Hopfions emerge in ferroelectrics

Luk’yanchuk, I.; Tikhonov, Y.; Razumnaya, A.; Vinokur, V. M.

doi:10.1038/s41467-020-16258-w

Hopfions emerge in ferroelectrics

Journal Article · Fri May 15 00:00:00 EDT 2020 · Nature Communications

DOI:https://doi.org/10.1038/s41467-020-16258-w· OSTI ID:1633730

Luk’yanchuk, I. ^[1]; Tikhonov, Y. ^[2]; ^[3]; ^[4]

Univ. of Picardie, Amiens (France)
Univ. of Picardie, Amiens (France); Southern Federal Univ., Rostov-on-Don (Russia)
Southern Federal Univ., Rostov-on-Don (Russia)
Argonne National Lab. (ANL), Argonne, IL (United States)

Paradigmatic knotted solitons, Hopfions, that are characterized by topological Hopf invariant, attract an intense attention in the diverse areas of physics ranging from high-energy physics, cosmology and astrophysics to biology, magneto- and hydrodynamics and condensed matter physics. Yet, while being of broad interest, they remain elusive and under-explored. Here we demonstrate that Hopfions emerge as a basic configuration of polarization field in confined ferroelectric nanoparticles. Our findings establish that Hopfions are of fundamental importance for the electromagnetic behavior of the nanocomposits and can result in advanced functionalities of these materials.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: Southern Federal University; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1633730

Journal Information:: Nature Communications, Journal Name: Nature Communications Journal Issue: 1 Vol. 11; ISSN 2041-1723

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (42)

Field-induced vortices in weakly anisotropic ferroelectrics Sené, A.; Baudry, L.; Luk’yanchuk, I. Superlattices and Microstructures, Vol. 49, Issue 3 https://doi.org/10.1016/j.spmi.2010.05.001	journal	March 2011
Ferroelectric symmetry-protected multibit memory cell Baudry, Laurent; Lukyanchuk, Igor; Vinokur, Valerii M. Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/srep42196	journal	February 2017
Abrupt appearance of the domain pattern and fatigue of thin ferroelectric films Bratkovsky, A. M. AIP Conference Proceedings https://doi.org/10.1063/1.1324458	conference	January 2000
Stability of Vortex Phases in Ferroelectric Easy-Plane Nano-Cylinders Lahoche, L.; Luk'Yanchuk, I.; Pascoli, G. Integrated Ferroelectrics, Vol. 99, Issue 1 https://doi.org/10.1080/10584580802107684	journal	June 2008
Toroidal Ferroelectricity in PbTiO 3 Nanoparticles Stachiotti, M. G.; Sepliarsky, M. Physical Review Letters, Vol. 106, Issue 13 https://doi.org/10.1103/physrevlett.106.137601	journal	March 2011
Ferroelectric Phase Transitions in Small Particles and Local Regions Levanyuk, A. P.; Blinc, R. Physical Review Letters, Vol. 111, Issue 9 https://doi.org/10.1103/physrevlett.111.097601	journal	August 2013
Reconfigurable knots and links in chiral nematic colloids Tkalec, Uroš; Ravnik, Miha; Čopar, Simon arXiv https://doi.org/10.48550/arxiv.1107.1619	text	January 2011
Ultrathin films of ferroelectric solid solutions under residual depolarizing field Kornev, Igor; Fu, Huaxiang; Bellaiche, L. arXiv https://doi.org/10.48550/arxiv.cond-mat/0403484	text	January 2004
Domains in Ferroic Crystals and Thin Films Tagantsev, Alexander K.; Cross, L. Eric; Fousek, Jan https://doi.org/10.1007/978-1-4419-1417-0	book	January 2010
Existence of invariant tori in three-dimensional measure-preserving mappings Cheng, Chong -Qing; Sun, Yi -Sui Celestial Mechanics and Dynamical Astronomy, Vol. 47, Issue 3 https://doi.org/10.1007/BF00053456	journal	January 1990
On the topological meaning of canonical Clebsch variables Kuznetsov, E. A.; Mikhailov, A. V. Physics Letters A, Vol. 77, Issue 1 https://doi.org/10.1016/0375-9601(80)90627-1	journal	April 1980
Phase-field simulations of ferroelectric/ferroelastic polarization switching Wang, Jie; Shi, San-Qiang; Chen, Long-Qing Acta Materialia, Vol. 52, Issue 3 https://doi.org/10.1016/j.actamat.2003.10.011	journal	February 2004
Modeling of ferroelectric domains in thin films and superlattices De Guerville, F.; Luk’yanchuk, I.; Lahoche, L. Materials Science and Engineering: B, Vol. 120, Issue 1-3 https://doi.org/10.1016/j.mseb.2005.02.039	journal	July 2005
Knots in electromagnetism Arrayás, M.; Bouwmeester, D.; Trueba, J. L. Physics Reports, Vol. 667 https://doi.org/10.1016/j.physrep.2016.11.001	journal	January 2017
Existence of invariant tori in volume-preserving diffeomorphisms Xia, Zhihong Ergodic Theory and Dynamical Systems, Vol. 12, Issue 3 https://doi.org/10.1017/S0143385700006969	journal	September 1992
Stable knot-like structures in classical field theory Faddeev, L.; Niemi, Antti J. Nature, Vol. 387, Issue 6628 https://doi.org/10.1038/387058a0	journal	May 1997
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
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
Discovery of stable skyrmionic state in ferroelectric nanocomposites Nahas, Y.; Prokhorenko, S.; Louis, L. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms9542	journal	October 2015
Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids Ackerman, Paul J.; Smalyukh, Ivan I. Nature Materials, Vol. 16, Issue 4 https://doi.org/10.1038/nmat4826	journal	December 2016
Let's twist again Sutcliffe, Paul Nature Materials, Vol. 16, Issue 4 https://doi.org/10.1038/nmat4883	journal	March 2017
Three-dimensional imaging of vortex structure in a ferroelectric nanoparticle driven by an electric field Karpov, D.; Liu, Z.; Rolo, T. dos Santos Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-00318-9	journal	August 2017
Observation of room-temperature polar skyrmions Das, S.; Tang, Y. L.; Hong, Z. Nature, Vol. 568, Issue 7752 https://doi.org/10.1038/s41586-019-1092-8	journal	April 2019
Harnessing ferroelectric domains for negative capacitance Luk’yanchuk, I.; Tikhonov, Y.; Sené, A. Communications Physics, Vol. 2, Issue 1 https://doi.org/10.1038/s42005-019-0121-0	journal	February 2019
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
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
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
Classification of electromagnetic and gravitational hopfions by algebraic type Thompson, Amy; Wickes, Alexander; Swearngin, Joe Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 20 https://doi.org/10.1088/1751-8113/48/20/205202	journal	April 2015
Low-dimensional ferroelectrics under different electrical and mechanical boundary conditions: Atomistic simulations Ponomareva, I.; Naumov, I. I.; Bellaiche, L. Physical Review B, Vol. 72, Issue 21 https://doi.org/10.1103/PhysRevB.72.214118	journal	December 2005
Characteristics and signatures of dipole vortices in ferroelectric nanodots: First-principles-based simulations and analytical expressions Prosandeev, S.; Bellaiche, L. Physical Review B, Vol. 75, Issue 9 https://doi.org/10.1103/PhysRevB.75.094102	journal	March 2007
Domain walls of ferroelectric BaTiO 3 within the Ginzburg-Landau-Devonshire phenomenological model Marton, P.; Rychetsky, I.; Hlinka, J. Physical Review B, Vol. 81, Issue 14 https://doi.org/10.1103/PhysRevB.81.144125	journal	April 2010
Electrodynamics of ferroelectric films with negative capacitance Luk'yanchuk, I.; Sené, A.; Vinokur, V. M. Physical Review B, Vol. 98, Issue 2 https://doi.org/10.1103/PhysRevB.98.024107	journal	July 2018
Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals Sohn, Hayley R. O.; Ackerman, Paul J.; Boyle, Timothy J. Physical Review E, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevE.97.052701	journal	May 2018
X-Ray Diffraction Studies of 180° Ferroelectric Domains in PbTiO 3 / SrTiO 3 Superlattices under an Applied Electric Field Zubko, P.; Stucki, N.; Lichtensteiger, C. Physical Review Letters, Vol. 104, Issue 18 https://doi.org/10.1103/PhysRevLett.104.187601	journal	May 2010
Toroidal Ferroelectricity in PbTiO 3 Nanoparticles Stachiotti, M. G.; Sepliarsky, M. Physical Review Letters, Vol. 106, Issue 13 https://doi.org/10.1103/PhysRevLett.106.137601	journal	March 2011
Ferroelectric Phase Transitions in Small Particles and Local Regions Levanyuk, A. P.; Blinc, R. Physical Review Letters, Vol. 111, Issue 9 https://doi.org/10.1103/PhysRevLett.111.097601	journal	August 2013
Topological Defects with Distinct Dipole Configurations in PbTiO 3 / SrTiO 3 Multilayer Films Lu, Lu; Nahas, Yousra; Liu, Ming Physical Review Letters, Vol. 120, Issue 17 https://doi.org/10.1103/PhysRevLett.120.177601	journal	April 2018
Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures Tai, Jung-Shen B.; Smalyukh, Ivan I. Physical Review Letters, Vol. 121, Issue 18 https://doi.org/10.1103/PhysRevLett.121.187201	journal	October 2018
Abrupt Appearance of the Domain Pattern and Fatigue of Thin Ferroelectric Films Bratkovsky, A. M.; Levanyuk, A. P. Physical Review Letters, Vol. 84, Issue 14 https://doi.org/10.1103/PhysRevLett.84.3177	journal	April 2000
Observation of Nanoscale 180 ° Stripe Domains in Ferroelectric P b T i O 3 Thin Films Streiffer, S. K.; Eastman, J. A.; Fong, D. D. Physical Review Letters, Vol. 89, Issue 6 https://doi.org/10.1103/PhysRevLett.89.067601	journal	July 2002
Ultrathin Films of Ferroelectric Solid Solutions under a Residual Depolarizing Field Kornev, Igor; Fu, Huaxiang; Bellaiche, L. Physical Review Letters, Vol. 93, Issue 19 https://doi.org/10.1103/PhysRevLett.93.196104	journal	November 2004
Reconfigurable Knots and Links in Chiral Nematic Colloids Tkalec, U.; Ravnik, M.; Copar, S. Science, Vol. 333, Issue 6038 https://doi.org/10.1126/science.1205705	journal	June 2011

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