangeri, John; Wang, Ruolin Journal of Applied Physics, Vol. 125, Issue 13 https://doi.org/10.1063/1.5088864	journal	April 2019
Metastable vortex-like polarization textures in ferroelectric nanoparticles of different shapes and sizes Pitike, Krishna Chaitanya; Mangeri, John; Whitelock, Hope Journal of Applied Physics, Vol. 124, Issue 6 https://doi.org/10.1063/1.5037163	journal	August 2018
Rotational polarization nanotopologies in BaTiO ₃ /SrTiO ₃ superlattices Estandía, Saúl; Sánchez, Florencio; Chisholm, Matthew F. Nanoscale, Vol. 11, Issue 44 https://doi.org/10.1039/c9nr08050c	journal	January 2019
Bragg coherent diffractive imaging of strain at the nanoscale Karpov, Dmitry; Fohtung, Edwin Journal of Applied Physics, Vol. 125, Issue 12 https://doi.org/10.1063/1.5054294	journal	March 2019
Electromechanical control of polarization vortex ordering in an interacting ferroelectric-dielectric composite dimer Mangeri, John; Alpay, S. Pamir; Nakhmanson, Serge Applied Physics Letters, Vol. 113, Issue 9 https://doi.org/10.1063/1.5046080	journal	August 2018
Combining Nanofocused X-Rays with Electrical Measurements at the NanoMAX Beamline Chayanun, Lert; Hammarberg, Susanna; Dierks, Hanna Crystals, Vol. 9, Issue 8 https://doi.org/10.3390/cryst9080432	journal	August 2019
Crossover of polar and toroidal orders in ferroelectric nanodots with a morphotropic phase boundary and nonvolatile polar-vortex transformations Ji, Ye; Chen, W. J.; Zheng, Yue Physical Review B, Vol. 100, Issue 1 https://doi.org/10.1103/physrevb.100.014101	journal	July 2019
An efficient space-time phase field discretization for ferroelectrics Lich, Le Van; Bui, Tinh Quoc; Nguyen, Thanh-Tung Modelling and Simulation in Materials Science and Engineering, Vol. 28, Issue 2 https://doi.org/10.1088/1361-651x/ab620a	journal	January 2020

Similar Records

Enhanced electric conductivity at ferroelectric vortex cores in BiFeO3

Journal Article · 2012 · Nature Physics · OSTI ID:1039635

Balke, Nina; Winchester, Ben; Ren, Wei; +13 more

Vortex Domain Walls in Ferroelectrics

Journal Article · 2021 · Nano Letters · OSTI ID:1806304

Hong, Zijian; Das, Sujit; Nelson, Christopher; +6 more

Structure and Dynamics of Domains in Ferroelectric Nanostructures – Phase-Field Modeling (Final Technical Report)

Technical Report · 2020 · OSTI ID:1616792

Chen, Long-Qing; Cheng, Xiao-Xing; Zorn, Jacob

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Imaging techniques
Nanoparticles
Phase transitions and critical phenomena
Structural properties

Title: Three-dimensional imaging of vortex structure in a ferroelectric nanoparticle driven by an electric field

Citation Formats

References (69)

Cited By (16)

Similar Records

Related Subjects