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Makarov D, Volkov OM, Kákay A, Pylypovskyi OV, Budinská B, Dobrovolskiy OV. New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2101758. [PMID: 34705309 DOI: 10.1002/adma.202101758] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Revised: 05/16/2021] [Indexed: 06/13/2023]
Abstract
Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.
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Affiliation(s)
- Denys Makarov
- Helmholtz-Zentrum Dresden - Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, 01328, Dresden, Germany
| | - Oleksii M Volkov
- Helmholtz-Zentrum Dresden - Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, 01328, Dresden, Germany
| | - Attila Kákay
- Helmholtz-Zentrum Dresden - Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, 01328, Dresden, Germany
| | - Oleksandr V Pylypovskyi
- Helmholtz-Zentrum Dresden - Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, 01328, Dresden, Germany
- Kyiv Academic University, Kyiv, 03142, Ukraine
| | - Barbora Budinská
- Superconductivity and Spintronics Laboratory, Nanomagnetism and Magnonics, Faculty of Physics, University of Vienna, Vienna, 1090, Austria
| | - Oleksandr V Dobrovolskiy
- Superconductivity and Spintronics Laboratory, Nanomagnetism and Magnonics, Faculty of Physics, University of Vienna, Vienna, 1090, Austria
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Kravchuk VP, Sheka DD, Kákay A, Volkov OM, Rößler UK, van den Brink J, Makarov D, Gaididei Y. Multiplet of Skyrmion States on a Curvilinear Defect: Reconfigurable Skyrmion Lattices. PHYSICAL REVIEW LETTERS 2018; 120:067201. [PMID: 29481278 DOI: 10.1103/physrevlett.120.067201] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2017] [Revised: 08/11/2017] [Indexed: 06/08/2023]
Abstract
Typically, the chiral magnetic Skyrmion is a single-state excitation. Here we propose a system, where multiplet of Skyrmion states appears and one of these states can be the ground one. We show that the presence of a localized curvilinear defect drastically changes the magnetic properties of a thin perpendicularly magnetized ferromagnetic film. For a large enough defect amplitude a discrete set of equilibrium magnetization states appears forming a ladder of energy levels. Each equilibrium state has either a zero or a unit topological charge; i.e., topologically trivial and Skyrmion multiplets generally appear. Transitions between the levels with the same topological charge are allowed and can be utilized to encode and switch a bit of information. There is a wide range of geometrical and material parameters, where the Skyrmion level has the lowest energy. Thus, periodically arranged curvilinear defects can result in a Skyrmion lattice as the ground state.
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Affiliation(s)
- Volodymyr P Kravchuk
- Bogolyubov Institute for Theoretical Physics of National Academy of Sciences of Ukraine, 03680 Kyiv, Ukraine
- Leibniz-Institut für Festkörper- und Werkstoffforschung, IFW Dresden, D-01171 Dresden, Germany
| | - Denis D Sheka
- Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine
| | - Attila Kákay
- Helmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, 01328 Dresden, Germany
| | - Oleksii M Volkov
- Helmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, 01328 Dresden, Germany
| | - Ulrich K Rößler
- Leibniz-Institut für Festkörper- und Werkstoffforschung, IFW Dresden, D-01171 Dresden, Germany
| | - Jeroen van den Brink
- Leibniz-Institut für Festkörper- und Werkstoffforschung, IFW Dresden, D-01171 Dresden, Germany
- Institute for Theoretical Physics, TU Dresden, 01069 Dresden, Germany
| | - Denys Makarov
- Helmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, 01328 Dresden, Germany
| | - Yuri Gaididei
- Bogolyubov Institute for Theoretical Physics of National Academy of Sciences of Ukraine, 03680 Kyiv, Ukraine
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Chae SC, Horibe Y, Jeong DY, Rodan S, Lee N, Cheong SW. Self-organization, condensation, and annihilation of topological vortices and antivortices in a multiferroic. Proc Natl Acad Sci U S A 2010; 107:21366-70. [PMID: 21115846 PMCID: PMC3003016 DOI: 10.1073/pnas.1011380107] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The interaction among topological defects can induce novel phenomena such as disclination pairs in liquid crystals and superconducting vortex lattices. Nanoscale topological vortices with swirling ferroelectric, magnetic, and structural antiphase relationships were found in multiferroic h-YMnO(3). Herein, we report the discovery of intriguing, but seemingly irregular configurations of a zoo of topological vortices and antivortices. These configurations can be neatly analyzed in terms of graph theory and reflect the nature of self-organized criticality in complexity phenomena. External stimuli such as chemistry-driven or electric poling can induce the condensation and eventual annihilation of topological vortex-antivortex pairs.
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Affiliation(s)
- S. C. Chae
- Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, NJ 08854; and
| | - Y. Horibe
- Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, NJ 08854; and
| | - D. Y. Jeong
- Department of Mathematics, Soongsil University, Seoul 156-743, Korea
| | - S. Rodan
- Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, NJ 08854; and
| | - N. Lee
- Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, NJ 08854; and
| | - S.-W. Cheong
- Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, NJ 08854; and
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Kevrekidis PG, Williams FL, Bishop AR, Kevrekidis IG, Malomed BA. Coupling fields and underlying space curvature: an augmented Lagrangian approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:047602. [PMID: 12786538 DOI: 10.1103/physreve.67.047602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2002] [Indexed: 05/24/2023]
Abstract
We demonstrate a systematic implementation of coupling between a scalar field and the geometry of the space which carries the field. This naturally gives rise to a feedback mechanism between the field and the geometry. We develop a systematic model for the feedback in a general form, inspired by a specific implementation in the context of molecular dynamics (the so-called Rahman-Parrinello molecular dynamics, or RP-MD). We use a generalized Lagrangian that allows for the coupling of the space's metric tensor to the scalar field, and add terms motivated by RP-MD. We present two implementations of the scheme: one in which the metric is only time-dependent (which gives rise to an ordinary differential equation for its temporal evolution), and the other with spatiotemporal dependence (wherein the metric's evolution is governed by a partial differential equation). Numerical results are reported for the (1+1)-dimensional model with a nonlinearity of the sine-Gordon type.
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Affiliation(s)
- P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
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Kevrekidis PG, Saxena A, Bishop AR. Interaction between sine-Gordon breathers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:026613. [PMID: 11497736 DOI: 10.1103/physreve.64.026613] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2001] [Indexed: 05/23/2023]
Abstract
Using the exact breather lattice solution of the sine-Gordon equation, we obtain the asymptotic interaction between two breathers. We identify the exponential dependence of the interaction on the breather separation as well as its power-law dependence on the breather frequency. Numerical simulation of the breather lattice demonstrates its instability. However, stabilization of such structures is found to be feasible through ac driving and damping. Finally, other limits of the original periodic solution are traced, obtaining the leading-order terms in the interaction between "pseudosphere" solutions and kink-antikink pairs.
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Affiliation(s)
- P G Kevrekidis
- Theoretical Division, Los Alamos National Laboratory, New Mexico 87545, USA
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Gaididei YB, Mingaleev SF, Christiansen PL. Curvature-induced symmetry breaking in nonlinear Schrodinger models. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:R53-R56. [PMID: 11088523 DOI: 10.1103/physreve.62.r53] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2000] [Indexed: 05/23/2023]
Abstract
We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. We show that the energy of localized states decreases with increasing curvature, i.e., bending is a trap for nonlinear excitations. A violation of the Vakhitov-Kolokolov stability criterion is found in the case where the instability is due to the softening of the Peierls internal mode.
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Affiliation(s)
- YB Gaididei
- Bogolyubov Institute for Theoretical Physics, 03143 Kiev, Ukraine
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Villain-Guillot S, Dandoloff R, Saxena A, Bishop AR. Topological solitons and geometrical frustration. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:6712-6722. [PMID: 9981900 DOI: 10.1103/physrevb.52.6712] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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