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Dynamics of Topological Textures in Antiferromagnetic Nanostructures

Research Project

Project/Area Number 25800184
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Condensed matter physics II
Research InstitutionTohoku University

Principal Investigator

Tretiakov Oleg  東北大学, 金属材料研究所, 助教 (50643425)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords反強磁性体 / 磁壁ダイナミクス / トポロジカルスピンテクスチャー / スキルミオン / トポロジカルスピンテクス チャ / トポロジカルスピンテクスチャ / skyrmions
Outline of Final Research Achievements

We derived equations of motion for the staggered dynamics in antiferromagnets by using collective coordinates approach [Phys. Rev. Lett. 110, 127208 (2013)]. Based on it we were able to describe the dynamics of antiferromagnetic skyrmions [Phys. Rev. Lett. 116, 147203 (2016)]. An antiferromagnetic Skyrmion is a compound topological object with a similar but of opposite sign spin texture on each sublattice, which results in the absence of topological Hall effect. We find that this composite nature gives rise to different dynamical behavior, both due to current and temperature effects. Another achievement is related to the study of domain wall dynamics in a magnetoelectric antiferromagnet and its implications for magnetoelectric memory applications [Appl. Phys. Lett. 108, 132403 (2016)]. We found that the domain wall mobility has a maximum as a function of electric field due to the induced gyrotropic coupling.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (58 results)

All 2016 2015 2014 2013 Other

All Journal Article (10 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 10 results,  Acknowledgement Compliant: 10 results,  Open Access: 1 results) Presentation (48 results) (of which Int'l Joint Research: 21 results,  Invited: 45 results)

  • [Journal Article] Dzyaloshinskii-Moriya domain walls in magnetic nanotubes2016

    • Author(s)
      A. Goussev, J. M. Robbins, V. Slastikov, and Oleg A. Tretiakov
    • Journal Title

      Physical Review B

      Volume: 93 Issue: 5

    • DOI

      10.1103/physrevb.93.054418

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Stability of skyrmion lattices and symmetries of quasi-two-dimensional chiral magnets2016

    • Author(s)
      U. Gungordu, R. Nepal, Oleg A. Tretiakov, K. Belashchenko, and A. A. Kovalev
    • Journal Title

      Physical Review B

      Volume: 93 Issue: 6

    • DOI

      10.1103/physrevb.93.064428

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Electrically controlled pinning of Dzyaloshinskii-Moriya domain walls2016

    • Author(s)
      K. Sato and Oleg A. Tretiakov
    • Journal Title

      Applied Physics Letters

      Volume: 108 Issue: 12

    • DOI

      10.1063/1.4944664

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Magnetoelectric domain wall dynamics and its implications for magnetoelectric memory2016

    • Author(s)
      K. D. Belashchenko, O. Tchernyshyov, A. A. Kovalev, and Oleg A. Tretiakov
    • Journal Title

      Applied Physics Letters

      Volume: 108 Issue: 13

    • DOI

      10.1063/1.4944996

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Static and Dynamical Properties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature2016

    • Author(s)
      J. Barker and Oleg A. Tretiakov
    • Journal Title

      Physical Review Letters

      Volume: 116 Issue: 14

    • DOI

      10.1103/physrevlett.116.147203

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Spin Seebeck Power Conversion2015

    • Author(s)
      A. B. Cahaya, Oleg A. Tretiakov, and G. E. W. Bauer
    • Journal Title

      IEEE Transactions on Magnetics

      Volume: 51 Issue: 9 Pages: 0800414-0800414

    • DOI

      10.1109/tmag.2015.2436362

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Topologically protected dynamics of spin textures2015

    • Author(s)
      O. A. Tretiakov and Ar. Abanov
    • Journal Title

      Journal of Magnetism and Magnetic Materials

      Volume: 383 Pages: 65-68

    • DOI

      10.1016/j.jmmm.2014.12.088

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Magnetoelectric effect in topological insulator films beyond the linear response regime2014

    • Author(s)
      Dashdeleg Baasanjav, O. A. Tretiakov, and Kentaro Nomura
    • Journal Title

      Phys. Rev. B

      Volume: 90 Issue: 4

    • DOI

      10.1103/physrevb.90.045149

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Spin Seebeck power generators2014

    • Author(s)
      Cahaya, AB, Tretiakov, OA, Bauer, GEW
    • Journal Title

      APPLIED PHYSICS LETTERS

      Volume: 104 Issue: 4 Pages: 042402-042402

    • DOI

      10.1063/1.4863084

    • Related Report
      2014 Research-status Report 2013 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Spin resonance in a Luttinger liquid with spin-orbit interaction2013

    • Author(s)
      O. A. Tretiakov, K. S. Tikhonov and V. L. Pokrovsky
    • Journal Title

      Physical Review B

      Volume: 88 Issue: 12 Pages: 125143-125143

    • DOI

      10.1103/physrevb.88.125143

    • Related Report
      2013 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Antiferromagnetic Skyrmions2016

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      APS March Meeting 2016
    • Place of Presentation
      Baltimore, MD, USA
    • Year and Date
      2016-03-14
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Dynamical and Thermal Properties of Antiferromagnetic Skyrmions2016

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      Joint ATI Spin Conversion Theory Meeting 2016
    • Place of Presentation
      Ochanomizu, Tokyo, Japan
    • Year and Date
      2016-03-04
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability and Dynamics of Merons and Skyrmions in Magnetic Systems2016

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      Theory of Condensed Matter seminar
    • Place of Presentation
      Radboud University Nijmegen, Nijmegen, Netherlands
    • Year and Date
      2016-02-24
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability and Dynamics of Antiferromagnetic Skyrmions2016

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      Zernike Institute for Advanced Materials seminar
    • Place of Presentation
      University of Groningen, Groningen, Netherlands
    • Year and Date
      2016-02-21
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Thermal and Dynamical Properties of Antiferromagnetic Skyrmions2016

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      23rd Joint Interlaboratory Workshop on Nano-Magnetics
    • Place of Presentation
      Akiyu, Japan
    • Year and Date
      2016-02-11
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Skyrmion Dynamics in Ferromagnetic and Antiferromagnetic Systems2016

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      Spintronics Winter Workshop 2016
    • Place of Presentation
      Zao, Japan
    • Year and Date
      2016-02-07
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Static and Dynamical Properties of Antiferromagnetic Skyrmions2016

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      13th Joint MMM-Intermag Conference 2016
    • Place of Presentation
      San Diego, CA, USA
    • Year and Date
      2016-01-11
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Spin Seebeck and Spin Spiral Systems2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      School of Natural Sciences seminar
    • Place of Presentation
      FEFU, Vladivostok, Russia
    • Year and Date
      2015-12-24
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Static and Dynamic Properties of Antiferromagnetic Skyrmions2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      RIKEN Condensed Matter seminar
    • Place of Presentation
      RIKEN, Wako, Japan
    • Year and Date
      2015-12-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Magnetization Dynamics and Motion of Topological Spin Textures2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      lecture at TFC Elementary Spintronics School
    • Place of Presentation
      TFC, Tohoku University, Sendai, Japan
    • Year and Date
      2015-11-11
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Spin Seebeck Thermoelectrics2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      ICSS 2015 conference
    • Place of Presentation
      Phuket, Thailand
    • Year and Date
      2015-11-04
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Skyrmions, Dzyaloshinskii-Moriya interaction and other magnetic beasts2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      condensed-matter physics seminar
    • Place of Presentation
      Far Eastern Federal University, Vladivostok, Russia
    • Year and Date
      2015-10-26
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Ferromagnetic and Antiferromagnetic Skyrmions2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      seminar of School of Mathematics
    • Place of Presentation
      University of Bristol, Bristol, United Kingdom
    • Year and Date
      2015-09-22
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Ferromagnetic and Antiferromagnetic Skyrmions2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      Condensed Matter Physics seminar
    • Place of Presentation
      University of York, York, United Kingdom
    • Year and Date
      2015-09-21
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Static and Dynamic Properties of Antiferromagnetic Skyrmions2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      Unite Mixte de Physique CNRS/Thales Physics seminar
    • Place of Presentation
      Unite Mixte de Physique CNRS/Thales, Palaiseau, France
    • Year and Date
      2015-09-16
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Antiferromagnetic Skyrmions2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      International Baltic Conference on Magnetism and Biomedical Applications
    • Place of Presentation
      Svetlogorsk, Russia
    • Year and Date
      2015-08-30
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Antiferromagnetic Skyrmions2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      Solid State Physics seminar
    • Place of Presentation
      University of Mainz, Mainz, Germany
    • Year and Date
      2015-07-19
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Antiferromagnetic Skyrmions2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      Condensed Matter Theory Seminar
    • Place of Presentation
      University of Cologne, Cologne, Germany
    • Year and Date
      2015-07-11
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Antiferromagnetic Skyrmions2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      4th International conference on Theoretical Physics and its Applications
    • Place of Presentation
      Moscow, Russia
    • Year and Date
      2015-07-02
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Antiferromagnetic Skyrmions2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      International workshop on New Perspectives in Spintronic and Mesoscopic Physics (NPSMP 2015)
    • Place of Presentation
      ISSP, University of Tokyo, Kashiwa, Japan
    • Year and Date
      2015-06-01
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Internal Skyrmion Dynamics2015

    • Author(s)
      Oleg A. Tretiakov
    • Organizer
      International Conference "Spin physics, spin chemistry and spin technology"
    • Place of Presentation
      St. Petersburg, Russia
    • Year and Date
      2015-06-01
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Dzyaloshinskii-Moriya Spin Textures with Curvature and Antiferromagnetic Skyrmions2015

    • Author(s)
      O.A. Tretiakov
    • Organizer
      UCLA Condensed Matter Seminar
    • Place of Presentation
      UCLA, Los Angeles, CA (USA)
    • Year and Date
      2015-03-25
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Dzyaloshinskii-Moriya Spin Textures with Curvature and Antiferromagnetic Skyrmions2015

    • Author(s)
      O.A. Tretiakov
    • Organizer
      Western Digital seminar
    • Place of Presentation
      Western Digital, San Jose, CA (USA)
    • Year and Date
      2015-03-13
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Antiferromagnetic Skyrmions2015

    • Author(s)
      O.A. Tretiakov
    • Organizer
      Condensed-Matter Theory seminar
    • Place of Presentation
      University of Texas at Austin, TX (USA)
    • Year and Date
      2015-03-11
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Antiferromagnetic Skyrmions2015

    • Author(s)
      O.A. Tretiakov
    • Organizer
      2nd Zao Spintronics International Workshop
    • Place of Presentation
      Ohira Hotal, Zao, Yamagata (Japan)
    • Year and Date
      2015-01-18 – 2015-01-19
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Topologically Protected Dynamics of Dzyaloshinskii-Moriya Spin Textures2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      ISSP seminar
    • Place of Presentation
      ISSP, University of Tokyo, Kashiwa (Japan)
    • Year and Date
      2014-10-31
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Statics and dynamics of Dzyaloshinskii-Moriya spin textures2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      Zao Spintronics Workshop
    • Place of Presentation
      Ohira Hotal, Zao, Yamagata (Japan)
    • Year and Date
      2014-10-06 – 2014-10-08
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Dynamics of Dzyaloshinskii-Moriya Spin Textures in Nanotubes2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      Institute of Physics talk
    • Place of Presentation
      Johannes Gutenberg-University Mainz, Mainz (Germany)
    • Year and Date
      2014-09-25
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Topological Dynamics of Dzyaloshinskii-Moriya Spin Textures in Curved Spaces2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      condensed matter physics seminar
    • Place of Presentation
      University of Konstanz, Konstanz (Germany)
    • Year and Date
      2014-09-24
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Statics and Dynamics of Dzyaloshinskii-Moriya Spin Textures2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      Solid State Physics Seminar
    • Place of Presentation
      Forschungszentrum Juelich, Juelich (Germany)
    • Year and Date
      2014-09-23
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Topological Dynamics of Dzyaloshinskii-Moriya Spin Textures2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      SPINTEC seminar
    • Place of Presentation
      SPINTEC, Grenoble (France)
    • Year and Date
      2014-09-22
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Magnetoelectric and Thermoelectric Properties of Topological Insulators2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      IMPMC seminar
    • Place of Presentation
      Sorbonne Universities, Paris (France)
    • Year and Date
      2014-09-12
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Dynamics of Topological Spin Textures2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      condensed matter seminar
    • Place of Presentation
      Beijing Normal University, Beijing (China)
    • Year and Date
      2014-07-24
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Topologically Protected Dynamics of Spin Textures2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      Moscow International Symposium on Magnetism MISM-2014
    • Place of Presentation
      Moscow (Russia)
    • Year and Date
      2014-06-29 – 2014-07-03
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Spin Texture Dynamics in Ferromagnetic and Antiferromagnetic Structures2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      ICC-IMR / 20th REIMEI International Workshop “Spin Mechanics 2”
    • Place of Presentation
      IMR, Tohoku University, Sendai (Japan)
    • Year and Date
      2014-06-21 – 2014-06-24
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Dynamics of Topological Spin Textures2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      condensed matter seminar, Imperial College
    • Place of Presentation
      London (UK)
    • Year and Date
      2014-05-23
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Topological and Spin Seebeck Thermoelectrics2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      Condensed Matter Physics seminar
    • Place of Presentation
      The University of York, York (UK)
    • Year and Date
      2014-05-22
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Topologically Protected Dynamics of Spin Textures2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      Department of Mathematics seminar
    • Place of Presentation
      Northumbria University, Newcastle (UK)
    • Year and Date
      2014-05-21
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Thermoelectrics based on topological insulators and spin Seebeck devices2014

    • Author(s)
      O.A. Tretiakov
    • Organizer
      Department of Physics seminar, The Hong Kong University of Science and Technology
    • Place of Presentation
      Hong Kong
    • Year and Date
      2014-04-30
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Spin Flip Resonance in Spin-Orbit Split Quantum Wires2013

    • Author(s)
      Oleg Tretiakov
    • Organizer
      KITP Program "Spintronics 2013"
    • Place of Presentation
      KITP, UC, Santa Barbara, CA, USA
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Topologically Protected Domain-Wall Dynamics in Ferromagnets and Antiferromagnets2013

    • Author(s)
      Oleg Tretiakov
    • Organizer
      International Workshop on Topological Quantum Phenomena in Condensed Matter with Broken Symmetries 2013
    • Place of Presentation
      Okinawa, Japan
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Domain-Wall Dynamics in Ferromagnets and Antiferromagnets2013

    • Author(s)
      Oleg Tretiakov
    • Organizer
      JEMS 2013 Conference
    • Place of Presentation
      Rhodes, Greece
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Domain-Wall Dynamics in Ferromagnets and Antiferromagnets2013

    • Author(s)
      Oleg Tretiakov
    • Organizer
      plenary talk at the 3rd Interna- tional Conference on Theoretical Physics "Theoretical Physics and its Applications"
    • Place of Presentation
      Moscow, Russia
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Topologically Protected Domain-Wall Dynamics in Ferromagnets and Antiferromagnets

    • Author(s)
      Oleg Tretiakov
    • Organizer
      condensed matter physics seminar
    • Place of Presentation
      University of Nebraska - Lincoln, NE, USA
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Thermoelectric power generators based on topological insulators and spin Seebeck devices

    • Author(s)
      Oleg Tretiakov
    • Organizer
      Nebraska Center for Materials and Nanoscience Seminar
    • Place of Presentation
      University of Nebraska, Lincoln, NE, USA
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Electron Spin Resonance in Quantum Wires with Spin-Orbit Coupling

    • Author(s)
      Oleg Tretiakov
    • Organizer
      condensed matter physics seminar
    • Place of Presentation
      RIKEN, Wako, Japan
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Topologically Protected Domain-Wall Dynamics in Ferromagnets and Antiferromagnets

    • Author(s)
      Oleg Tretiakov
    • Organizer
      SpinNet Minisymposium on Spintronics
    • Place of Presentation
      JGU Mainz, Germany
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Spin Flip Resonance in Spin-Orbit Split Quantum Wires

    • Author(s)
      Oleg Tretiakov
    • Organizer
      MSD seminar
    • Place of Presentation
      Argonne National Lab, Argonne, IL, USA
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2014-07-25   Modified: 2020-05-15  

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