1
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Yue WC, Yuan Z, Huang P, Sun Y, Gao T, Lyu YY, Tu X, Dong S, He L, Dong Y, Cao X, Kang L, Wang H, Wu P, Nisoli C, Wang YL. Toroidic phase transitions in a direct-kagome artificial spin ice. NATURE NANOTECHNOLOGY 2024; 19:1101-1107. [PMID: 38684808 DOI: 10.1038/s41565-024-01666-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 03/27/2024] [Indexed: 05/02/2024]
Abstract
Ferrotoroidicity-the fourth form of primary ferroic order-breaks both space and time-inversion symmetry. So far, direct observation of ferrotoroidicity in natural materials remains elusive, which impedes the exploration of ferrotoroidic phase transitions. Here we overcome the limitations of natural materials using an artificial nanomagnet system that can be characterized at the constituent level and at different effective temperatures. We design a nanomagnet array as to realize a direct-kagome spin ice. This artificial spin ice exhibits robust toroidal moments and a quasi-degenerate ground state with two distinct low-temperature toroidal phases: ferrotoroidicity and paratoroidicity. Using magnetic force microscopy and Monte Carlo simulation, we demonstrate a phase transition between ferrotoroidicity and paratoroidicity, along with a cross-over to a non-toroidal paramagnetic phase. Our quasi-degenerate artificial spin ice in a direct-kagome structure provides a model system for the investigation of magnetic states and phase transitions that are inaccessible in natural materials.
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Affiliation(s)
- Wen-Cheng Yue
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Zixiong Yuan
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Peiyuan Huang
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Yizhe Sun
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China
| | - Tan Gao
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Yang-Yang Lyu
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Xuecou Tu
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Sining Dong
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China.
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China.
| | - Liang He
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China
| | - Ying Dong
- College of Metrology Measurement and Instrument, China Jiliang University, Hangzhou, China
| | - Xun Cao
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
| | - Lin Kang
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Huabing Wang
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
- Purple Mountain Laboratories, Nanjing, China.
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China.
| | - Peiheng Wu
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Cristiano Nisoli
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA.
| | - Yong-Lei Wang
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
- Purple Mountain Laboratories, Nanjing, China.
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China.
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China.
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2
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Keppert S, Aichner B, Rohringer P, Bodea MA, Müller B, Karrer M, Kleiner R, Goldobin E, Koelle D, Pedarnig JD, Lang W. Temporal Evolution of Defects and Related Electric Properties in He-Irradiated YBa 2Cu 3O 7-δ Thin Films. Int J Mol Sci 2024; 25:7877. [PMID: 39063119 PMCID: PMC11277344 DOI: 10.3390/ijms25147877] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2024] [Revised: 07/15/2024] [Accepted: 07/16/2024] [Indexed: 07/28/2024] Open
Abstract
Thin films of the superconductor YBa2Cu3O7-δ (YBCO) were modified by low-energy light-ion irradiation employing collimated or focused He+ beams, and the long-term stability of irradiation-induced defects was investigated. For films irradiated with collimated beams, the resistance was measured in situ during and after irradiation and analyzed using a phenomenological model. The formation and stability of irradiation-induced defects are highly influenced by temperature. Thermal annealing experiments conducted in an Ar atmosphere at various temperatures demonstrated a decrease in resistivity and allowed us to determine diffusion coefficients and the activation energy ΔE=(0.31±0.03) eV for diffusive oxygen rearrangement within the YBCO unit cell basal plane. Additionally, thin YBCO films, nanostructured by focused He+-beam irradiation into vortex pinning arrays, displayed significant commensurability effects in magnetic fields. Despite the strong modulation of defect densities in these pinning arrays, oxygen diffusion during room-temperature annealing over almost six years did not compromise the signatures of vortex matching, which remained precisely at their magnetic fields predicted by the pattern geometry. Moreover, the critical current increased substantially within the entire magnetic field range after long-term storage in dry air. These findings underscore the potential of ion irradiation in tailoring the superconducting properties of thin YBCO films.
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Affiliation(s)
- Sandra Keppert
- Institute of Applied Physics, Johannes Kepler University Linz, 4040 Linz, Austria; (S.K.); (J.D.P.)
| | - Bernd Aichner
- Faculty of Physics, University of Vienna, 1090 Vienna, Austria; (B.A.)
| | - Philip Rohringer
- Faculty of Physics, University of Vienna, 1090 Vienna, Austria; (B.A.)
| | - Marius-Aurel Bodea
- Institute of Applied Physics, Johannes Kepler University Linz, 4040 Linz, Austria; (S.K.); (J.D.P.)
| | - Benedikt Müller
- Physikalisches Institut, Center for Quantum Science (CQ) and LISA+, University of Tübingen, 72076 Tübingen, Germany (R.K.); (E.G.); (D.K.)
| | - Max Karrer
- Physikalisches Institut, Center for Quantum Science (CQ) and LISA+, University of Tübingen, 72076 Tübingen, Germany (R.K.); (E.G.); (D.K.)
| | - Reinhold Kleiner
- Physikalisches Institut, Center for Quantum Science (CQ) and LISA+, University of Tübingen, 72076 Tübingen, Germany (R.K.); (E.G.); (D.K.)
| | - Edward Goldobin
- Physikalisches Institut, Center for Quantum Science (CQ) and LISA+, University of Tübingen, 72076 Tübingen, Germany (R.K.); (E.G.); (D.K.)
| | - Dieter Koelle
- Physikalisches Institut, Center for Quantum Science (CQ) and LISA+, University of Tübingen, 72076 Tübingen, Germany (R.K.); (E.G.); (D.K.)
| | - Johannes D. Pedarnig
- Institute of Applied Physics, Johannes Kepler University Linz, 4040 Linz, Austria; (S.K.); (J.D.P.)
| | - Wolfgang Lang
- Faculty of Physics, University of Vienna, 1090 Vienna, Austria; (B.A.)
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3
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El Hage R, Sánchez-Manzano D, Humbert V, Carreira S, Rouco V, Sander A, Cuellar F, Seurre K, Lagarrigue A, Mesoraca S, Briatico J, Trastoy J, Santamaría J, Villegas JE. Disentangling Photodoping, Photoconductivity, and Photosuperconductivity in the Cuprates. PHYSICAL REVIEW LETTERS 2024; 132:066001. [PMID: 38394577 DOI: 10.1103/physrevlett.132.066001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Accepted: 01/02/2024] [Indexed: 02/25/2024]
Abstract
The normal-state conductivity and superconducting critical temperature of oxygen-deficient YBa_{2}Cu_{3}O_{7-δ} can be persistently enhanced by illumination. Strongly debated for years, the origin of those effects-termed persistent photoconductivity and photosuperconductivity (PPS)-has remained an unsolved critical problem, whose comprehension may provide key insights to harness the origin of high-temperature superconductivity itself. Here, we make essential steps toward understanding PPS. While the models proposed so far assume that it is caused by a carrier-density increase (photodoping) observed concomitantly, our experiments contradict such conventional belief: we demonstrate that it is instead linked to a photo-induced decrease of the electronic scattering rate. Furthermore, we find that the latter effect and photodoping are completely disconnected and originate from different microscopic mechanisms, since they present different wavelength and oxygen-content dependences as well as strikingly different relaxation dynamics. Besides helping disentangle photodoping, persistent photoconductivity, and PPS, our results provide new evidence for the intimate relation between critical temperature and scattering rate, a key ingredient in modern theories on high-temperature superconductivity.
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Affiliation(s)
- R El Hage
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - D Sánchez-Manzano
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - V Humbert
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - S Carreira
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - V Rouco
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - A Sander
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - F Cuellar
- GFMC, Departamento de Física de Materiales, Universidad de Ciencias Físicas, Facultad Complutense de Madrid, 28040 Madrid, Spain
| | - K Seurre
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - A Lagarrigue
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - S Mesoraca
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - J Briatico
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - J Trastoy
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - J Santamaría
- GFMC, Departamento de Física de Materiales, Universidad de Ciencias Físicas, Facultad Complutense de Madrid, 28040 Madrid, Spain
| | - Javier E Villegas
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
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4
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Bi X, Tian F, Chen G, Li Z, Qin F, Lv YY, Huang J, Qiu C, Ao L, Chen Y, Gu G, Chen Y, Yuan H. A Superconducting Micro-Magnetometer for Quantum Vortex in Superconducting Nanoflakes. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2211409. [PMID: 36808146 DOI: 10.1002/adma.202211409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Revised: 01/30/2023] [Indexed: 05/12/2023]
Abstract
Superconducting quantum interferometer device (SQUID) plays a key role in understanding electromagnetic properties and emergent phenomena in quantum materials. The technological appeal of SQUID is that its detection accuracy for the electromagnetic signal can precisely reach the quantum level of a single magnetic flux. However, conventional SQUID techniques normally can only be applied to a bulky sample and do not have the capability to probe the magnetic properties of micro-scale samples with small magnetic signals. Herein, it is demonstrated that, based on a specially designed superconducting nano-hole array, the contactless detection of magnetic properties and quantized vortices in micro-sized superconducting nanoflakes is realized. An anomalous hysteresis loop and a suppression of Little-Parks oscillation are observed in the detected magnetoresistance signal, which originates from the disordered distribution of the pinned vortices in Bi2 Sr2 CaCu2 O8+δ . Therefore, the density of pinning centers of the quantized vortices on such micro-sized superconducting samples can be quantitatively evaluated, which is technically inaccessible for conventional SQUID detection. The superconducting micro-magnetometer provides a new approach to exploring mesoscopic electromagnetic phenomena of quantum materials.
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Affiliation(s)
- Xiangyu Bi
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, College of Engineering and Applied Sciences, Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210000, P. R. China
| | - Feifan Tian
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, College of Engineering and Applied Sciences, Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210000, P. R. China
| | - Ganyu Chen
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, College of Engineering and Applied Sciences, Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210000, P. R. China
| | - Zeya Li
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, College of Engineering and Applied Sciences, Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210000, P. R. China
| | - Feng Qin
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, College of Engineering and Applied Sciences, Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210000, P. R. China
| | - Yang-Yang Lv
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing, 210000, P. R. China
| | - Junwei Huang
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, College of Engineering and Applied Sciences, Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210000, P. R. China
| | - Caiyu Qiu
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, College of Engineering and Applied Sciences, Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210000, P. R. China
| | - Lingyi Ao
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, College of Engineering and Applied Sciences, Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210000, P. R. China
| | - Yanbin Chen
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing, 210000, P. R. China
| | - Genda Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - Yanfeng Chen
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, College of Engineering and Applied Sciences, Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210000, P. R. China
| | - Hongtao Yuan
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, College of Engineering and Applied Sciences, Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210000, P. R. China
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5
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Backmeister L, Aichner B, Karrer M, Wurster K, Kleiner R, Goldobin E, Koelle D, Lang W. Ordered Bose Glass of Vortices in Superconducting YBa 2Cu 3O 7-δ Thin Films with a Periodic Pin Lattice Created by Focused Helium Ion Irradiation. NANOMATERIALS (BASEL, SWITZERLAND) 2022; 12:3491. [PMID: 36234619 PMCID: PMC9565813 DOI: 10.3390/nano12193491] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Revised: 09/30/2022] [Accepted: 10/02/2022] [Indexed: 06/16/2023]
Abstract
The defect-rich morphology of YBa2Cu3O7-δ (YBCO) thin films leads to a glass-like arrangement of Abrikosov vortices which causes the resistance to disappear in vanishing current densities. This vortex glass consists of entangled vortex lines and is identified by a characteristic scaling of the voltage-current isotherms. Randomly distributed columnar defects stratify the vortex lines and lead to a Bose glass. Here, we report on the observation of an ordered Bose glass in a YBCO thin film with a hexagonal array of columnar defects with 30 nm spacings. The periodic pinning landscape was engineered by a focused beam of 30 keV He+ ions in a helium-ion microscope.
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Affiliation(s)
| | - Bernd Aichner
- Faculty of Physics, University of Vienna, A-1090 Wien, Austria
| | - Max Karrer
- Physikalisches Institut, Center for Quantum Science (CQ) and LISA, Universität Tübingen, D-72076 Tübingen, Germany
| | - Katja Wurster
- Physikalisches Institut, Center for Quantum Science (CQ) and LISA, Universität Tübingen, D-72076 Tübingen, Germany
| | - Reinhold Kleiner
- Physikalisches Institut, Center for Quantum Science (CQ) and LISA, Universität Tübingen, D-72076 Tübingen, Germany
| | - Edward Goldobin
- Physikalisches Institut, Center for Quantum Science (CQ) and LISA, Universität Tübingen, D-72076 Tübingen, Germany
| | - Dieter Koelle
- Physikalisches Institut, Center for Quantum Science (CQ) and LISA, Universität Tübingen, D-72076 Tübingen, Germany
| | - Wolfgang Lang
- Faculty of Physics, University of Vienna, A-1090 Wien, Austria
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6
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Duzgun A, Nisoli C. Skyrmion Spin Ice in Liquid Crystals. PHYSICAL REVIEW LETTERS 2021; 126:047801. [PMID: 33576672 DOI: 10.1103/physrevlett.126.047801] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Revised: 10/17/2020] [Accepted: 12/23/2020] [Indexed: 06/12/2023]
Abstract
We propose the first skyrmion spin ice, realized via confined, interacting liquid crystal skyrmions. Skyrmions in a chiral nematic liquid crystal behave as quasiparticles that can be dynamically confined, bound, and created or annihilated individually with ease and precision. We show that these quasiparticles can be employed to realize binary variables that interact to form ice-rule states. Because of their unique versatility, liquid crystal skyrmions can open entirely novel avenues in the field of frustrated systems. More broadly, our findings also demonstrate the viability of liquid crystal skyrmions as elementary degrees of freedom in the design of collective complex behaviors.
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Affiliation(s)
- Ayhan Duzgun
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Cristiano Nisoli
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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7
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Lyu YY, Ma X, Xu J, Wang YL, Xiao ZL, Dong S, Janko B, Wang H, Divan R, Pearson JE, Wu P, Kwok WK. Reconfigurable Pinwheel Artificial-Spin-Ice and Superconductor Hybrid Device. NANO LETTERS 2020; 20:8933-8939. [PMID: 33252230 DOI: 10.1021/acs.nanolett.0c04093] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The ability to control the potential landscape in a medium of interacting particles could lead to intriguing collective behavior and innovative functionalities. Here, we utilize spatially reconfigurable magnetic potentials of a pinwheel artificial-spin-ice (ASI) structure to tailor the motion of superconducting vortices. The reconstituted chain structures of the magnetic charges in the pinwheel ASI and the strong interaction between magnetic charges and superconducting vortices allow significant modification of the transport properties of the underlying superconducting thin film, resulting in a reprogrammable resistance state that enables a reversible and switchable vortex Hall effect. Our results highlight an effective and simple method of using ASI as an in situ reconfigurable nanoscale energy landscape to design reprogrammable superconducting electronics, which could also be applied to the in situ control of properties and functionalities in other magnetic particle systems, such as magnetic skyrmions.
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Affiliation(s)
- Yang-Yang Lyu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Xiaoyu Ma
- Department of Physics, University of Notre Dame, Notre Dame 46556, Indiana United States
| | - Jing Xu
- Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Yong-Lei Wang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
| | - Zhi-Li Xiao
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, United States
| | - Sining Dong
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
| | - Boldizsar Janko
- Department of Physics, University of Notre Dame, Notre Dame 46556, Indiana United States
| | - Huabing Wang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
- Purple Mountain Laboratories, Nanjing 211111, China
| | - Ralu Divan
- Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - John E Pearson
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Peiheng Wu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
| | - Wai-Kwong Kwok
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
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8
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Menezes RM, Sardella E, Cabral LRE, de Souza Silva CC. Self-assembled vortex crystals induced by inhomogeneous magnetic textures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:175402. [PMID: 30699395 DOI: 10.1088/1361-648x/ab035a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We investigate the self-assembly of vortices in a type-II superconducting disk subjected to highly nonuniform confining potentials produced by inhomogeneous magnetic textures. Using a series of numerical experiments performed within the Ginzburg-Landau theory, we show that vortices can arrange spontaneously in highly nonuniform, defect-free crystals, reminiscent of conformal lattices, even though the strict conditions for the conformal crystal are not fulfilled. These results contradict continuum-limit theory, which predicts that the order of a nonuniform crystal is unavoidably frustrated by the presence of topological defects. By testing different cooling routes of the superconductor, we observed several different self-assembled configurations, each of which corresponding to one in a set of allowed conformal transformations, which depends on the magnetic and thermal histories of the system.
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Affiliation(s)
- Raí M Menezes
- Departamento de Física, Universidade Federal de Pernambuco, Cidade Universitária, 50670-901, Recife-PE, Brazil
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9
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Libál A, Lee DY, Ortiz-Ambriz A, Reichhardt C, Reichhardt CJO, Tierno P, Nisoli C. Ice rule fragility via topological charge transfer in artificial colloidal ice. Nat Commun 2018; 9:4146. [PMID: 30297820 PMCID: PMC6175946 DOI: 10.1038/s41467-018-06631-1] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2018] [Accepted: 09/05/2018] [Indexed: 11/09/2022] Open
Abstract
Artificial particle ices are model systems of constrained, interacting particles. They have been introduced theoretically to study ice-manifolds emergent from frustration, along with domain wall and grain boundary dynamics, doping, pinning-depinning, controlled transport of topological defects, avalanches, and memory effects. Recently such particle-based ices have been experimentally realized with vortices in nano-patterned superconductors or gravitationally trapped colloids. Here we demonstrate that, although these ices are generally considered equivalent to magnetic spin ices, they can access a novel spectrum of phenomenologies that are inaccessible to the latter. With experiments, theory and simulations we demonstrate that in mixed coordination geometries, entropy-driven negative monopoles spontaneously appear at a density determined by the vertex-mixture ratio. Unlike its spin-based analogue, the colloidal system displays a "fragile ice" manifold, where local energetics oppose the ice rule, which is instead enforced through conservation of the global topological charge. The fragile colloidal ice, stabilized by topology, can be spontaneously broken by topological charge transfer.
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Affiliation(s)
- András Libál
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.,Mathematics and Computer Science Department, Babeş-Bolyai University, Cluj, 400084, Romania
| | - Dong Yun Lee
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, 08028, España
| | - Antonio Ortiz-Ambriz
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, 08028, España.,Institut de Nanociència i Nanotecnologia, Universitat de Barcelona, Barcelona, 08028, Spain
| | - Charles Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | | | - Pietro Tierno
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, 08028, España.,Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona, 08028, Spain.,Institut de Nanociència i Nanotecnologia, Universitat de Barcelona, Barcelona, 08028, Spain
| | - Cristiano Nisoli
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA. .,Institute for Materials Science, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
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10
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Sung D, Jung C, Cho BG, Jo W, Han HS, Lee KS, Bhat V, Farmer B, De Long LE, Lee KB, Keavney DJ, Lee DR, Song C. Imaging the magnetic structures of artificial quasicrystal magnets using resonant coherent diffraction of circularly polarized X-rays. NANOSCALE 2018; 10:13159-13164. [PMID: 29963676 DOI: 10.1039/c8nr03733g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Unraveling nanoscale spin structures has long been an important activity addressing various scientific interests, that are also readily adaptable to technological applications. This has invigorated the development of versatile nanoprobes suitable for imaging specimens under native conditions. Here we have demonstrated the resonant coherent diffraction of an artificial quasicrystal magnet with circularly polarized X-rays. The nanoscale magnetic structure was revealed from X-ray speckle patterns by comparing with micromagnetic simulations, as a step toward understanding the intricate relationship between the chemical and spin structures in an aperiodic quasicrystal lattice. Femtosecond X-ray pulses from free electron lasers are expected to immediately extend the current work to nanoscale structure investigations of ultrafast spin dynamics, surpassing the present spatio-temporal resolution.
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Affiliation(s)
- Daeho Sung
- Department of Physics, POSTECH, Pohang 37673, Korea.
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11
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Tunable and switchable magnetic dipole patterns in nanostructured superconductors. Nat Commun 2018; 9:2576. [PMID: 29968732 PMCID: PMC6030140 DOI: 10.1038/s41467-018-05045-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2017] [Accepted: 06/08/2018] [Indexed: 11/08/2022] Open
Abstract
Design and manipulation of magnetic moment arrays have been at the focus of studying the interesting cooperative physical phenomena in various magnetic systems. However, long-range ordered magnetic moments are rather difficult to achieve due to the excited states arising from the relatively weak exchange interactions between the localized moments. Here, using a nanostructured superconductor, we investigate a perfectly ordered magnetic dipole pattern with the magnetic poles having the same distribution as the magnetic charges in an artificial spin ice. The magnetic states can simply be switched on/off by applying a current flowing through nanopatterned area. Moreover, by coupling magnetic dipoles with the pinned vortex lattice, we are able to erase the positive/negative poles, resulting in a magnetic dipole pattern of only one polarity, analogous to the recently predicted vortex ice. These switchable and tunable magnetic dipole patterns open pathways for the study of exotic ordering phenomena in magnetic systems.
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12
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Wang YL, Ma X, Xu J, Xiao ZL, Snezhko A, Divan R, Ocola LE, Pearson JE, Janko B, Kwok WK. Switchable geometric frustration in an artificial-spin-ice-superconductor heterosystem. NATURE NANOTECHNOLOGY 2018; 13:560-565. [PMID: 29892018 DOI: 10.1038/s41565-018-0162-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2017] [Accepted: 05/03/2018] [Indexed: 06/08/2023]
Abstract
Geometric frustration emerges when local interaction energies in an ordered lattice structure cannot be simultaneously minimized, resulting in a large number of degenerate states. The numerous degenerate configurations may lead to practical applications in microelectronics1, such as data storage, memory and logic2. However, it is difficult to achieve very high degeneracy, especially in a two-dimensional system3,4. Here, we showcase in situ controllable geometric frustration with high degeneracy in a two-dimensional flux-quantum system. We create this in a superconducting thin film placed underneath a reconfigurable artificial-spin-ice structure5. The tunable magnetic charges in the artificial-spin-ice strongly interact with the flux quanta in the superconductor, enabling switching between frustrated and crystallized flux quanta states. The different states have measurable effects on the superconducting critical current profile, which can be reconfigured by precise selection of the spin-ice magnetic state through the application of an external magnetic field. We demonstrate the applicability of these effects by realizing a reprogrammable flux quanta diode. The tailoring of the energy landscape of interacting 'particles' using artificial-spin-ices provides a new paradigm for the design of geometric frustration, which could illuminate a path to control new functionalities in other material systems, such as magnetic skyrmions6, electrons and holes in two-dimensional materials7,8, and topological insulators9, as well as colloids in soft materials10-13.
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Affiliation(s)
- Yong-Lei Wang
- Materials Science Division, Argonne National Laboratory, Argonne, IL, USA.
- Department of Physics, University of Notre Dame, Notre Dame, IN, USA.
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
| | - Xiaoyu Ma
- Department of Physics, University of Notre Dame, Notre Dame, IN, USA
| | - Jing Xu
- Materials Science Division, Argonne National Laboratory, Argonne, IL, USA
- Department of Physics, Northern Illinois University, DeKalb, IL, USA
| | - Zhi-Li Xiao
- Materials Science Division, Argonne National Laboratory, Argonne, IL, USA.
- Department of Physics, Northern Illinois University, DeKalb, IL, USA.
| | - Alexey Snezhko
- Materials Science Division, Argonne National Laboratory, Argonne, IL, USA
| | - Ralu Divan
- Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL, USA
| | - Leonidas E Ocola
- Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL, USA
- IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA
| | - John E Pearson
- Materials Science Division, Argonne National Laboratory, Argonne, IL, USA
| | - Boldizsar Janko
- Department of Physics, University of Notre Dame, Notre Dame, IN, USA.
| | - Wai-Kwong Kwok
- Materials Science Division, Argonne National Laboratory, Argonne, IL, USA
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13
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Nisoli C. Unexpected Phenomenology in Particle-Based Ice Absent in Magnetic Spin Ice. PHYSICAL REVIEW LETTERS 2018; 120:167205. [PMID: 29756919 DOI: 10.1103/physrevlett.120.167205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2017] [Indexed: 06/08/2023]
Abstract
While particle-based ices are often considered essentially equivalent to magnet-based spin ices, the two differ essentially in frustration and energetics. We show that at equilibrium particle-based ices correspond exactly to spin ices coupled to a background field. In trivial geometries, such a field has no effect, and the two systems are indeed thermodynamically equivalent. In other cases, however, the field controls a richer phenomenology, absent in magnetic ices, and still largely unexplored: ice rule fragility, topological charge transfer, radial polarization, decimation induced disorder, and glassiness.
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Affiliation(s)
- Cristiano Nisoli
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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14
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Libál A, Nisoli C, Reichhardt CJO, Reichhardt C. Inner Phases of Colloidal Hexagonal Spin Ice. PHYSICAL REVIEW LETTERS 2018; 120:027204. [PMID: 29376707 DOI: 10.1103/physrevlett.120.027204] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2017] [Indexed: 06/07/2023]
Abstract
Using numerical simulations that mimic recent experiments on hexagonal colloidal ice, we show that colloidal hexagonal artificial spin ice exhibits an inner phase within its ice state that has not been observed previously. Under increasing colloid-colloid repulsion, the initially paramagnetic system crosses into a disordered ice regime, then forms a topologically charge ordered state with disordered colloids, and finally reaches a threefold degenerate, ordered ferromagnetic state. This is reminiscent of, yet distinct from, the inner phases of the magnetic kagome spin ice analog. The difference in the inner phases of the two systems is explained by their difference in energetics and frustration.
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Affiliation(s)
- A Libál
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Mathematics and Computer Science Department, Babeş-Bolyai University, Cluj 400084, Romania
| | - C Nisoli
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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15
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Bošković B, Brglez F, Brest J. Low-autocorrelation binary sequences: On improved merit factors and runtime predictions to achieve them. Appl Soft Comput 2017. [DOI: 10.1016/j.asoc.2017.02.024] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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16
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Dynamic Control of Topological Defects in Artificial Colloidal Ice. Sci Rep 2017; 7:651. [PMID: 28381863 PMCID: PMC5428472 DOI: 10.1038/s41598-017-00452-w] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2016] [Accepted: 02/27/2017] [Indexed: 11/23/2022] Open
Abstract
We demonstrate the use of an external field to stabilize and control defect lines connecting topological monopoles in spin ice. For definiteness we perform Brownian dynamics simulations with realistic units mimicking experimentally realized artificial colloidal spin ice systems, and show how defect lines can grow, shrink or move under the action of direct and alternating fields. Asymmetric alternating biasing forces can cause the defect line to ratchet in either direction, making it possible to precisely position the line at a desired location. Such manipulation could be employed to achieve mobile information storage in these metamaterials.
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17
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Serrano IG, Sesé J, Guillamón I, Suderow H, Vieira S, Ibarra MR, De Teresa JM. Thickness-modulated tungsten-carbon superconducting nanostructures grown by focused ion beam induced deposition for vortex pinning up to high magnetic fields. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2016; 7:1698-1708. [PMID: 28144519 PMCID: PMC5238659 DOI: 10.3762/bjnano.7.162] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/29/2016] [Accepted: 10/21/2016] [Indexed: 06/06/2023]
Abstract
We report efficient vortex pinning in thickness-modulated tungsten-carbon-based (W-C) nanostructures grown by focused ion beam induced deposition (FIBID). By using FIBID, W-C superconducting films have been created with thickness modulation properties exhibiting periodicity from 60 to 140 nm, leading to a strong pinning potential for the vortex lattice. This produces local minima in the resistivity up to high magnetic fields (2.2 T) in a broad temperature range due to commensurability effects between the pinning potential and the vortex lattice. The results show that the combination of single-step FIBID fabrication of superconducting nanostructures with built-in artificial pinning landscapes and the small intrinsic random pinning potential of this material produces strong periodic pinning potentials, maximizing the opportunities for the investigation of fundamental aspects in vortex science under changing external stimuli (e.g., temperature, magnetic field, electrical current).
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Affiliation(s)
- Ismael García Serrano
- Laboratorio de Microscopías Avanzadas (LMA), Instituto de Nanociencia de Aragón (INA), Universidad de Zaragoza, 50018 Zaragoza, Spain
- Departamento de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - Javier Sesé
- Laboratorio de Microscopías Avanzadas (LMA), Instituto de Nanociencia de Aragón (INA), Universidad de Zaragoza, 50018 Zaragoza, Spain
- Departamento de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - Isabel Guillamón
- Laboratorio de Bajas Temperaturas, Unidad Asociada UAM/CSIC, Instituto Nicolás Cabrera, Condensed Matter Physics Center (IFIMAC), Departa-mento de Física de la Materia Condensada, Universidad Autónoma de Madrid, Spain
| | - Hermann Suderow
- Laboratorio de Bajas Temperaturas, Unidad Asociada UAM/CSIC, Instituto Nicolás Cabrera, Condensed Matter Physics Center (IFIMAC), Departa-mento de Física de la Materia Condensada, Universidad Autónoma de Madrid, Spain
| | - Sebastián Vieira
- Laboratorio de Bajas Temperaturas, Unidad Asociada UAM/CSIC, Instituto Nicolás Cabrera, Condensed Matter Physics Center (IFIMAC), Departa-mento de Física de la Materia Condensada, Universidad Autónoma de Madrid, Spain
| | - Manuel Ricardo Ibarra
- Laboratorio de Microscopías Avanzadas (LMA), Instituto de Nanociencia de Aragón (INA), Universidad de Zaragoza, 50018 Zaragoza, Spain
- Departamento de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - José María De Teresa
- Laboratorio de Microscopías Avanzadas (LMA), Instituto de Nanociencia de Aragón (INA), Universidad de Zaragoza, 50018 Zaragoza, Spain
- Departamento de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain
- Instituto de Ciencia de Materiales de Aragón (ICMA), CSIC - Universidad de Zaragoza, 50009 Zaragoza, Spain
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18
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Wang YL, Xiao ZL, Snezhko A, Xu J, Ocola LE, Divan R, Pearson JE, Crabtree GW, Kwok WK. Rewritable artificial magnetic charge ice. Science 2016; 352:962-6. [DOI: 10.1126/science.aad8037] [Citation(s) in RCA: 106] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2015] [Accepted: 04/13/2016] [Indexed: 11/02/2022]
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19
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Industrial-strength bonds. Nature 2015; 527:S76-9. [PMID: 26560455 DOI: 10.1038/527s76a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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20
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Rocci M, Azpeitia J, Trastoy J, Perez-Muñoz A, Cabero M, Luccas RF, Munuera C, Mompean FJ, Garcia-Hernandez M, Bouzehouane K, Sefrioui Z, Leon C, Rivera-Calzada A, Villegas JE, Santamaria J. Proximity Driven Commensurate Pinning in YBa2Cu3O7 through All-Oxide Magnetic Nanostructures. NANO LETTERS 2015; 15:7526-7531. [PMID: 26441137 DOI: 10.1021/acs.nanolett.5b03261] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The design of artificial vortex pinning landscapes is a major goal toward large scale applications of cuprate superconductors. Although disordered nanometric inclusions have shown to modify their vortex phase diagram and to produce enhancements of the critical current ( MacManus-Driscoll , J. L. ; Foltyn , S. R. ; Jia , Q. X. ; Wang , H. ; Serquis , A. ; Civale , L. ; Maiorov , B. ; Hawley , M. E. ; Maley , M. P. ; Peterson , D. E. Nat. Mater. 2004 , 3 , 439 - 443 and Yamada , Y. ; Takahashi , K. ; Kobayashi , H. ; Konishi , M. ; Watanabe , T. ; Ibi , A. ; Muroga , T. ; Miyata , S. ; Kato , T. ; Hirayama , T. ; Shiohara , Y. Appl. Phys. Lett. 2005 , 87 , 1 - 3 ), the effect of ordered oxide nanostructures remains essentially unexplored. This is due to the very small nanostructure size imposed by the short coherence length, and to the technological difficulties in the nanofabrication process. Yet, the novel phenomena occurring at oxide interfaces open a wide spectrum of technological opportunities to interplay with the superconductivity in cuprates. Here, we show that the unusual long-range suppression of the superconductivity occurring at the interface between manganites and cuprates affects vortex nucleation and provides a novel vortex pinning mechanism. In particular, we show evidence of commensurate pinning in YBCO films with ordered arrays of LCMO ferromagnetic nanodots. Vortex pinning results from the proximity induced reduction of the condensation energy at the vicinity of the magnetic nanodots, and yields an enhanced friction between the nanodot array and the moving vortex lattice in the liquid phase. This result shows that all-oxide ordered nanostructures constitute a powerful, new route for the artificial manipulation of vortex matter in cuprates.
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Affiliation(s)
- M Rocci
- GFMC, Dpto. Fisica Aplicada III, Univ. Complutense Madrid , 28040 Madrid, Spain
- Unidad Asociada Laboratorio de Heteroestructuras con Aplicación en Espintrónica" UCM-CSIC , 28049 Madrid, Spain
| | - J Azpeitia
- Instituto de Ciencia de Materiales de Madrid , 28049 Madrid, Spain
- Unidad Asociada Laboratorio de Heteroestructuras con Aplicación en Espintrónica" UCM-CSIC , 28049 Madrid, Spain
| | - J Trastoy
- Unité Mixte de Physique, CNRS, Thales, Univ. Paris-Sud, Université , Paris-Saclay, 91767, Palaiseau, France
- Université Paris Sud , 91407 Orsay, France
| | - A Perez-Muñoz
- GFMC, Dpto. Fisica Aplicada III, Univ. Complutense Madrid , 28040 Madrid, Spain
- Unidad Asociada Laboratorio de Heteroestructuras con Aplicación en Espintrónica" UCM-CSIC , 28049 Madrid, Spain
| | - M Cabero
- GFMC, Dpto. Fisica Aplicada III, Univ. Complutense Madrid , 28040 Madrid, Spain
- Unidad Asociada Laboratorio de Heteroestructuras con Aplicación en Espintrónica" UCM-CSIC , 28049 Madrid, Spain
| | - R F Luccas
- Instituto de Ciencia de Materiales de Madrid , 28049 Madrid, Spain
- Unidad Asociada Laboratorio de Heteroestructuras con Aplicación en Espintrónica" UCM-CSIC , 28049 Madrid, Spain
| | - C Munuera
- Instituto de Ciencia de Materiales de Madrid , 28049 Madrid, Spain
- Unidad Asociada Laboratorio de Heteroestructuras con Aplicación en Espintrónica" UCM-CSIC , 28049 Madrid, Spain
| | - F J Mompean
- Instituto de Ciencia de Materiales de Madrid , 28049 Madrid, Spain
- Unidad Asociada Laboratorio de Heteroestructuras con Aplicación en Espintrónica" UCM-CSIC , 28049 Madrid, Spain
| | - M Garcia-Hernandez
- Instituto de Ciencia de Materiales de Madrid , 28049 Madrid, Spain
- Unidad Asociada Laboratorio de Heteroestructuras con Aplicación en Espintrónica" UCM-CSIC , 28049 Madrid, Spain
| | - K Bouzehouane
- Unité Mixte de Physique, CNRS, Thales, Univ. Paris-Sud, Université , Paris-Saclay, 91767, Palaiseau, France
- Université Paris Sud , 91407 Orsay, France
| | - Z Sefrioui
- GFMC, Dpto. Fisica Aplicada III, Univ. Complutense Madrid , 28040 Madrid, Spain
- Unidad Asociada Laboratorio de Heteroestructuras con Aplicación en Espintrónica" UCM-CSIC , 28049 Madrid, Spain
| | - C Leon
- GFMC, Dpto. Fisica Aplicada III, Univ. Complutense Madrid , 28040 Madrid, Spain
- Unidad Asociada Laboratorio de Heteroestructuras con Aplicación en Espintrónica" UCM-CSIC , 28049 Madrid, Spain
| | - A Rivera-Calzada
- GFMC, Dpto. Fisica Aplicada III, Univ. Complutense Madrid , 28040 Madrid, Spain
- Unidad Asociada Laboratorio de Heteroestructuras con Aplicación en Espintrónica" UCM-CSIC , 28049 Madrid, Spain
| | - J E Villegas
- Unité Mixte de Physique, CNRS, Thales, Univ. Paris-Sud, Université , Paris-Saclay, 91767, Palaiseau, France
- Université Paris Sud , 91407 Orsay, France
| | - J Santamaria
- GFMC, Dpto. Fisica Aplicada III, Univ. Complutense Madrid , 28040 Madrid, Spain
- Unidad Asociada Laboratorio de Heteroestructuras con Aplicación en Espintrónica" UCM-CSIC , 28049 Madrid, Spain
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