Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures

Tai, Jung-Shen B.; Smalyukh, Ivan I.

doi:10.1103/PhysRevLett.121.187201

Title: Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures

Journal Article · Tue Oct 30 00:00:00 EDT 2018 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.121.187201· OSTI ID:1594985

Tai, Jung-Shen B. ^[1]; Smalyukh, Ivan I. ^[1]

Univ. of Colorado, Boulder, CO (United States)

Two-dimensional topological solitons, commonly called Skyrmions, are extensively studied in solid-state magnetic nanostructures and promise many spintronics applications. However, three-dimensional topological solitons dubbed hopfions have not been demonstrated as stable spatially localized structures in solid-state magnetic materials. Here we model the existence of such static solitons with different Hopf index values in noncentrosymmetric solid magnetic nanostructures with a perpendicular interfacial magnetic anisotropy. We show how this surface anisotropy, along with the Dzyaloshinskii-Moriya interactions and the geometry of nanostructures, stabilize hopfions. We show knots in emergent field lines and computer simulate Lorentz transmission electron microscopy images of such solitonic configurations to guide their experimental discovery in magnetic solids.

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Research Organization:: Univ. of Colorado, Boulder, CO (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE

Grant/Contract Number:: SC0019293; ER46921; SC0010305

OSTI ID:: 1594985

Alternate ID(s):: OSTI ID: 1479857

Journal Information:: Physical Review Letters, Vol. 121, Issue 18; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 63 works

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References (55)

Landau–de Gennes modelling of nematic liquid crystal colloids Ravnik, Miha; Žumer, Slobodan Liquid Crystals, Vol. 36, Issue 10-11 https://doi.org/10.1080/02678290903056095	journal	August 2009
Knots in the Skyrme–Faddeev model Sutcliffe, Paul Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 463, Issue 2087 https://doi.org/10.1098/rspa.2007.0038	journal	August 2007
Skyrmions on the track Fert, Albert; Cros, Vincent; Sampaio, João Nature Nanotechnology, Vol. 8, Issue 3 https://doi.org/10.1038/nnano.2013.29	journal	March 2013
An Expression of Hopf's Invariant as an Integral Whitehead, J. H. C. Proceedings of the National Academy of Sciences, Vol. 33, Issue 5 https://doi.org/10.1073/pnas.33.5.117	journal	May 1947
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
Partially Dual Variables in SU(2) Yang-Mills Theory Faddeev, Ludvig; Niemi, Antti J. Physical Review Letters, Vol. 82, Issue 8 https://doi.org/10.1103/PhysRevLett.82.1624	journal	February 1999
Manipulation of the spin helix in FeGe thin films and FeGe/Fe multilayers Porter, Nicholas A.; Spencer, Charles S.; Temple, Rowan C. Physical Review B, Vol. 92, Issue 14 https://doi.org/10.1103/PhysRevB.92.144402	journal	October 2015
Perpendicular magnetic anisotropy at transition metal/oxide interfaces and applications Dieny, B.; Chshiev, M. Reviews of Modern Physics, Vol. 89, Issue 2 https://doi.org/10.1103/RevModPhys.89.025008	journal	June 2017
Thermodynamically stable magnetic vortex states in magnetic crystals Bogdanov, A.; Hubert, A. Journal of Magnetism and Magnetic Materials, Vol. 138, Issue 3 https://doi.org/10.1016/0304-8853(94)90046-9	journal	December 1994
Extended Skyrmion Phase in Epitaxial $FeGe (111)$ Thin Films Huang, S. X.; Chien, C. L. Physical Review Letters, Vol. 108, Issue 26 https://doi.org/10.1103/PhysRevLett.108.267201	journal	June 2012
Hidden symmetry and knot solitons in a charged two-condensate Bose system Babaev, Egor; Faddeev, Ludvig D.; Niemi, Antti J. Physical Review B, Vol. 65, Issue 10 https://doi.org/10.1103/PhysRevB.65.100512	journal	February 2002
Linear momentum in ferromagnets Volovik, G. E. Journal of Physics C: Solid State Physics, Vol. 20, Issue 7 https://doi.org/10.1088/0022-3719/20/7/003	journal	March 1987
Dynamical toroidal Hopfions in a ferromagnet with easy-axis anisotropy Borisov, A. B.; Rybakov, F. N. JETP Letters, Vol. 90, Issue 7 https://doi.org/10.1134/S0021364009190102	journal	December 2009
Knots as Stable Soliton Solutions in a Three-Dimensional Classical Field Theory Battye, Richard A.; Sutcliffe, P. M. Physical Review Letters, Vol. 81, Issue 22 https://doi.org/10.1103/PhysRevLett.81.4798	journal	November 1998
Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe Yu, X. Z.; Kanazawa, N.; Onose, Y. Nature Materials, Vol. 10, Issue 2 https://doi.org/10.1038/nmat2916	journal	December 2010
Dynamics of Skyrmion Crystals in Metallic Thin Films Zang, Jiadong; Mostovoy, Maxim; Han, Jung Hoon Physical Review Letters, Vol. 107, Issue 13 https://doi.org/10.1103/PhysRevLett.107.136804	journal	September 2011
Topological Solitons Manton, Nicholas; Sutcliffe, Paul https://doi.org/10.1017/CBO9780511617034	book	January 2010
Topological properties and dynamics of magnetic skyrmions Nagaosa, Naoto; Tokura, Yoshinori Nature Nanotechnology, Vol. 8, Issue 12 https://doi.org/10.1038/nnano.2013.243	journal	December 2013
Spin-wave spectroscopy of the Dzyaloshinskii-Moriya interaction in room-temperature chiral magnets hosting skyrmions Takagi, R.; Morikawa, D.; Karube, K. Physical Review B, Vol. 95, Issue 22 https://doi.org/10.1103/PhysRevB.95.220406	journal	June 2017
Scattering of knotted vortices (Hopfions) in the Faddeev–Skyrme model Hietarinta, J.; Palmu, J.; Jäykkä, J. New Journal of Physics, Vol. 14, Issue 1 https://doi.org/10.1088/1367-2630/14/1/013013	journal	January 2012
Real-space observation of a two-dimensional skyrmion crystal Yu, X. Z.; Onose, Y.; Kanazawa, N. Nature, Vol. 465, Issue 7300 https://doi.org/10.1038/nature09124	journal	June 2010
Observation of the magnetic flux and three-dimensional structure of skyrmion lattices by electron holography Park, Hyun Soon; Yu, Xiuzhen; Aizawa, Shinji Nature Nanotechnology, Vol. 9, Issue 5 https://doi.org/10.1038/nnano.2014.52	journal	April 2014
Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals Tai, Jung-Shen B.; Ackerman, Paul J.; Smalyukh, Ivan I. Proceedings of the National Academy of Sciences, Vol. 115, Issue 5 https://doi.org/10.1073/pnas.1716887115	journal	January 2018
Quantitative Fresnel Lorentz microscopy and the transport of intensity equation McVitie, S.; Cushley, M. Ultramicroscopy, Vol. 106, Issue 4-5 https://doi.org/10.1016/j.ultramic.2005.12.001	journal	March 2006
A new class of chiral materials hosting magnetic skyrmions beyond room temperature Tokunaga, Y.; Yu, X. Z.; White, J. S. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms8638	journal	July 2015
Skyrmion Knots in Frustrated Magnets Sutcliffe, Paul Physical Review Letters, Vol. 118, Issue 24 https://doi.org/10.1103/PhysRevLett.118.247203	journal	June 2017
Experimental observation of chiral magnetic bobbers in B20-type FeGe Zheng, Fengshan; Rybakov, Filipp N.; Borisov, Aleksandr B. Nature Nanotechnology, Vol. 13, Issue 6 https://doi.org/10.1038/s41565-018-0093-3	journal	April 2018
Skyrmion Lattice in a Chiral Magnet Muhlbauer, S.; Binz, B.; Jonietz, F. Science, Vol. 323, Issue 5916 https://doi.org/10.1126/science.1166767	journal	February 2009
Unwinding of a Skyrmion Lattice by Magnetic Monopoles Milde, P.; Kohler, D.; Seidel, J. Science, Vol. 340, Issue 6136 https://doi.org/10.1126/science.1234657	journal	May 2013
Comments on Nonlinear Wave Equations as Models for Elementary Particles Derrick, G. H. Journal of Mathematical Physics, Vol. 5, Issue 9 https://doi.org/10.1063/1.1704233	journal	September 1964
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
A strategy for the design of skyrmion racetrack memories Tomasello, R.; Martinez, E.; Zivieri, R. Scientific Reports, Vol. 4, Issue 1 https://doi.org/10.1038/srep06784	journal	October 2014
Control of morphology and formation of highly geometrically confined magnetic skyrmions Jin, Chiming; Li, Zi-An; Kovács, András Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15569	journal	June 2017
Vortex rings in ferromagnets: Numerical simulations of the time-dependent three-dimensional Landau-Lifshitz equation Sutcliffe, Paul Physical Review B, Vol. 76, Issue 18 https://doi.org/10.1103/PhysRevB.76.184439	journal	November 2007
Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids Smalyukh, Ivan I.; Lansac, Yves; Clark, Noel A. Nature Materials, Vol. 9, Issue 2 https://doi.org/10.1038/nmat2592	journal	December 2009
Temperature and Magnetic Field Dependence of the Internal and Lattice Structures of Skyrmions by Off-Axis Electron Holography Shibata, K.; Kovács, A.; Kiselev, N. S. Physical Review Letters, Vol. 118, Issue 8 https://doi.org/10.1103/PhysRevLett.118.087202	journal	February 2017
Diversity of Knot Solitons in Liquid Crystals Manifested by Linking of Preimages in Torons and Hopfions Ackerman, Paul J.; Smalyukh, Ivan I. Physical Review X, Vol. 7, Issue 1 https://doi.org/10.1103/PhysRevX.7.011006	journal	January 2017
Chiral modulations and reorientation effects in MnSi thin films Karhu, E. A.; Rößler, U. K.; Bogdanov, A. N. Physical Review B, Vol. 85, Issue 9 https://doi.org/10.1103/PhysRevB.85.094429	journal	March 2012
Propagating Magnetic Vortex Rings in Ferromagnets Cooper, N. R. Physical Review Letters, Vol. 82, Issue 7 https://doi.org/10.1103/PhysRevLett.82.1554	journal	February 1999
Generalization of the Landau-Lifshitz-Gilbert Equation for Conducting Ferromagnets Zhang, Shufeng; Zhang, Steven S. -L. Physical Review Letters, Vol. 102, Issue 8 https://doi.org/10.1103/PhysRevLett.102.086601	journal	February 2009
Magnetic anisotropy in metallic multilayers Johnson, M. T.; Bloemen, P. J. H.; Broeder, F. J. A. den Reports on Progress in Physics, Vol. 59, Issue 11 https://doi.org/10.1088/0034-4885/59/11/002	journal	November 1996
Stable Skyrmions in Two-Component Bose-Einstein Condensates Battye, Richard A.; Cooper, N. R.; Sutcliffe, Paul M. Physical Review Letters, Vol. 88, Issue 8 https://doi.org/10.1103/PhysRevLett.88.080401	journal	February 2002
Skyrmionic magnetization configurations at chiral magnet/ferromagnet heterostructures Kawaguchi, Yuki; Tanaka, Yukio; Nagaosa, Naoto Physical Review B, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevB.93.064416	journal	February 2016
Selecta Heinz hopf James, I. M. Journal of the London Mathematical Society, Vol. s1-40, Issue 1 https://doi.org/10.1112/jlms/s1-40.1.755	journal	January 1965
Topological solitons Shnir, Ya. M. Physics of Particles and Nuclei Letters, Vol. 9, Issue 9-10 https://doi.org/10.1134/s1547477112070151	journal	December 2012
Selecta Heinz Hopf. Massey, W. S. The American Mathematical Monthly, Vol. 73, Issue 4 https://doi.org/10.2307/2315446	journal	April 1966
Knots in the Skyrme-Faddeev model Sutcliffe, Paul arXiv https://doi.org/10.48550/arxiv.0705.1468	text	January 2007
Skyrmion Lattice in a Chiral Magnet Mühlbauer, S.; Binz, B.; Jonietz, F. arXiv https://doi.org/10.48550/arxiv.0902.1968	text	January 2009
Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy Borisov, A. B.; Rybakov, F. N. arXiv https://doi.org/10.48550/arxiv.0911.0451	text	January 2009
Dynamics of Skyrmion Crystals in Metallic Thin Films Zang, Jiadong; Mostovoy, Maxim; Han, Jung Hoon arXiv https://doi.org/10.48550/arxiv.1102.5384	text	January 2011
A new class of chiral materials hosting magnetic skyrmions beyond room temperature Tokunaga, Y.; Yu, X. Z.; White, J. S. arXiv https://doi.org/10.48550/arxiv.1503.05651	text	January 2015
Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions Ackerman, P. J.; Smalyukh, I. I. arXiv https://doi.org/10.48550/arxiv.1704.08196	text	January 2017
Skyrmion knots in frustrated magnets Sutcliffe, Paul arXiv https://doi.org/10.48550/arxiv.1705.10966	text	January 2017
Hidden symmetry and knot solitons in a charged two-condensate Bose system Babaev, Egor; Faddeev, Ludvig D.; Niemi, Antti J. arXiv https://doi.org/10.48550/arxiv.cond-mat/0106152	text	January 2001
Partially Dual variables in SU(2) Yang-Mills Theory Faddeev, Ludvig; Niemi, Antti J. arXiv https://doi.org/10.48550/arxiv.hep-th/9807069	text	January 1998

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