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Castro M, Gálvez-Poblete D, Castillo-Sepúlveda S, Carvalho-Santos VL, Nunez AS, Allende S. Bimerons as Edge States in Thin Magnetic Strips. NANO LETTERS 2025; 25:7249-7257. [PMID: 40243373 DOI: 10.1021/acs.nanolett.4c06167] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/18/2025]
Abstract
Magnetic bimerons offer a compelling alternative to skyrmions in next-generation spintronic devices. These topologically equivalent structures arise in chiral magnetic systems with in-plane magnetization driven by anisotropies or external magnetic fields. However, their use in current-driven systems is hindered by the bimeron Hall effect, which causes transverse motion and edge annihilation. Addressing these limitations, we uncover a novel mechanism for stabilizing bimeron propagation under current-driven conditions. We demonstrate that bimerons can propagate along thin ferromagnetic strips without annihilation when the easy-axis anisotropy and electric current are orthogonal. Our findings show a 6-fold velocity increase near strip edges due to boundary interactions. Furthermore, bimerons remain stable in curved geometries, allowing robust propagation in complex racetracks. This behavior also extends to bimeron chains, which propagate in parallel, forming stable and efficient configurations for information transport. These findings open new pathways toward practical and efficient bimeron-based racetrack memory technologies.
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Affiliation(s)
- Mario Castro
- Departamento de Física, FCFM, Universidad de Chile, Santiago 8370448, Chile
| | - David Gálvez-Poblete
- Departamento de Física, Universidad de Santiago de Chile, Santiago 9170124, Chile
- Centro de Nanociencia y Nanotecnología CEDENNA, Avda. Ecuador 3493, Santiago 9170124, Chile
| | - Sebastián Castillo-Sepúlveda
- Grupo de Investigación en Física Aplicada (GIFA), Facultad de Ingeniería, Universidad Autónoma de Chile, Av. Pedro de Valdivia 425, Providencia, Santiago 7500912, Chile
| | - Vagson L Carvalho-Santos
- Departamento de Física, Universidade Federal de Viçosa, Av. PH Rolfs s/n, 36570-900 Viçosa, Brazil
| | - Alvaro S Nunez
- Departamento de Física, FCFM, Universidad de Chile, Santiago 8370448, Chile
| | - Sebastian Allende
- Departamento de Física, Universidad de Santiago de Chile, Santiago 9170124, Chile
- Centro de Nanociencia y Nanotecnología CEDENNA, Avda. Ecuador 3493, Santiago 9170124, Chile
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Zhou Y, Li S, Liang X, Zhou Y. Topological Spin Textures: Basic Physics and Devices. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2025; 37:e2312935. [PMID: 38861696 DOI: 10.1002/adma.202312935] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2023] [Revised: 05/24/2024] [Indexed: 06/13/2024]
Abstract
In the face of escalating modern data storage demands and the constraints of Moore's Law, exploring spintronic solutions, particularly the devices based on magnetic skyrmions, has emerged as a promising frontier in scientific research. Since the first experimental observation of skyrmions, topological spin textures have been extensively studied for their great potential as efficient information carriers in spintronic devices. However, significant challenges have emerged alongside this progress. This review aims to synthesize recent advances in skyrmion research while addressing the major issues encountered in the field. Additionally, current research on promising topological spin structures in addition to skyrmions is summarized. Beyond 2D structures, exploration also extends to 1D magnetic solitons and 3D spin textures. In addition, a diverse array of emerging magnetic materials is introduced, including antiferromagnets and 2D van der Waals magnets, broadening the scope of potential materials hosting topological spin textures. Through a systematic examination of magnetic principles, topological categorization, and the dynamics of spin textures, a comprehensive overview of experimental and theoretical advances in the research of topological magnetism is provided. Finally, both conventional and unconventional applications are summarized based on spin textures proposed thus far. This review provides an outlook on future development in applied spintronics.
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Affiliation(s)
- Yuqing Zhou
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong, 518172, China
| | - Shuang Li
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong, 518172, China
| | - Xue Liang
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong, 518172, China
| | - Yan Zhou
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong, 518172, China
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Shen Z, Lu S, Xiong X. Optical generation and continuous transformation of plasmonic skyrmions. OPTICS EXPRESS 2024; 32:48289-48301. [PMID: 39876138 DOI: 10.1364/oe.546017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2024] [Accepted: 11/24/2024] [Indexed: 01/30/2025]
Abstract
Topological quasiparticles, including skyrmions and merons, are topological textures with sophisticated vectorial structures that can be used for high-density information storage, precision metrology, position sensing, etc. Here, we realized the optical generation and continuous transformation of plasmonic field skyrmions. We generated the isolated Néel-type skyrmion using surface plasmon polaritons (SPPs) excited by a focused structured light on a silver film. We used a square and a hexagonal aperture for symmetry constraints and successfully generated the meron lattice and the skyrmion lattice. We unveiled the mechanism of topological texture generation and transformation and optimized the distribution of skyrmion and meron topologies. We further demonstrated the continuous transformation among the isolated skyrmion, the meron lattice, and the skyrmion lattice using well-designed circular-fourfold, circular-sixfold, and fourfold-sixfold symmetry apertures, respectively. This work can open up a pathway for the generation and transformation of skyrmion and meron topologies, which is expected to facilitate new applications in optical information storage and encoding.
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Wu K, Zhao Y, Hao H, Yang S, Li S, Liu Q, Zhang S, Zhang X, Åkerman J, Xi L, Zhang Y, Cai K, Zhou Y. Topological transformation of synthetic ferromagnetic skyrmions: thermal assisted switching of helicity by spin-orbit torque. Nat Commun 2024; 15:10463. [PMID: 39622790 PMCID: PMC11612389 DOI: 10.1038/s41467-024-54851-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2024] [Accepted: 11/25/2024] [Indexed: 12/06/2024] Open
Abstract
This study demonstrates the controllable switching of skyrmion helicity using spin-orbit torque, enhanced by thermal effects. Electric current pulses applied to a [Pt/Co]3/Ru/[Co/Pt]3 multilayer stripe drive skyrmions in a direction opposite to the current flow. Continuous pulsing results in an unexpected reversal of skyrmion motion. Micromagnetic simulations reveal that skyrmions in the upper and lower ferromagnetic layers exhibit distinct helicities, forming a hybrid synthetic skyrmion. The helicity switch of this hybrid structure accounts for the motion reversal. This study introduces innovative helicity control methods, advancing spintronic device applications, including data storage and quantum computing based on skyrmion helicity.
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Affiliation(s)
- Kai Wu
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China
| | - Yuelei Zhao
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China
| | - Hongyuan Hao
- School of Physical Science and Technology, Lanzhou University, Lanzhou, China
| | - Sheng Yang
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China
| | - Shuang Li
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China
| | - Qingfang Liu
- School of Physical Science and Technology, Lanzhou University, Lanzhou, China
| | - Senfu Zhang
- School of Physical Science and Technology, Lanzhou University, Lanzhou, China.
- Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia.
| | - Xixiang Zhang
- Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
| | - Johan Åkerman
- Department of Physics, University of Gothenburg, Gothenburg, Sweden
- Center for Science and Innovation in Spintronics, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Japan
- Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Japan
| | - Li Xi
- School of Physical Science and Technology, Lanzhou University, Lanzhou, China
| | - Ying Zhang
- State Key Laboratory of Magnetism, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
| | - Kaiming Cai
- School of Physics, Huazhong University of Science and Technology, Wuhan, China
| | - Yan Zhou
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China.
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Yu X, Kanazawa N, Zhang X, Takahashi Y, Iakoubovskii KV, Nakajima K, Tanigaki T, Mochizuki M, Tokura Y. Spontaneous Vortex-Antivortex Pairs and Their Topological Transitions in a Chiral-Lattice Magnet. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024; 36:e2306441. [PMID: 37712832 DOI: 10.1002/adma.202306441] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Revised: 09/12/2023] [Indexed: 09/16/2023]
Abstract
The spontaneous formation and topological transitions of vortex-antivortex pairs have implications for a broad range of emergent phenomena, for example, from superconductivity to quantum computing. Unlike magnets exhibiting collinear spin textures, helimagnets with noncollinear spin textures provide unique opportunities to manipulate topological forms such as (anti)merons and (anti)skyrmions. However, it is challenging to achieve multiple topological states and their interconversion in a single helimagnet due to the topological protection for each state. Here, the on-demand creation of multiple topological states in a helimagnet Fe0.5 Co0.5 Ge, including a spontaneous vortex pair of meron with topological charge N = -1/2 and antimeron with N = 1/2, and a vortex-antivortex bundle, that is, a bimeron (meron pair) with N = -1 is reported. The mutual transformation between skyrmions and bimerons with respect to the competitive effects of magnetic field and magnetic shape anisotropy is demonstrated. It is shown that electric currents drive the individual bimerons to form their connecting assembly and then into a skyrmion lattice. These findings signify the feasibility of designing topological states and offer new insights into the manipulation of noncollinear spin textures for potential applications in various fields.
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Affiliation(s)
- Xiuzhen Yu
- RIKEN Center for Emergent Matter Science (CEMS), Wako, 351-0198, Japan
| | - Naoya Kanazawa
- Institute of Industrial Science, The University of Tokyo, Tokyo, 153-8505, Japan
| | - Xichao Zhang
- Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan
| | - Yoshio Takahashi
- Research and Development Group, Hitachi, Ltd., Hatoyama, 350-0395, Japan
| | | | - Kiyomi Nakajima
- RIKEN Center for Emergent Matter Science (CEMS), Wako, 351-0198, Japan
| | - Toshiaki Tanigaki
- Research and Development Group, Hitachi, Ltd., Hatoyama, 350-0395, Japan
| | - Masahito Mochizuki
- Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan
| | - Yoshinori Tokura
- RIKEN Center for Emergent Matter Science (CEMS), Wako, 351-0198, Japan
- Department of Applied Physics and Tokyo College, The University of Tokyo, Tokyo, 113-8656, Japan
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Silva RL, Silva RC, Pereira AR. Releasing antiferromagnetic skyrmions from local magnetic-anisotropy defects. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 36:135803. [PMID: 38100826 DOI: 10.1088/1361-648x/ad162d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Accepted: 12/15/2023] [Indexed: 12/17/2023]
Abstract
Lattice defects may work as a kind of apparatus for catching topological excitations, preventing their escape. So, the problem of removing skyrmions from eventual local defects in magnetic materials must be closely related to new technologies such as skyrmionic. Here, we examine the conditions for drawing a skyrmion from a magnetic impurity in a two-dimensional antiferromagnetic system by applying spin-polarized currents (SPC). Two types of impurities are investigated (local easy-axis and easy-plane anisotropy defects). Also, two methods to release the skyrmion with SPC are explored. In principle, our results could be qualitatively relevant to any other type of lattice defect.
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Affiliation(s)
- R L Silva
- Departamento de Ciências Naturais, Universidade Federal do Espírito Santo, Rodovia Governador Mário Covas, Km 60, Bairro Litorâneo, São Mateus, ES CEP 29932-540, Brazil
| | - R C Silva
- Departamento de Ciências Naturais, Universidade Federal do Espírito Santo, Rodovia Governador Mário Covas, Km 60, Bairro Litorâneo, São Mateus, ES CEP 29932-540, Brazil
| | - A R Pereira
- Departamento de Física, Universidade Federal de Viçosa, Viçosa, Minas Gerais 36570-000, Brazil
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Du W, Dou K, He Z, Dai Y, Huang B, Ma Y. Bloch-type magnetic skyrmions in two-dimensional lattices. MATERIALS HORIZONS 2023; 10:5071-5078. [PMID: 37668420 DOI: 10.1039/d3mh00868a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/06/2023]
Abstract
Magnetic skyrmions in two-dimensional lattices are a prominent topic of condensed matter physics and materials science. Current research efforts in this field are exclusively constrained to Néel-type and antiskyrmions, while Bloch-type magnetic skyrmions are rarely explored. Here, we report the discovery of Bloch-type magnetic skyrmions in a two-dimensional lattice of MnInP2Te6, using first-principles calculations and Monte-Carlo simulations. Arising from the joint effect of broken inversion symmetry and strong spin-orbit coupling, monolayer MnInP2Te6 presents large Dzyaloshinskii-Moriya interaction. This, along with ferromagnetic exchange interaction and out-of-plane magnetic anisotropy, gives rise to skyrmion physics in monolayer MnInP2Te6, in the absence of a magnetic field. Remarkably, different from all previous works on two-dimensional lattices, the resultant magnetic skyrmions feature Bloch-type magnetism, which is protected by D3 symmetry. Furthermore, Bloch-type magnetic bimerons are also identified in monolayer MnTlP2Te6. The phase diagrams of these Bloch-type topological magnetisms under a magnetic field, temperature and strain are mapped out. Our results greatly enrich the research on magnetic skyrmions in two-dimensional lattices.
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Affiliation(s)
- Wenhui Du
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Shandanan Street 27, Jinan 250100, China.
| | - Kaiying Dou
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Shandanan Street 27, Jinan 250100, China.
| | - Zhonglin He
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Shandanan Street 27, Jinan 250100, China.
| | - Ying Dai
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Shandanan Street 27, Jinan 250100, China.
| | - Baibiao Huang
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Shandanan Street 27, Jinan 250100, China.
| | - Yandong Ma
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Shandanan Street 27, Jinan 250100, China.
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8
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Galvez D, Castro M, Bittencourt G, Carvalho V, Allende S. Magnetic Bimerons in Cylindrical Nanotubes. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:2841. [PMID: 37947687 PMCID: PMC10648566 DOI: 10.3390/nano13212841] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Revised: 09/30/2023] [Accepted: 10/02/2023] [Indexed: 11/12/2023]
Abstract
This work presents the analysis of the stability of magnetic bimerons in a cylindrical nanotube. Through micromagnetic simulations, we study the influence of magnetic and geometrical parameters on the bimeron existence and size. The obtained results allow us to present diagram states showing the stability region of a bimeron as a function of the nanotube's height and radius for different anisotropy and Dzyaloshinskii-Moriya interaction strengths. We also obtain two other magnetic states in the range of parameters where the bimeron is not stable: helicoidal and saturated states.
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Affiliation(s)
- David Galvez
- Departamento de Física, CEDENNA, Universidad de Santiago de Chile, Santiago 9170124, Chile
| | - Mario Castro
- Departamento de Física, CEDENNA, Universidad de Santiago de Chile, Santiago 9170124, Chile
| | - Guilherme Bittencourt
- Departamento de Física, Universidade Federal de Viçosa, Viçosa 36570-900, Brazil; (G.B.)
| | - Vagson Carvalho
- Departamento de Física, Universidade Federal de Viçosa, Viçosa 36570-900, Brazil; (G.B.)
| | - Sebastian Allende
- Departamento de Física, CEDENNA, Universidad de Santiago de Chile, Santiago 9170124, Chile
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9
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Truc B, Sapozhnik AA, Tengdin P, Viñas Boström E, Schönenberger T, Gargiulo S, Madan I, LaGrange T, Magrez A, Verdozzi C, Rubio A, Rønnow HM, Carbone F. Light-Induced Metastable Hidden Skyrmion Phase in the Mott Insulator Cu 2 OSeO 3. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2304197. [PMID: 37282751 DOI: 10.1002/adma.202304197] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Indexed: 06/08/2023]
Abstract
The discovery of a novel long-lived metastable skyrmion phase in the multiferroic insulator Cu2 OSeO3 visualized with Lorentz transmission electron microscopy for magnetic fields below the equilibrium skyrmion pocket is reported. This phase can be accessed by exciting the sample non-adiabatically with near-infrared femtosecond laser pulses and cannot be reached by any conventional field-cooling protocol, referred as a hidden phase. From the strong wavelength dependence of the photocreation process and via spin-dynamics simulations, the magnetoelastic effect is identified as the most likely photocreation mechanism. This effect results in a transient modification of the magnetic free energy landscape extending the equilibrium skyrmion pocket to lower magnetic fields. The evolution of the photoinduced phase is monitored for over 15 min and no decay is found. Because such a time is much longer than the duration of any transient effect induced by a laser pulse in a material, it is assumed that the newly discovered skyrmion state is stable for practical purposes, thus breaking ground for a novel approach to control magnetic state on demand at ultrafast timescales and drastically reducing heat dissipation relevant for next-generation spintronic devices.
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Affiliation(s)
- Benoit Truc
- Laboratory for Ultrafast Microscopy and Electron Scattering, Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
| | - Alexey A Sapozhnik
- Laboratory for Ultrafast Microscopy and Electron Scattering, Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
| | - Phoebe Tengdin
- Laboratory for Ultrafast Microscopy and Electron Scattering, Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
| | - Emil Viñas Boström
- Max Planck Institute for the Structure and Dynamics of Matter, 22761, Hamburg, Germany
| | - Thomas Schönenberger
- Laboratory for Quantum Magnetism, Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
| | - Simone Gargiulo
- Laboratory for Ultrafast Microscopy and Electron Scattering, Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
| | - Ivan Madan
- Laboratory for Ultrafast Microscopy and Electron Scattering, Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
| | - Thomas LaGrange
- Laboratory for Ultrafast Microscopy and Electron Scattering, Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
| | - Arnaud Magrez
- Crystal Growth Facility, Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
| | - Claudio Verdozzi
- Division of Mathematical Physics and ETSF, Lund University, Lund, 223 63, Sweden
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter, 22761, Hamburg, Germany
- Center for Computational Quantum Physics (CCQ), The Flatiron Institute, New York, 10010, USA
| | - Henrik M Rønnow
- Laboratory for Quantum Magnetism, Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
| | - Fabrizio Carbone
- Laboratory for Ultrafast Microscopy and Electron Scattering, Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland
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10
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Song C, Zhao L, Liu J, Jiang W. Experimental Realization of a Skyrmion Circulator. NANO LETTERS 2022; 22:9638-9644. [PMID: 36411254 DOI: 10.1021/acs.nanolett.2c03789] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Magnetic skyrmions are mobile topological spin textures that can be manipulated by different means. Their applications have been frequently discussed in the context of information carriers for racetrack memory devices, which on the other hand, exhibit a skyrmion Hall effect as a result of the nontrivial real-space topology. While the skyrmion Hall effect is believed to be detrimental for constructing racetrack devices, we show here that it can be implemented for realizing a three-terminal skyrmion circulator. In analogy to the microwave circulator, nonreciprocal transportation and circulation of skyrmions are studied both numerically and experimentally. In particular, successful control of the circulating direction of being either clockwise or counterclockwise is demonstrated, simply by changing the sign of the topological charge. Our studies suggest that the topological property of skyrmions can be incorporated for enabling novel spintronic functionalities; the skyrmion circulator is just one example.
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Affiliation(s)
- Chengkun Song
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing100084, China
- Frontier Science Center for Quantum Information, Tsinghua University, Beijing100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing100084, China
| | - Le Zhao
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing100084, China
- Frontier Science Center for Quantum Information, Tsinghua University, Beijing100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing100084, China
| | - Jiahao Liu
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing100084, China
- Frontier Science Center for Quantum Information, Tsinghua University, Beijing100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing100084, China
- Institute for Quantum Information & State Key Laboratory of High-Performance Computing, College of Computer, National University of Defense Technology, Changsha410073, China
| | - Wanjun Jiang
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing100084, China
- Frontier Science Center for Quantum Information, Tsinghua University, Beijing100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing100084, China
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