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Jeon KR, Hazra BK, Kim JK, Jeon JC, Han H, Meyerheim HL, Kontos T, Cottet A, Parkin SSP. Chiral antiferromagnetic Josephson junctions as spin-triplet supercurrent spin valves and d.c. SQUIDs. NATURE NANOTECHNOLOGY 2023; 18:747-753. [PMID: 36997754 PMCID: PMC10359187 DOI: 10.1038/s41565-023-01336-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2021] [Accepted: 01/31/2023] [Indexed: 06/19/2023]
Abstract
Spin-triplet supercurrent spin valves are of practical importance for the realization of superconducting spintronic logic circuits. In ferromagnetic Josephson junctions, the magnetic-field-controlled non-collinearity between the spin-mixer and spin-rotator magnetizations switches the spin-polarized triplet supercurrents on and off. Here we report an antiferromagnetic equivalent of such spin-triplet supercurrent spin valves in chiral antiferromagnetic Josephson junctions as well as a direct-current superconducting quantum interference device. We employ the topological chiral antiferromagnet Mn3Ge, in which the Berry curvature of the band structure produces fictitious magnetic fields, and the non-collinear atomic-scale spin arrangement accommodates triplet Cooper pairing over long distances (>150 nm). We theoretically verify the observed supercurrent spin-valve behaviours under a small magnetic field of <2 mT for current-biased junctions and the direct-current superconducting quantum interference device functionality. Our calculations reproduce the observed hysteretic field interference of the Josephson critical current and link these to the magnetic-field-modulated antiferromagnetic texture that alters the Berry curvature. Our work employs band topology to control the pairing amplitude of spin-triplet Cooper pairs in a single chiral antiferromagnet.
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Affiliation(s)
- Kun-Rok Jeon
- Max Planck Institute of Microstructure Physics, Halle (Saale), Germany.
- Department of Physics, Chung-Ang University (CAU), Seoul, Republic of Korea.
| | | | - Jae-Keun Kim
- Max Planck Institute of Microstructure Physics, Halle (Saale), Germany
| | - Jae-Chun Jeon
- Max Planck Institute of Microstructure Physics, Halle (Saale), Germany
| | - Hyeon Han
- Max Planck Institute of Microstructure Physics, Halle (Saale), Germany
| | | | - Takis Kontos
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Paris, France
| | - Audrey Cottet
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Paris, France.
| | - Stuart S P Parkin
- Max Planck Institute of Microstructure Physics, Halle (Saale), Germany.
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2
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Fermin R, van Dinter D, Hubert M, Woltjes B, Silaev M, Aarts J, Lahabi K. Superconducting Triplet Rim Currents in a Spin-Textured Ferromagnetic Disk. NANO LETTERS 2022; 22:2209-2216. [PMID: 35239357 PMCID: PMC8949790 DOI: 10.1021/acs.nanolett.1c04051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Revised: 02/23/2022] [Indexed: 06/14/2023]
Abstract
Since the discovery of the long-range superconducting proximity effect, the interaction between spin-triplet Cooper pairs and magnetic structures such as domain walls and vortices has been the subject of intense theoretical discussions, while the relevant experiments remain scarce. We have developed nanostructured Josephson junctions with highly controllable spin texture, based on a disk-shaped Nb/Co bilayer. Here, the vortex magnetization of Co and the Cooper pairs of Nb conspire to induce long-range triplet (LRT) superconductivity in the ferromagnet. Surprisingly, the LRT correlations emerge in highly localized (sub-80 nm) channels at the rim of the ferromagnet, despite its trivial band structure. We show that these robust rim currents arise from the magnetization texture acting as an effective spin-orbit coupling, which results in spin accumulation at the bilayer-vacuum boundary. Lastly, we demonstrate that by altering the spin texture of a single ferromagnet, both 0 and π channels can be realized in the same device.
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Affiliation(s)
- Remko Fermin
- Huygens-Kamerlingh
Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Dyon van Dinter
- Huygens-Kamerlingh
Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Michel Hubert
- Huygens-Kamerlingh
Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Bart Woltjes
- Huygens-Kamerlingh
Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Mikhail Silaev
- Department
of Physics and Nanoscience Center, University
of Jyväskylä, P.O. Box 35 (YFL), FI-40014 Jyväskylä, Finland
- Computational
Physics Laboratory, Physics Unit, Faculty of Engineering and Natural
Sciences, Tampere University, P.O. Box 692, FI-33014 Tampere, Finland
| | - Jan Aarts
- Huygens-Kamerlingh
Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Kaveh Lahabi
- Huygens-Kamerlingh
Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
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3
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Sanchez-Manzano D, Mesoraca S, Cuellar FA, Cabero M, Rouco V, Orfila G, Palermo X, Balan A, Marcano L, Sander A, Rocci M, Garcia-Barriocanal J, Gallego F, Tornos J, Rivera A, Mompean F, Garcia-Hernandez M, Gonzalez-Calbet JM, Leon C, Valencia S, Feuillet-Palma C, Bergeal N, Buzdin AI, Lesueur J, Villegas JE, Santamaria J. Extremely long-range, high-temperature Josephson coupling across a half-metallic ferromagnet. NATURE MATERIALS 2022; 21:188-194. [PMID: 34857910 DOI: 10.1038/s41563-021-01162-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Accepted: 10/21/2021] [Indexed: 06/13/2023]
Abstract
The Josephson effect results from the coupling of two superconductors across a spacer such as an insulator, a normal metal or a ferromagnet to yield a phase coherent quantum state. However, in junctions with ferromagnetic spacers, very long-range Josephson effects have remained elusive. Here we demonstrate extremely long-range (micrometric) high-temperature (tens of kelvins) Josephson coupling across the half-metallic manganite La0.7Sr0.3MnO3 combined with the superconducting cuprate YBa2Cu3O7. These planar junctions, in addition to large critical currents, display the hallmarks of Josephson physics, such as critical current oscillations driven by magnetic flux quantization and quantum phase locking effects under microwave excitation (Shapiro steps). The latter display an anomalous doubling of the Josephson frequency predicted by several theories. In addition to its fundamental interest, the marriage between high-temperature, dissipationless quantum coherent transport and full spin polarization brings opportunities for the practical realization of superconducting spintronics, and opens new perspectives for quantum computing.
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Affiliation(s)
- D Sanchez-Manzano
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - S Mesoraca
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, Palaiseau, France
| | - F A Cuellar
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - M Cabero
- IMDEA Nanoscience Institute, Universidad Autonoma, Cantoblanco, Spain
- Centro Nacional de Microscopia Electronica, Universidad Complutense, Madrid, Spain
| | - V Rouco
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - G Orfila
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - X Palermo
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, Palaiseau, France
| | - A Balan
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, Palaiseau, France
| | - L Marcano
- Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, Germany
| | - A Sander
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, Palaiseau, France
| | - M Rocci
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
- Instituto Nanoscienze, Consiglio Thales Alenia Space Italia, L'Aquila, Italy
| | | | - F Gallego
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - J Tornos
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - A Rivera
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - F Mompean
- Instituto de Ciencia de Materiales de Madrid (ICMM, CSIC), Cantoblanco, Spain
- Laboratorio de Heteroestructuras con Aplicación en Spintrónica, Unidad Asociada (UCM-CSIC), Madrid, Spain
| | - M Garcia-Hernandez
- Instituto de Ciencia de Materiales de Madrid (ICMM, CSIC), Cantoblanco, Spain
- Laboratorio de Heteroestructuras con Aplicación en Spintrónica, Unidad Asociada (UCM-CSIC), Madrid, Spain
| | - J M Gonzalez-Calbet
- Centro Nacional de Microscopia Electronica, Universidad Complutense, Madrid, Spain
- Departamento Química Inorgánica, Facultad de Química, Universidad Complutense, Madrid, Spain
| | - C Leon
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - S Valencia
- Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, Germany
| | - C Feuillet-Palma
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, CNRS, PSL Research University, Sorbonne University, Paris, France
| | - N Bergeal
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, CNRS, PSL Research University, Sorbonne University, Paris, France
| | - A I Buzdin
- LOMA, CNRS, Université Bordeaux, Talence, France
- Digital Biodesign and Personalized Healthcare, Sechenov First Moscow State Medical University, Moscow, Russia
| | - J Lesueur
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, CNRS, PSL Research University, Sorbonne University, Paris, France
| | - Javier E Villegas
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, Palaiseau, France.
| | - J Santamaria
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain.
- Laboratorio de Heteroestructuras con Aplicación en Spintrónica, Unidad Asociada (UCM-CSIC), Madrid, Spain.
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Kapran OM, Morari R, Golod T, Borodianskyi EA, Boian V, Prepelita A, Klenov N, Sidorenko AS, Krasnov VM. In situ transport characterization of magnetic states in Nb/Co superconductor/ferromagnet heterostructures. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2021; 12:913-923. [PMID: 34497739 PMCID: PMC8381831 DOI: 10.3762/bjnano.12.68] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 07/25/2021] [Indexed: 06/13/2023]
Abstract
Employment of the non-trivial proximity effect in superconductor/ferromagnet (S/F) heterostructures for the creation of novel superconducting devices requires accurate control of magnetic states in complex thin-film multilayers. In this work, we study experimentally in-plane transport properties of microstructured Nb/Co multilayers. We apply various transport characterization techniques, including magnetoresistance, Hall effect, and the first-order-reversal-curves (FORC) analysis. We demonstrate how FORC can be used for detailed in situ characterization of magnetic states. It reveals that upon reduction of the external field, the magnetization in ferromagnetic layers first rotates in a coherent scissor-like manner, then switches abruptly into the antiparallel state and after that splits into the polydomain state, which gradually turns into the opposite parallel state. The polydomain state is manifested by a profound enhancement of resistance caused by a flux-flow phenomenon, triggered by domain stray fields. The scissor state represents the noncollinear magnetic state in which the unconventional odd-frequency spin-triplet order parameter should appear. The non-hysteretic nature of this state allows for reversible tuning of the magnetic orientation. Thus, we identify the range of parameters and the procedure for in situ control of devices based on S/F heterostructures.
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Affiliation(s)
- Olena M Kapran
- Department of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden
| | - Roman Morari
- Institute of Electronic Engineering and Nanotechnologies, MD2028 Chisinau, Moldova
- Moscow Institute of Physics and Technology, State University, 141700 Dolgoprudny, Russia
| | - Taras Golod
- Department of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden
| | - Evgenii A Borodianskyi
- Department of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden
| | - Vladimir Boian
- Institute of Electronic Engineering and Nanotechnologies, MD2028 Chisinau, Moldova
| | - Andrei Prepelita
- Institute of Electronic Engineering and Nanotechnologies, MD2028 Chisinau, Moldova
| | - Nikolay Klenov
- Lomonosov Moscow State University, Faculty of Physics, Moscow, 119991, Russia
- Moscow Technical University of Communication and Informatics, 111024 Moscow, Russia
| | - Anatoli S Sidorenko
- Institute of Electronic Engineering and Nanotechnologies, MD2028 Chisinau, Moldova
- Moscow Institute of Physics and Technology, State University, 141700 Dolgoprudny, Russia
- Laboratory of Functional Nanostructures, Orel State University named after I.S. Turgenev, 302026, Russia
| | - Vladimir M Krasnov
- Department of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden
- Moscow Institute of Physics and Technology, State University, 141700 Dolgoprudny, Russia
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5
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Satchell N, Mitchell T, Shepley PM, Darwin E, Hickey BJ, Burnell G. Pt and CoB trilayer Josephson [Formula: see text] junctions with perpendicular magnetic anisotropy. Sci Rep 2021; 11:11173. [PMID: 34045523 PMCID: PMC8159980 DOI: 10.1038/s41598-021-90432-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2020] [Accepted: 04/05/2021] [Indexed: 11/13/2022] Open
Abstract
We report on the electrical transport properties of Nb based Josephson junctions with Pt/Co[Formula: see text]B[Formula: see text]/Pt ferromagnetic barriers. The barriers exhibit perpendicular magnetic anisotropy, which has the main advantage for potential applications over magnetisation in-plane systems of not affecting the Fraunhofer response of the junction. In addition, we report that there is no magnetic dead layer at the Pt/Co[Formula: see text]B[Formula: see text] interfaces, allowing us to study barriers with ultra-thin Co[Formula: see text]B[Formula: see text]. In the junctions, we observe that the magnitude of the critical current oscillates with increasing thickness of the Co[Formula: see text]B[Formula: see text] strong ferromagnetic alloy layer. The oscillations are attributed to the ground state phase difference across the junctions being modified from zero to [Formula: see text]. The multiple oscillations in the thickness range [Formula: see text] nm suggests that we have access to the first zero-[Formula: see text] and [Formula: see text]-zero phase transitions. Our results fuel the development of low-temperature memory devices based on ferromagnetic Josephson junctions.
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Affiliation(s)
- N. Satchell
- School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT UK
| | - T. Mitchell
- School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT UK
| | - P. M. Shepley
- School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT UK
| | - E. Darwin
- School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT UK
| | - B. J. Hickey
- School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT UK
| | - G. Burnell
- School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT UK
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6
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Bhatia E, Srivastava A, Devine-Stoneman J, Stelmashenko NA, Barber ZH, Robinson JWA, Senapati K. Nanoscale Domain Wall Engineered Spin-Triplet Josephson Junctions and SQUID. NANO LETTERS 2021; 21:3092-3097. [PMID: 33724857 DOI: 10.1021/acs.nanolett.1c00273] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Spin-singlet Cooper pairs convert to spin-triplet Cooper pairs on passing through a magnetically noncollinear structure at a superconductor(S)/ferromagnet(F) interface. In this context, the generation of triplet supercurrents through intrinsic ferromagnetic domain walls, which are naturally occurring noncollinear magnetic features, was proposed theoretically in the past decade. However, an experimental demonstration has been lacking in the literature, particularly because of the difficulty in accessing a single domain wall, which is typically buried between two domains in a ferromagnetic material. By patterning a ferromagnetic nanoconstriction, we have been able to realize a nanoscale S/F/S planar junction, where a single domain wall (pinned at the nanoconstriction) acts as a Josephson barrier. In this geometry, we are able to show the predicted long-range triplet supercurrent across a ferromagnetic barrier exceeding 70 nm. Using this technique, we have demonstrated a ferromagnetic planar nano-SQUID device consisting of two Nb/Ni/Nb spin-triplet Josephson junctions.
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Affiliation(s)
- Ekta Bhatia
- School of Physical Sciences, National Institute of Science Education and Research (NISER), HBNI, Bhubaneswar, Odisha 752050, India
| | - Anand Srivastava
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - James Devine-Stoneman
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - Nadia A Stelmashenko
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - Zoe H Barber
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - Jason W A Robinson
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - Kartik Senapati
- School of Physical Sciences, National Institute of Science Education and Research (NISER), HBNI, Bhubaneswar, Odisha 752050, India
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7
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Zhang DL, Zhu J, Qu T, Lattery DM, Victora RH, Wang X, Wang JP. High-frequency magnetoacoustic resonance through strain-spin coupling in perpendicular magnetic multilayers. SCIENCE ADVANCES 2020; 6:6/38/eabb4607. [PMID: 32948586 PMCID: PMC7500926 DOI: 10.1126/sciadv.abb4607] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2020] [Accepted: 07/29/2020] [Indexed: 05/29/2023]
Abstract
It is desirable to experimentally demonstrate an extremely high resonant frequency, assisted by strain-spin coupling, in technologically important perpendicular magnetic materials for device applications. Here, we directly observe the coupling of magnons and phonons in both time and frequency domains upon femtosecond laser excitation. This strain-spin coupling leads to a magnetoacoustic resonance in perpendicular magnetic [Co/Pd] n multilayers, reaching frequencies in the extremely high frequency (EHF) band, e.g., 60 GHz. We propose a theoretical model to explain the physical mechanism underlying the strain-spin interaction. Our model explains the amplitude increase of the magnetoacoustic resonance state with time and quantitatively predicts the composition of the combined strain-spin state near the resonance. We also detail its precise dependence on the magnetostriction. The results of this work offer a potential pathway to manipulating both the magnitude and timing of EHF and strongly coupled magnon-phonon excitations.
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Affiliation(s)
- De-Lin Zhang
- Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA
| | - Jie Zhu
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
| | - Tao Qu
- School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA
| | - Dustin M Lattery
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
| | - R H Victora
- Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA.
- School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA
| | - Xiaojia Wang
- Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA.
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
| | - Jian-Ping Wang
- Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA.
- School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA
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Birge NO. Spin-triplet supercurrents in Josephson junctions containing strong ferromagnetic materials. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:20150150. [PMID: 29941625 PMCID: PMC6030151 DOI: 10.1098/rsta.2015.0150] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/28/2015] [Indexed: 06/08/2023]
Abstract
The proximity effect between a superconducting material and a non-superconducting normal metal can extend over distances of the order of micrometres at sufficiently low temperatures. If the normal metal is replaced by a ferromagnetic material, the spatial extent of the proximity effect drops precipitously due to the exchange splitting between the majority and minority spin bands in the ferromagnet. In 2001, several theorists predicted that spin-triplet pair correlations could be induced in proximity systems involving multiple ferromagnetic materials (or multiple domains in one material) with non-collinear magnetizations. Such spin-triplet pair correlations should extend deep into the ferromagnet, producing a long-range proximity effect. In this paper, we review our experimental work in this area, which has focused primarily on Josephson junctions containing strong ferromagnetic materials. We show that Josephson junctions containing particular combinations of strong ferromagnetic materials can carry spin-triplet supercurrent over distances of at least several tens of nanometres, whereas spin-singlet supercurrent in similar samples decays over a length scale of about 1 nm. We also mention important work by other groups; however, this article is not intended to be a review of the whole field.This article is part of the theme issue 'Andreev bound states'.
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Affiliation(s)
- Norman O Birge
- Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
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