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Birch MT, Cortés-Ortuño D, Turnbull LA, Wilson MN, Groß F, Träger N, Laurenson A, Bukin N, Moody SH, Weigand M, Schütz G, Popescu H, Fan R, Steadman P, Verezhak JAT, Balakrishnan G, Loudon JC, Twitchett-Harrison AC, Hovorka O, Fangohr H, Ogrin FY, Gräfe J, Hatton PD. Real-space imaging of confined magnetic skyrmion tubes. Nat Commun 2020; 11:1726. [PMID: 32265449 PMCID: PMC7138844 DOI: 10.1038/s41467-020-15474-8] [Citation(s) in RCA: 40] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Accepted: 03/13/2020] [Indexed: 11/23/2022] Open
Abstract
Magnetic skyrmions are topologically nontrivial particles with a potential application as information elements in future spintronic device architectures. While they are commonly portrayed as two dimensional objects, in reality magnetic skyrmions are thought to exist as elongated, tube-like objects extending through the thickness of the host material. The study of this skyrmion tube state (SkT) is vital for furthering the understanding of skyrmion formation and dynamics for future applications. However, direct experimental imaging of skyrmion tubes has yet to be reported. Here, we demonstrate the real-space observation of skyrmion tubes in a lamella of FeGe using resonant magnetic x-ray imaging and comparative micromagnetic simulations, confirming their extended structure. The formation of these structures at the edge of the sample highlights the importance of confinement and edge effects in the stabilisation of the SkT state, opening the door to further investigation into this unexplored dimension of the skyrmion spin texture.
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Affiliation(s)
- M T Birch
- Centre for Materials Physics, Durham University, Durham, DH1 3LE, UK
- Diamond Light Source, Didcot, OX11 0DE, UK
| | - D Cortés-Ortuño
- Faculty of Engineering and Physical Sciences, University of Southampton, Southampton, SO17 1BJ, UK
| | - L A Turnbull
- Centre for Materials Physics, Durham University, Durham, DH1 3LE, UK
| | - M N Wilson
- Centre for Materials Physics, Durham University, Durham, DH1 3LE, UK
| | - F Groß
- Max Planck Institute for Intelligent Systems, 70569, Stuttgart, Germany
| | - N Träger
- Max Planck Institute for Intelligent Systems, 70569, Stuttgart, Germany
| | - A Laurenson
- School of Physics and Astronomy, University of Exeter, Exeter, EX4 4QL, UK
| | - N Bukin
- School of Physics and Astronomy, University of Exeter, Exeter, EX4 4QL, UK
| | - S H Moody
- Centre for Materials Physics, Durham University, Durham, DH1 3LE, UK
| | - M Weigand
- Max Planck Institute for Intelligent Systems, 70569, Stuttgart, Germany
- Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Institut Nanospektroskopie, Kekuléstrasse 5, 12489, Berlin, Germany
| | - G Schütz
- Max Planck Institute for Intelligent Systems, 70569, Stuttgart, Germany
| | - H Popescu
- Synchrotron SOLEIL, Saint Aubin, BP 48, 91192, Gif-sur-Yvette, France
| | - R Fan
- Diamond Light Source, Didcot, OX11 0DE, UK
| | - P Steadman
- Diamond Light Source, Didcot, OX11 0DE, UK
| | - J A T Verezhak
- Department of Physics, University of Warwick, Coventry, CV4 7AL, UK
| | - G Balakrishnan
- Department of Physics, University of Warwick, Coventry, CV4 7AL, UK
| | - J C Loudon
- Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, CB3 0FS, UK
| | - A C Twitchett-Harrison
- Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, CB3 0FS, UK
| | - O Hovorka
- Faculty of Engineering and Physical Sciences, University of Southampton, Southampton, SO17 1BJ, UK
| | - H Fangohr
- Faculty of Engineering and Physical Sciences, University of Southampton, Southampton, SO17 1BJ, UK
- European XFEL GmbH, Holzkoppel 4, 22869, Schenefeld, Germany
| | - F Y Ogrin
- School of Physics and Astronomy, University of Exeter, Exeter, EX4 4QL, UK
| | - J Gräfe
- Max Planck Institute for Intelligent Systems, 70569, Stuttgart, Germany
| | - P D Hatton
- Centre for Materials Physics, Durham University, Durham, DH1 3LE, UK.
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Gallardo RA, Cortés-Ortuño D, Schneider T, Roldán-Molina A, Ma F, Troncoso RE, Lenz K, Fangohr H, Lindner J, Landeros P. Flat Bands, Indirect Gaps, and Unconventional Spin-Wave Behavior Induced by a Periodic Dzyaloshinskii-Moriya Interaction. Phys Rev Lett 2019; 122:067204. [PMID: 30822086 DOI: 10.1103/physrevlett.122.067204] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2018] [Revised: 10/26/2018] [Indexed: 06/09/2023]
Abstract
Periodically patterned metamaterials are known for exhibiting wave properties similar to the ones observed in electronic band structures in crystal lattices. In particular, periodic ferromagnetic materials are characterized by the presence of bands and band gaps in their spin-wave spectrum at tunable GHz frequencies. Recently, the fabrication of magnets hosting Dzyaloshinskii-Moriya interactions has been pursued with high interest since properties, such as the stabilization of chiral spin textures and nonreciprocal spin-wave propagation, emerge from this antisymmetric exchange coupling. In this context, to further engineer the magnon band structure, we propose the implementation of magnonic crystals with periodic Dzyaloshinskii-Moriya interactions, which can be obtained, for instance, via patterning of periodic arrays of heavy metal wires on top of an ultrathin magnetic film. We demonstrate through theoretical calculations and micromagnetic simulations that such systems show an unusual evolution of the standing spin waves around the gaps. We also predict the emergence of indirect gaps and flat bands, effects that depend on the strength of the Dzyaloshinskii-Moriya interaction. Such phenomena, which have been previously observed in different systems, are observed here simultaneously, opening new routes towards engineered metamaterials for spin-wave-based devices.
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Affiliation(s)
- R A Gallardo
- Departamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile
- Center for the Development of Nanoscience and Nanotechnology (CEDENNA), 917-0124 Santiago, Chile
| | - D Cortés-Ortuño
- Faculty of Engineering and Physical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - T Schneider
- Helmholtz-Zentrum Dresden-Rossendorf, Institut of Ion Beam Physics and Materials Research, Bautzner Landstr. 400, 01328 Dresden, Germany
- Department of Physics, Technische Universität Chemnitz, Reichenhainer Str. 70, 09126 Chemnitz, Germany
| | - A Roldán-Molina
- Universidad de Aysén, Calle Obispo Vielmo 62, Coyhaique, Chile
| | - Fusheng Ma
- Jiangsu Key Lab on Opto-Electronic Technology, Center for Quantum Transport and Thermal Energy Science, School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China
| | - R E Troncoso
- Departamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - K Lenz
- Helmholtz-Zentrum Dresden-Rossendorf, Institut of Ion Beam Physics and Materials Research, Bautzner Landstr. 400, 01328 Dresden, Germany
| | - H Fangohr
- Faculty of Engineering and Physical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom
- European XFEL GmbH, Holzkoppel 4, 22869 Schenefeld, Germany
| | - J Lindner
- Helmholtz-Zentrum Dresden-Rossendorf, Institut of Ion Beam Physics and Materials Research, Bautzner Landstr. 400, 01328 Dresden, Germany
| | - P Landeros
- Departamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile
- Center for the Development of Nanoscience and Nanotechnology (CEDENNA), 917-0124 Santiago, Chile
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Xu XB, Fangohr H, Gu M, Chen W, Wang ZH, Zhou F, Shi DQ, Dou SX. Simulation of the phase diagram of magnetic vortices in two-dimensional superconductors: evidence for vortex chain formation. J Phys Condens Matter 2014; 26:115702. [PMID: 24589983 DOI: 10.1088/0953-8984/26/11/115702] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We study the superconducting vortex states induced by the interplay of long-range Pearl repulsion and short-range intervortex attraction using Langevin dynamics simulations. We show that at low temperatures the vortices form an ordered Abrikosov lattice both in low and high fields. The vortices show distinctive modulated structures at intermediate fields depending on the effective intervortex attraction: ordered vortex chain and kagome-like vortex structures for weak attraction; bubble, stripe and antibubble lattices for strong attraction. Moreover, in the regime of the chain state, the vortices display structural transitions from chain to labyrinthine (or disordered chain) and/or to disordered states depending on the strength of the disorder.
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Affiliation(s)
- X B Xu
- Center for Superconducting Physics and Materials, National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, People's Republic of China
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Xu XB, Fangohr H, Xu XN, Gu M, Wang ZH, Ji SM, Ding SY, Shi DQ, Dou SX. Peak effect in the critical current of type II superconductors with strong magnetic vortex pinning. Phys Rev Lett 2008; 101:147002. [PMID: 18851560 DOI: 10.1103/physrevlett.101.147002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2008] [Indexed: 05/26/2023]
Abstract
We perform 2D Langevin simulations studying the peak effect (PE) of the critical current taking into account the temperature dependence of the competing forces. We observe and report that the PE results from the competition of vortex-vortex interactions and vortex-pin interactions which have different temperature dependencies. The simulations reveal that the PE can take place only for certain pinning strengths, densities of pinning centers, and driving forces, which is in good agreement with experiments. No apparent vortex order-disorder transition is observed across the PE regime. In addition, the PE is a dynamical phenomenon, and thermal fluctuations can speed up the process for the formation of the PE.
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Affiliation(s)
- X B Xu
- National Laboratory of Solid State Microstructures, Department of Physics, Nanjing University, Nanjing 210093, People's Republic of China.
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Bowden GJ, de Groot PAJ, Rainford BD, Wang K, Martin KN, Zimmermann JP, Fangohr H. Magnetic anisotropy terms in [110] MBE-grown REFe(2) films involving the strain term ε(xy). J Phys Condens Matter 2006; 18:5861-5871. [PMID: 21690802 DOI: 10.1088/0953-8984/18/26/006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The magnetic anisotropy parameters in [110] MBE-grown films of REFe(2) (RE, rare earth) compounds are not the same as those in the bulk. This is due to the presence of a shear strain ε(xy), frozen-in during crystal growth. In this paper, magnetic anisotropy parameters for [110] MBE-grown REFe(2) films, that directly involve the shear strain ε(xy), are presented and discussed. In addition to the usual first-order Callen and Callen term [Formula: see text], there are nine second-order terms, six of which involve cross-terms between ε(xy) and the cubic crystal field terms B(4) and B(6). Two of the second-order cross-terms are identified as being important: [Formula: see text] and [Formula: see text]. Of these, the rank-two term [Formula: see text] dominates over a large temperature range. It has the same angular dependence as the first-order term [Formula: see text], but with a more rapid temperature dependence. The correction at T = 0 K for TbFe(2), DyFe(2), HoFe(2), ErFe(2) and TmFe(2), amounts to ∼+9.2%, -13.9%, -11.6%, +14.3%, and 27.1%, respectively. Similar comments are made concerning the rank-four [Formula: see text] term.
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Affiliation(s)
- G J Bowden
- School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK
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Grigorenko AN, Bending SJ, Van Bael MJ, Lange M, Moshchalkov VV, Fangohr H, de Groot PAJ. Symmetry locking and commensurate vortex domain formation in periodic pinning arrays. Phys Rev Lett 2003; 90:237001. [PMID: 12857280 DOI: 10.1103/physrevlett.90.237001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2002] [Indexed: 05/24/2023]
Abstract
The spontaneous formation of domains of commensurate vortex patterns near rational fractional matching fields of a periodic pinning array has been investigated with high resolution scanning Hall probe microscopy. We show that domain formation is promoted due to the efficient incorporation of mismatched excess vortices and vacancies at the corners of domain walls, which outweighs the energetic cost of creating them. Molecular dynamics simulations with a generic pinning potential reveal that domains are formed only when vortex-vortex interactions are long range.
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Affiliation(s)
- A N Grigorenko
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
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