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Kamashev AA, Garif’yanov NN, Validov AA, Kataev V, Osin AS, Fominov YV, Garifullin IA. Superconducting spin valve effect in Co/Pb/Co heterostructures with insulating interlayers. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2024; 15:457-464. [PMID: 38711583 PMCID: PMC11070957 DOI: 10.3762/bjnano.15.41] [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: 11/24/2023] [Accepted: 04/09/2024] [Indexed: 05/08/2024]
Abstract
We report the superconducting properties of Co/Pb/Co heterostructures with thin insulating interlayers. The main specific feature of these structures is the intentional oxidation of both superconductor/ferromagnet (S/F) interfaces. We study the variation of the critical temperature of our systems due to switching between parallel and antiparallel configurations of the magnetizations of the two magnetic layers. Common knowledge suggests that this spin valve effect, which is due to the S/F proximity effect, is most pronounced in the case of perfect metallic contacts at the interfaces. Nevertheless, in our structures with intentionally deteriorated interfaces, we observed a significant full spin valve effect. A shift of the superconducting transition temperature Tc by switching the mutual orientation of the magnetizations of the two ferromagnetic Co layers from antiparallel to parallel amounted to ΔTc = 0.2 K at the optimal thickness of the superconducting Pb layer. Our findings verify the so far unconfirmed earlier results by Deutscher and Meunier on an F1/S/F2 heterostructure with oxidized interlayers [Deutscher, G.; Meunier, F. Phys. Rev. Lett. 1969, 22, 395. https://doi.org/10.1103/PhysRevLett.22.395] and suggest an alternative route to optimize the performance of superconducting spin valves.
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Affiliation(s)
- Andrey A Kamashev
- Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS, 420029 Kazan, Russia
| | - Nadir N Garif’yanov
- Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS, 420029 Kazan, Russia
| | - Aidar A Validov
- Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS, 420029 Kazan, Russia
| | - Vladislav Kataev
- Leibniz Institute for Solid State and Materials Research, Helmholtzstr. 20, D-01069 Dresden, Germany
| | - Alexander S Osin
- L. D. Landau Institute for Theoretical Physics RAS, 142432 Chernogolovka, Russia
| | - Yakov V Fominov
- L. D. Landau Institute for Theoretical Physics RAS, 142432 Chernogolovka, Russia
- Laboratory for Condensed Matter Physics, HSE University, 101000 Moscow, Russia
| | - Ilgiz A Garifullin
- Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS, 420029 Kazan, Russia
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Johnsen LG, Svalland K, Linder J. Controlling the Superconducting Transition by Rotation of an Inversion Symmetry-Breaking Axis. PHYSICAL REVIEW LETTERS 2020; 125:107002. [PMID: 32955310 DOI: 10.1103/physrevlett.125.107002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2019] [Revised: 04/28/2020] [Accepted: 08/10/2020] [Indexed: 06/11/2023]
Abstract
We consider a hybrid structure where a material with Rashba-like spin-orbit coupling is proximity coupled to a conventional superconductor. We find that the superconducting critical temperature T_{c} can be tuned by rotating the vector n characterizing the axis of broken inversion symmetry. This is explained by a leakage of s-wave singlet Cooper pairs out of the superconducting region, and by conversion of s-wave singlets into other types of correlations, among these s-wave odd-frequency pairs robust to impurity scattering. These results demonstrate a conceptually different way of tuning T_{c} compared to the previously studied variation of T_{c} in magnetic hybrids.
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Affiliation(s)
- Lina G Johnsen
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Kristian Svalland
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Jacob Linder
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
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Komori S, Di Bernardo A, Buzdin AI, Blamire MG, Robinson JWA. Magnetic Exchange Fields and Domain Wall Superconductivity at an All-Oxide Superconductor-Ferromagnet Insulator Interface. PHYSICAL REVIEW LETTERS 2018; 121:077003. [PMID: 30169105 DOI: 10.1103/physrevlett.121.077003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2018] [Revised: 05/20/2018] [Indexed: 06/08/2023]
Abstract
At a superconductor-ferromagnet (S/F) interface, the F layer can introduce a magnetic exchange field within the S layer, which acts to locally spin split the superconducting density of states. The effect of magnetic exchange fields on superconductivity has been thoroughly explored at S-ferromagnet insulator (S/FI) interfaces for isotropic s-wave S and a thickness that is smaller than the superconducting coherence length. Here we report a magnetic exchange field effect at an all-oxide S/FI interface involving the anisotropic d-wave high temperature superconductor praseodymium cerium copper oxide (PCCO) and the FI praseodymium calcium manganese oxide (PCMO). The magnetic exchange field in PCCO, detected via magnetotransport measurements through the superconducting transition, is localized to the PCCO/PCMO interface with an average magnitude that depends on the presence or absence of magnetic domain walls in PCMO. The results are promising for the development of all-oxide superconducting spintronic devices involving unconventional pairing and high temperature superconductors.
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Affiliation(s)
- S Komori
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - A Di Bernardo
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - A I Buzdin
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
- University Bordeaux, LOMA UMR-CNRS 5798, F-33405 Talence Cedex, France
| | - M G Blamire
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - J W A Robinson
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
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Breunig D, Burset P, Trauzettel B. Creation of Spin-Triplet Cooper Pairs in the Absence of Magnetic Ordering. PHYSICAL REVIEW LETTERS 2018; 120:037701. [PMID: 29400487 DOI: 10.1103/physrevlett.120.037701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2017] [Revised: 12/20/2017] [Indexed: 06/07/2023]
Abstract
In superconducting spintronics, it is essential to generate spin-triplet Cooper pairs on demand. Up to now, proposals to do so concentrate on hybrid structures in which a superconductor (SC) is combined with a magnetically ordered material (or an external magnetic field). We, instead, identify a novel way to create and isolate spin-triplet Cooper pairs in the absence of any magnetic ordering. This achievement is only possible because we drive a system with strong spin-orbit interaction-the Dirac surface states of a strong topological insulator (TI)-out of equilibrium. In particular, we consider a bipolar TI-SC-TI junction, where the electrochemical potentials in the outer leads differ in their overall sign. As a result, we find that nonlocal singlet pairing across the junction is completely suppressed for any excitation energy. Hence, this junction acts as a perfect spin-triplet filter across the SC, generating equal-spin Cooper pairs via crossed Andreev reflection.
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Affiliation(s)
- Daniel Breunig
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
| | - Pablo Burset
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Björn Trauzettel
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
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Kamashev A, Validov A, Garif’yanov N, Fominov Y, Leksin P, Schumann J, Thomas J, Kataev V, Büchner B, Garifullin I. Isolation of proximity-induced triplet pairing channel in a superconductor/ferromagnet spin valve. EPJ WEB OF CONFERENCES 2018. [DOI: 10.1051/epjconf/201818508001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In the present work we have studied the proximity-induced superconducting triplet pairing in CoOx/Py1/Cu/Py2/Cu/Pb spin-valve structure (where Py = Ni0:81Fe0:19). For CoOx(3 nm)/Py(3 nm)/Cu(4 nm)/Py(0.6 nm)/Cu(2 nm)/Pb(70 nm) we have studied the dependence of the Tc on the angle α between the direction of the cooling field and the external field both applied in the plane of the sample. We obtained that the Tc does not change monotonically with the angle but passes through a minimum. To observe an “isolated” triplet spin-valve effect we exploited the oscillatory feature of the magnitude of the ordinary spin-valve effect ΔTc in the dependence of the Py2-layer thickness dPy2. We determined the value of dPy2 at which ΔTc caused by the ordinary spin-valve effect is suppressed. This means that the difference in the Tc between the antiparallel and parallel mutual orientation of magnetizations of the Py1 and Py2 layers is zero. For such a sample a “pure” triplet spin-valve effect which causes the minimum in Tc at the orthogonal configuration of magnetizations has been observed.
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Kumar J, Nemade HB, Giri PK. Density functional theory investigation of negative differential resistance and efficient spin filtering in niobium-doped armchair graphene nanoribbons. Phys Chem Chem Phys 2017; 19:29685-29692. [DOI: 10.1039/c7cp05921c] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
A niobium-doped AGNR for efficient negative differential resistance and spin filtering applications.
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Affiliation(s)
- Jitendra Kumar
- Centre for Nanotechnology
- Indian Institute of Technology Guwahati
- Guwahati-781039
- India
| | - Harshal B. Nemade
- Department of Electrical & Electronics Engineering
- Indian Institute of Technology Guwahati
- Guwahati-781039
- India
| | - P. K. Giri
- Department of Physics
- Indian Institute of Technology Guwahati
- Guwahati-781039
- India
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Ouassou JA, Di Bernardo A, Robinson JWA, Linder J. Electric control of superconducting transition through a spin-orbit coupled interface. Sci Rep 2016; 6:29312. [PMID: 27426887 PMCID: PMC4947909 DOI: 10.1038/srep29312] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2016] [Accepted: 06/16/2016] [Indexed: 11/09/2022] Open
Abstract
We demonstrate theoretically all-electric control of the superconducting transition temperature using a device comprised of a conventional superconductor, a ferromagnetic insulator, and semiconducting layers with intrinsic spin-orbit coupling. By using analytical calculations and numerical simulations, we show that the transition temperature of such a device can be controlled by electric gating which alters the ratio of Rashba to Dresselhaus spin-orbit coupling. The results offer a new pathway to control superconductivity in spintronic devices.
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Affiliation(s)
- Jabir Ali Ouassou
- Department of Physics, NTNU, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
| | - Angelo Di Bernardo
- 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
| | - Jacob Linder
- Department of Physics, NTNU, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
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Lenk D, Zdravkov VI, Kehrle JM, Obermeier G, Ullrich A, Morari R, Krug von Nidda HA, Müller C, Kupriyanov MY, Sidorenko AS, Horn S, Deminov RG, Tagirov LR, Tidecks R. Thickness dependence of the triplet spin-valve effect in superconductor-ferromagnet-ferromagnet heterostructures. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2016; 7:957-969. [PMID: 27547613 PMCID: PMC4979884 DOI: 10.3762/bjnano.7.88] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/25/2016] [Accepted: 06/13/2016] [Indexed: 06/06/2023]
Abstract
BACKGROUND In nanoscale layered S/F1/N/F2/AF heterostructures, the generation of a long-range, odd-in-frequency spin-projection one triplet component of superconductivity, arising at non-collinear alignment of the magnetizations of F1 and F2, exhausts the singlet state. This yields the possibility of a global minimum of the superconducting transition temperature T c, i.e., a superconducting triplet spin-valve effect, around mutually perpendicular alignment. RESULTS The superconducting triplet spin valve is realized with S = Nb a singlet superconductor, F1 = Cu41Ni59 and F2 = Co ferromagnetic metals, AF = CoO x an antiferromagnetic oxide, and N = nc-Nb a normal conducting (nc) non-magnetic metal, which serves to decouple F1 and F2. The non-collinear alignment of the magnetizations is obtained by applying an external magnetic field parallel to the layers of the heterostructure and exploiting the intrinsic perpendicular easy-axis of the magnetization of the Cu41Ni59 thin film in conjunction with the exchange bias between CoO x and Co. The magnetic configurations are confirmed by superconducting quantum interference device (SQUID) magnetic moment measurements. The triplet spin-valve effect has been investigated for different layer thicknesses, d F1, of F1 and was found to decay with increasing d F1. The data is described by an empirical model and, moreover, by calculations using the microscopic theory. CONCLUSION The long-range triplet component of superconducting pairing is generated from the singlet component mainly at the N/F2 interface, where the amplitude of the singlet component is suppressed exponentially with increasing distance d F1. The decay length of the empirical model is found to be comparable to twice the electron mean free path of F1 and, thus, to the decay length of the singlet component in F1. Moreover, the obtained data is in qualitative agreement with the microscopic theory, which, however, predicts a (not investigated) breakdown of the triplet spin-valve effect for d F1 smaller than 0.3 to 0.4 times the magnetic coherence length, ξF1.
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Affiliation(s)
- Daniel Lenk
- Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86159 Augsburg, Germany
| | - Vladimir I Zdravkov
- Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86159 Augsburg, Germany
- D. Ghitsu Institute of Electronic Engineering and Nanotechnologies ASM, Academiei Str. 3/3, MD2028 Kishinev, Moldova
| | - Jan-Michael Kehrle
- Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86159 Augsburg, Germany
| | - Günter Obermeier
- Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86159 Augsburg, Germany
| | - Aladin Ullrich
- Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86159 Augsburg, Germany
| | - Roman Morari
- Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86159 Augsburg, Germany
- D. Ghitsu Institute of Electronic Engineering and Nanotechnologies ASM, Academiei Str. 3/3, MD2028 Kishinev, Moldova
- Solid State Physics Department, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russian Federation
| | | | - Claus Müller
- Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86159 Augsburg, Germany
| | - Mikhail Yu Kupriyanov
- Solid State Physics Department, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russian Federation
- Skobeltsyn Institute of Nuclear Physics, Moscow State University, Leninskie gory, GSP-1, Moscow 119992, Russia
| | - Anatolie S Sidorenko
- D. Ghitsu Institute of Electronic Engineering and Nanotechnologies ASM, Academiei Str. 3/3, MD2028 Kishinev, Moldova
| | - Siegfried Horn
- Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86159 Augsburg, Germany
| | - Rafael G Deminov
- Solid State Physics Department, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russian Federation
| | - Lenar R Tagirov
- Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86159 Augsburg, Germany
- Solid State Physics Department, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russian Federation
| | - Reinhard Tidecks
- Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86159 Augsburg, Germany
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Di Bernardo A, Diesch S, Gu Y, Linder J, Divitini G, Ducati C, Scheer E, Blamire M, Robinson J. Signature of magnetic-dependent gapless odd frequency states at superconductor/ferromagnet interfaces. Nat Commun 2015; 6:8053. [PMID: 26329811 PMCID: PMC4569701 DOI: 10.1038/ncomms9053] [Citation(s) in RCA: 102] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2015] [Accepted: 07/13/2015] [Indexed: 11/24/2022] Open
Abstract
The theory of superconductivity developed by Bardeen, Cooper and Schrieffer (BCS) explains the stabilization of electron pairs into a spin-singlet, even frequency, state by the formation of an energy gap within which the density of states is zero. At a superconductor interface with an inhomogeneous ferromagnet, a gapless odd frequency superconducting state is predicted, in which the Cooper pairs are in a spin-triplet state. Although indirect evidence for such a state has been obtained, the gap structure and pairing symmetry have not so far been determined. Here we report scanning tunnelling spectroscopy of Nb superconducting films proximity coupled to epitaxial Ho. These measurements reveal pronounced changes to the Nb subgap superconducting density of states on driving the Ho through a metamagnetic transition from a helical antiferromagnetic to a homogeneous ferromagnetic state for which a BCS-like gap is recovered. The results prove odd frequency spin-triplet superconductivity at superconductor/inhomogeneous magnet interfaces.
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Affiliation(s)
- A. Di Bernardo
- Department of Material Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, UK
| | - S. Diesch
- Department of Physics, University of Konstanz, Konstanz 78457, Germany
| | - Y. Gu
- Department of Material Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, UK
| | - J. Linder
- Department of Physics, Norwegian University of Science and Technology, Trondheim N-7491, Norway
| | - G. Divitini
- Department of Material Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, UK
| | - C. Ducati
- Department of Material Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, UK
| | - E. Scheer
- Department of Physics, University of Konstanz, Konstanz 78457, Germany
| | - M.G. Blamire
- Department of Material Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, UK
| | - J.W.A. Robinson
- Department of Material Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, UK
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Gu Y, Halász GB, Robinson JWA, Blamire MG. Large Superconducting Spin Valve Effect and Ultrasmall Exchange Splitting in Epitaxial Rare-Earth-Niobium Trilayers. PHYSICAL REVIEW LETTERS 2015; 115:067201. [PMID: 26296128 DOI: 10.1103/physrevlett.115.067201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2015] [Indexed: 06/04/2023]
Abstract
Epitaxial Ho/Nb/Ho and Dy/Nb/Dy superconducting spin valves show a reversible change in the zero-field critical temperature (ΔT(c0)) of ∼400 mK and an infinite magnetoresistance on changing the relative magnetization of the Ho or Dy layers. Unlike transition-metal superconducting spin valves, which show much smaller ΔT(c0) values, our results can be quantitatively modeled. However, the fits require an extraordinarily low induced exchange splitting which is dramatically lower than known values for rare-earth Fermi-level electrons, implying that new models for the magnetic proximity effect may be required.
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Affiliation(s)
- Yuanzhou Gu
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - Gábor B Halász
- Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom
| | - J W A Robinson
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - M G Blamire
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
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Blamire MG, Robinson JWA. The interface between superconductivity and magnetism: understanding and device prospects. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:453201. [PMID: 25318455 DOI: 10.1088/0953-8984/26/45/453201] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
Ferromagnetism and conventional singlet superconductivity can be regarded as competing ordering phenomena. A considerable body of theoretical work over the past twenty years has predicted that at interfaces between the two systems competition or coupling between superconducting and magnetic phenomena are possible. Despite the very short lengthscales over which some of the phenomena exist, many of these predictions have been experimentally realized. The aim of this topical review is to provide an overview of the experimental position and to discuss the potential developments and applications of existing results.
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Affiliation(s)
- M G Blamire
- Department of Materials Science, University of Cambridge, 27 Charles Babbage Road, Cambridge, UK
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12
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Reversible control of spin-polarized supercurrents in ferromagnetic Josephson junctions. Nat Commun 2014; 5:4771. [PMID: 25154467 DOI: 10.1038/ncomms5771] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Accepted: 07/22/2014] [Indexed: 11/08/2022] Open
Abstract
Magnetic inhomogeneity at a superconductor (S)-ferromagnet (F) interface converts spin-singlet Cooper pairs into spin-one triplet pairs. These pairs are immune to the pair-breaking exchange field in F and support a long-range proximity effect. Although recent experiments have confirmed the existence of spin-polarized triplet supercurrents in S-F-S Josephson junctions, reversible control of the supercurrent has been impossible because of the robust preconfigured nature of the inhomogeneity. Here, we use a barrier comprising three F layers whose relative magnetic orientation, and hence the interfacial inhomogeneity, can be controlled by small magnetic fields; we show that this enables full control of the triplet supercurrent and, by using finite element micromagnetic simulations, we can directly relate the experimental data to the theoretical models which provide a general framework to understand the role played by magnetic states in long-range supercurrent modulation.
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