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Gu Y, Gu Y, Liu F, Ohira-Kawamura S, Murai N, Zhao J. Signatures of Kitaev Interactions in the van der Waals Ferromagnet VI_{3}. PHYSICAL REVIEW LETTERS 2024; 132:246702. [PMID: 38949369 DOI: 10.1103/physrevlett.132.246702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Revised: 04/30/2024] [Accepted: 05/10/2024] [Indexed: 07/02/2024]
Abstract
Materials manifesting the Kitaev model, characterized by bond-dependent interactions on a honeycomb lattice, can host exotic phenomena like quantum spin liquid states and topological magnetic excitations. However, finding such materials remains a formidable challenge. Here, we report high-resolution inelastic neutron scattering measurements performed on VI_{3}, a van der Waals ferromagnetic Mott insulator, covering a wide range of reciprocal space. Our measurements unveil highly anisotropic magnetic excitations in momentum space. Through a comprehensive comparative analysis of various models that incorporate diverse symmetry-allowed magnetic interactions, we find the observed excitations are well captured by a model with a large bond-dependent Kitaev interaction. These results not only help to understand the intriguing properties of VI_{3}, such as the pronounced anomalous thermal Hall effects and strong pressure or structure dependence of magnetism, but also open a new avenue for exploring Kitaev physics.
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Affiliation(s)
- Yiqing Gu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | | | | | | | | | - Jun Zhao
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
- Institute of Nanoelectronics and Quantum Computing, Fudan University, Shanghai 200433, China
- Shanghai Branch, Hefei National Laboratory, Shanghai 201315, China
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2
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Rousochatzakis I, Perkins NB, Luo Q, Kee HY. Beyond Kitaev physics in strong spin-orbit coupled magnets. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:026502. [PMID: 38241723 DOI: 10.1088/1361-6633/ad208d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Accepted: 01/19/2024] [Indexed: 01/21/2024]
Abstract
We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To this end, we present a comprehensive overview of the key exchange interactions in candidate materials with a specific focus on systems featuring effectiveJeff=1/2magnetic moments. This includes, but not limited to,5d5iridates,4d5ruthenates and3d7cobaltates. Our exploration covers the microscopic origins of these interactions, along with a systematic attempt to map out the most intriguing correlated regimes of the multi-dimensional parameter space. Our approach is guided by robust symmetry and duality transformations as well as insights from a wide spectrum of analytical and numerical studies. We also survey higher spin Kitaev models and recent exciting results on quasi-one-dimensional models and discuss their relevance to higher-dimensional models. Finally, we highlight some of the key questions in the field as well as future directions.
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Affiliation(s)
| | - Natalia B Perkins
- School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, United States of America
- Technical University of Munich, Munich, Germany
- Institute for Advanced Study, D-85748 Garching, Germany
| | - Qiang Luo
- College of Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, People's Republic of China
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
| | - Hae-Young Kee
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
- Canadian Institute for Advanced Research, CIFAR Program in Quantum Materials, Toronto, Ontario M5G 1M1, Canada
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3
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Li X, Xu C, Liu B, Li X, Bellaiche L, Xiang H. Realistic Spin Model for Multiferroic NiI_{2}. PHYSICAL REVIEW LETTERS 2023; 131:036701. [PMID: 37540870 DOI: 10.1103/physrevlett.131.036701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2022] [Revised: 05/11/2023] [Accepted: 06/17/2023] [Indexed: 08/06/2023]
Abstract
A realistic first-principle-based spin Hamiltonian is constructed for the type-II multiferroic NiI_{2}, using a symmetry-adapted cluster expansion method. Besides single ion anisotropy and isotropic Heisenberg terms, this model further includes the Kitaev interaction and a biquadratic term, and can well reproduce striking features of the experimental helical ground state, that are, e.g., a proper screw state, canting of rotation plane, propagation direction, and period. Using this model to build a phase diagram, it is demonstrated that, (i) the in-plane propagation direction of ⟨11[over ¯]0⟩ is determined by the Kitaev interaction, instead of the long-believed exchange frustrations and (ii) the canting of rotation plane is also dominantly determined by Kitaev interaction, rather than interlayer couplings. Furthermore, additional Monte Carlo simulations reveal three equivalent domains and different topological defects. Since the ferroelectricity is induced by spins in type-II multiferroics, our work also implies that Kitaev interaction is closely related to the multiferroicity of NiI_{2}.
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Affiliation(s)
- Xuanyi Li
- Key Laboratory of Computational Physical Sciences (Ministry of Education), Institute of Computational Physical Sciences, State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, China
| | - Changsong Xu
- Key Laboratory of Computational Physical Sciences (Ministry of Education), Institute of Computational Physical Sciences, State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, China
- Shanghai Qi Zhi Institute, Shanghai 200030, China
| | - Boyu Liu
- Key Laboratory of Computational Physical Sciences (Ministry of Education), Institute of Computational Physical Sciences, State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, China
| | - Xueyang Li
- Key Laboratory of Computational Physical Sciences (Ministry of Education), Institute of Computational Physical Sciences, State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, China
| | - L Bellaiche
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Hongjun Xiang
- Key Laboratory of Computational Physical Sciences (Ministry of Education), Institute of Computational Physical Sciences, State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, China
- Shanghai Qi Zhi Institute, Shanghai 200030, China
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4
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Ma H. Z_{2} Spin Liquids in the Higher Spin-S Kitaev Honeycomb Model: An Exact Deconfined Z_{2} Gauge Structure in a Nonintegrable Model. PHYSICAL REVIEW LETTERS 2023; 130:156701. [PMID: 37115878 DOI: 10.1103/physrevlett.130.156701] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2022] [Accepted: 03/08/2023] [Indexed: 06/19/2023]
Abstract
The higher spin Kitaev model prominently features the extensive locally conserved quantities the same as the spin-1/2 Kitaev honeycomb model, although it is not exactly solvable. It remains an open question regarding the physical meaning of these conserved quantities in the higher spin model. In this Letter, by introducing a Majorana parton construction for a general spin-S we uncover that these conserved quantities are exactly the Z_{2} gauge fluxes in the general spin-S model, including the case of spin-1/2. Particularly, we find an even-odd effect that the Z_{2} gauge charges are fermions in the half integer spin model, but are bosons in the integer spin model. We further prove that the fermionic Z_{2} gauge charges are always deconfined; hence, the half integer spin Kitaev model would have nontrivial spin liquid ground states regardless of interaction strengths in the Hamiltonian. The bosonic Z_{2} gauge charges of the integer spin model, on the other hand, could condense, leading to a trivial product state, and this is indeed the case at the anisotropic limit of the model.
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Affiliation(s)
- Han Ma
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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5
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Wang QH, Bedoya-Pinto A, Blei M, Dismukes AH, Hamo A, Jenkins S, Koperski M, Liu Y, Sun QC, Telford EJ, Kim HH, Augustin M, Vool U, Yin JX, Li LH, Falin A, Dean CR, Casanova F, Evans RFL, Chshiev M, Mishchenko A, Petrovic C, He R, Zhao L, Tsen AW, Gerardot BD, Brotons-Gisbert M, Guguchia Z, Roy X, Tongay S, Wang Z, Hasan MZ, Wrachtrup J, Yacoby A, Fert A, Parkin S, Novoselov KS, Dai P, Balicas L, Santos EJG. The Magnetic Genome of Two-Dimensional van der Waals Materials. ACS NANO 2022; 16:6960-7079. [PMID: 35442017 PMCID: PMC9134533 DOI: 10.1021/acsnano.1c09150] [Citation(s) in RCA: 63] [Impact Index Per Article: 31.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Accepted: 02/23/2022] [Indexed: 05/23/2023]
Abstract
Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.
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Affiliation(s)
- Qing Hua Wang
- Materials
Science and Engineering, School for Engineering of Matter, Transport
and Energy, Arizona State University, Tempe, Arizona 85287, United States
| | - Amilcar Bedoya-Pinto
- NISE
Department, Max Planck Institute of Microstructure
Physics, 06120 Halle, Germany
- Instituto
de Ciencia Molecular (ICMol), Universitat
de València, 46980 Paterna, Spain
| | - Mark Blei
- Materials
Science and Engineering, School for Engineering of Matter, Transport
and Energy, Arizona State University, Tempe, Arizona 85287, United States
| | - Avalon H. Dismukes
- Department
of Chemistry, Columbia University, New York, New York 10027, United States
| | - Assaf Hamo
- Department
of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Sarah Jenkins
- Twist
Group,
Faculty of Physics, University of Duisburg-Essen, Campus Duisburg, 47057 Duisburg, Germany
| | - Maciej Koperski
- Institute
for Functional Intelligent Materials, National
University of Singapore, 117544 Singapore
| | - Yu Liu
- Condensed
Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Qi-Chao Sun
- Physikalisches
Institut, University of Stuttgart, 70569 Stuttgart, Germany
| | - Evan J. Telford
- Department
of Chemistry, Columbia University, New York, New York 10027, United States
- Department
of Physics, Columbia University, New York, New York 10027, United States
| | - Hyun Ho Kim
- School
of Materials Science and Engineering, Department of Energy Engineering
Convergence, Kumoh National Institute of
Technology, Gumi 39177, Korea
| | - Mathias Augustin
- Institute
for Condensed Matter Physics and Complex Systems, School of Physics
and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom
- Donostia
International Physics Center (DIPC), 20018 Donostia-San Sebastián, Basque Country, Spain
| | - Uri Vool
- Department
of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
- John Harvard
Distinguished Science Fellows Program, Harvard
University, Cambridge, Massachusetts 02138, United States
| | - Jia-Xin Yin
- Laboratory
for Topological Quantum Matter and Spectroscopy, Department of Physics, Princeton University, Princeton, New Jersey 08544, United States
| | - Lu Hua Li
- Institute
for Frontier Materials, Deakin University, Geelong Waurn Ponds Campus, Waurn Ponds, Victoria 3216, Australia
| | - Alexey Falin
- Institute
for Frontier Materials, Deakin University, Geelong Waurn Ponds Campus, Waurn Ponds, Victoria 3216, Australia
| | - Cory R. Dean
- Department
of Physics, Columbia University, New York, New York 10027, United States
| | - Fèlix Casanova
- CIC nanoGUNE
BRTA, 20018 Donostia - San Sebastián, Basque
Country, Spain
- IKERBASQUE,
Basque Foundation for Science, 48013 Bilbao, Basque Country, Spain
| | - Richard F. L. Evans
- Department
of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
| | - Mairbek Chshiev
- Université
Grenoble Alpes, CEA, CNRS, Spintec, 38000 Grenoble, France
- Institut
Universitaire de France, 75231 Paris, France
| | - Artem Mishchenko
- Department
of Physics and Astronomy, University of
Manchester, Manchester, M13 9PL, United Kingdom
- National
Graphene Institute, University of Manchester, Manchester, M13 9PL, United Kingdom
| | - Cedomir Petrovic
- Condensed
Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Rui He
- Department
of Electrical and Computer Engineering, Texas Tech University, 910 Boston Avenue, Lubbock, Texas 79409, United
States
| | - Liuyan Zhao
- Department
of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109, United States
| | - Adam W. Tsen
- Institute
for Quantum Computing and Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Brian D. Gerardot
- SUPA, Institute
of Photonics and Quantum Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, United Kingdom
| | - Mauro Brotons-Gisbert
- SUPA, Institute
of Photonics and Quantum Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, United Kingdom
| | - Zurab Guguchia
- Laboratory
for Muon Spin Spectroscopy, Paul Scherrer
Institute, CH-5232 Villigen PSI, Switzerland
| | - Xavier Roy
- Department
of Chemistry, Columbia University, New York, New York 10027, United States
| | - Sefaattin Tongay
- Materials
Science and Engineering, School for Engineering of Matter, Transport
and Energy, Arizona State University, Tempe, Arizona 85287, United States
| | - Ziwei Wang
- Department
of Physics and Astronomy, University of
Manchester, Manchester, M13 9PL, United Kingdom
- National
Graphene Institute, University of Manchester, Manchester, M13 9PL, United Kingdom
| | - M. Zahid Hasan
- Materials
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
- Princeton
Institute for Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, United States
- National
High Magnetic Field Laboratory, Florida
State University, Tallahassee, Florida 32310, United States
| | - Joerg Wrachtrup
- Physikalisches
Institut, University of Stuttgart, 70569 Stuttgart, Germany
- Max Planck
Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Amir Yacoby
- Department
of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
- John A.
Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Albert Fert
- Donostia
International Physics Center (DIPC), 20018 Donostia-San Sebastián, Basque Country, Spain
- Unité
Mixte de Physique, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
- Department
of Materials Physics UPV/EHU, 20018 Donostia - San Sebastián, Basque Country, Spain
| | - Stuart Parkin
- NISE
Department, Max Planck Institute of Microstructure
Physics, 06120 Halle, Germany
| | - Kostya S. Novoselov
- Institute
for Functional Intelligent Materials, National
University of Singapore, 117544 Singapore
| | - Pengcheng Dai
- Department
of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Luis Balicas
- National
High Magnetic Field Laboratory, Florida
State University, Tallahassee, Florida 32310, United States
- Department
of Physics, Florida State University, Tallahassee, Florida 32306, United States
| | - Elton J. G. Santos
- Institute
for Condensed Matter Physics and Complex Systems, School of Physics
and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom
- Donostia
International Physics Center (DIPC), 20018 Donostia-San Sebastián, Basque Country, Spain
- Higgs Centre
for Theoretical Physics, The University
of Edinburgh, Edinburgh EH9 3FD, United Kingdom
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6
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Vasilchikova T, Vasiliev A, Evstigneeva M, Nalbandyan V, Lee JS, Koo HJ, Whangbo MH. Magnetic Properties of A 2Ni 2TeO 6 (A = K, Li): Zigzag Order in the Honeycomb Layers of Ni 2+ Ions Induced by First and Third Nearest-Neighbor Spin Exchanges. MATERIALS 2022; 15:ma15072563. [PMID: 35407895 PMCID: PMC8999558 DOI: 10.3390/ma15072563] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/28/2022] [Revised: 03/23/2022] [Accepted: 03/24/2022] [Indexed: 01/27/2023]
Abstract
The static and dynamic magnetic properties and the specific heat of K2Ni2TeO6 and Li2Ni2TeO6 were examined and it was found that they undergo a long-range ordering at TN = 22.8 and 24.4 K, respectively, but exhibit a strong short-range order. At high temperature, the magnetic susceptibilities of K2Ni2TeO6 and Li2Ni2TeO6 are described by a Curie-Weiss law, with Curie-Weiss temperatures Θ of approximately -13 and -20 K, respectively, leading to the effective magnetic moment of about 4.46 ± 0.01 μB per formula unit, as expected for Ni2+ (S = 1) ions. In the paramagnetic region, the ESR spectra of K2Ni2TeO6 and Li2Ni2TeO6 show a single Lorentzian-shaped line characterized by the isotropic effective g-factor, g = 2.19 ± 0.01. The energy-mapping analysis shows that the honeycomb layers of A2Ni2TeO6 (A = K, Li) and Li3Ni2SbO6 adopt a zigzag order, in which zigzag ferromagnetic chains are antiferromagnetically coupled, because the third nearest-neighbor spin exchanges are strongly antiferromagnetic while the first nearest-neighbor spin exchanges are strongly ferromagnetic, and that adjacent zigzag-ordered honeycomb layers prefer to be ferromagnetically coupled. The short-range order of the zigzag-ordered honeycomb lattices of K2Ni2TeO6 and Li2Ni2TeO6 is equivalent to that of an antiferromagnetic uniform chain, and is related to the short-range order of the ferromagnetic chains along the direction perpendicular to the chains.
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Affiliation(s)
- Tatyana Vasilchikova
- Department of Low Temperature Physics and Superconductivity, Lomonosov Moscow State University, Moscow 119991, Russia;
| | - Alexander Vasiliev
- Department of Low Temperature Physics and Superconductivity, Lomonosov Moscow State University, Moscow 119991, Russia;
- Quantum Functional Materials Laboratory, National University of Science and Technology “MISiS”, Moscow 119049, Russia
- Department of Theoretical Physics and Applied Mathematics, Ural Federal University, Ekaterinburg 620002, Russia
- Correspondence: (A.V.); (H.-J.K.)
| | - Maria Evstigneeva
- Faculty of Chemistry, Southern Federal University, Rostov-on-Don 344090, Russia; (M.E.); (V.N.)
| | - Vladimir Nalbandyan
- Faculty of Chemistry, Southern Federal University, Rostov-on-Don 344090, Russia; (M.E.); (V.N.)
| | - Ji-Sun Lee
- Department of Chemistry and Research Institute for Basic Sciences, Kyung Hee University, Seoul 02447, Korea; (J.-S.L.); (M.-H.W.)
| | - Hyun-Joo Koo
- Department of Chemistry and Research Institute for Basic Sciences, Kyung Hee University, Seoul 02447, Korea; (J.-S.L.); (M.-H.W.)
- Correspondence: (A.V.); (H.-J.K.)
| | - Myung-Hwan Whangbo
- Department of Chemistry and Research Institute for Basic Sciences, Kyung Hee University, Seoul 02447, Korea; (J.-S.L.); (M.-H.W.)
- Department of Chemistry, North Carolina State University, Raleigh, NC 27695, USA
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7
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Xu C, Li X, Chen P, Zhang Y, Xiang H, Bellaiche L. Assembling Diverse Skyrmionic Phases in Fe 3 GeTe 2 Monolayers. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2107779. [PMID: 35023226 DOI: 10.1002/adma.202107779] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2021] [Revised: 01/05/2022] [Indexed: 06/14/2023]
Abstract
Skyrmionic magnetic states are promising in advanced spintronics. This topic is experiencing recent progress in 2D magnets, with, for example, a near 300 K Curie temperature observed in Fe3 GeTe2 . However, despite previous studies reporting skyrmions in Fe3 GeTe2 , such a system remains elusive, since it has been reported to host either Néel-type or Bloch-type textures, while a net Dzyaloshinskii-Moriya interaction (DMI) cannot occur in this compound for symmetry reasons. It is thus desirable to develop an accurate model to deeply understand Fe3 GeTe2 . Here, a newly developed method adopting spin invariants is applied to build a first-principle-based Hamiltonian, which predicts colorful topological defects assembled from the unit of Bloch lines, and reveals the critical role of specific forms of fourth-order interactions in Fe3 GeTe2 . Rather than the DMI, it is the multiple fourth-order interactions, with symmetry and spin-orbit couplings considered, that stabilize both Néel-type and Bloch-type skyrmions, as well as antiskyrmions, without any preference for clockwise versus counterclockwise spin rotation. This study also demonstrates that spin invariants can be used as a general approach to study complex magnetic interactions.
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Affiliation(s)
- Changsong Xu
- Key Laboratory of Computational Physical Sciences (Ministry of Education), Institute of Computational Physical Sciences, State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai, 200433, China
- Shanghai Qi Zhi Institute, Shanghai, 200232, China
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, AR, 72701, USA
| | - Xueyang Li
- Key Laboratory of Computational Physical Sciences (Ministry of Education), Institute of Computational Physical Sciences, State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai, 200433, China
- Shanghai Qi Zhi Institute, Shanghai, 200232, China
| | - Peng Chen
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, AR, 72701, USA
| | - Yun Zhang
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, AR, 72701, USA
- Department of Physics and Information Technology, Baoji University of Arts and Sciences, Baoji, 721016, China
| | - Hongjun Xiang
- Key Laboratory of Computational Physical Sciences (Ministry of Education), Institute of Computational Physical Sciences, State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai, 200433, China
- Shanghai Qi Zhi Institute, Shanghai, 200232, China
| | - Laurent Bellaiche
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, AR, 72701, USA
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8
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Kim C, Kim HS, Park JG. Spin-orbital entangled state and realization of Kitaev physics in 3 dcobalt compounds: a progress report. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:023001. [PMID: 34614480 DOI: 10.1088/1361-648x/ac2d5d] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2021] [Accepted: 10/06/2021] [Indexed: 06/13/2023]
Abstract
The realization of Kitaev's honeycomb magnetic model in real materials has become one of the most pursued topics in condensed matter physics and materials science. If found, it is expected to host exotic quantum phases of matter and offers potential realizations of fault-tolerant quantum computations. Over the past years, much effort has been made on 4d- or 5d-heavy transition metal compounds because of their intrinsic strong spin-orbit coupling. But more recently, there have been growing shreds of evidence that the Kitaev model could also be realized in 3d-transition metal systems with much weaker spin-orbit coupling. This review intends to serve as a guide to this fast-developing field focusing on systems withd7transition metal occupation. It overviews the current theoretical and experimental progress on realizing the Kitaev model in those systems. We examine the recent experimental observations of candidate materials with Co2+ions: e.g., CoPS3, Na3Co2SbO6, and Na2Co2TeO6, followed by a brief review of theoretical backgrounds. We conclude this article by comparing experimental observations with density functional theory calculations. We stress the importance of inter-t2ghopping channels and Hund's coupling in the realization of Kitaev interactions in Co-based compounds, which has been overlooked in previous studies. This review suggests future directions in the search for Kitaev physics in 3dcobalt compounds and beyond.
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Affiliation(s)
- Chaebin Kim
- Center for Quantum Materials, Seoul National University, Seoul 08826, Republic of Korea
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea
| | - Heung-Sik Kim
- Department of Physics and Institute for Accelerator Science, Kangwon National University, Chuncheon 24311, Republic of Korea
| | - Je-Geun Park
- Center for Quantum Materials, Seoul National University, Seoul 08826, Republic of Korea
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea
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9
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Bradley O, Oitmaa J, Sen D, Singh RRP. Thermodynamic behavior of modified integer-spin Kitaev models on the honeycomb lattice. Phys Rev E 2021; 103:022109. [PMID: 33736061 DOI: 10.1103/physreve.103.022109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2020] [Accepted: 12/22/2020] [Indexed: 11/07/2022]
Abstract
We study the thermodynamic behavior of modified spin-S Kitaev models introduced by Baskaran, Sen, and Shankar [Phys. Rev. B 78, 115116 (2008)PRBMDO1098-012110.1103/PhysRevB.78.115116]. These models have the property that for half-odd-integer spins their eigenstates map on to those of spin-1/2 Kitaev models, with well-known highly entangled quantum spin-liquid states and Majorana fermions. For integer spins, the Hamiltonian is made out of commuting local operators. Thus, the eigenstates can be chosen to be completely unentangled between different sites, though with a significant degeneracy for each eigenstate. For half-odd-integer spins, the thermodynamic properties can be related to the spin-1/2 Kitaev models apart from an additional degeneracy. Hence we focus here on the case of integer spins. We use transfer matrix methods, high-temperature expansions, and Monte Carlo simulations to study the thermodynamic properties of ferromagnetic and antiferromagnetic models with spin S=1 and S=2. Apart from large residual entropies, which all the models have, we find that they can have a variety of different behaviors. Transfer matrix calculations show that for the different models, the correlation lengths can be finite as T→0, become critical as T→0, or diverge exponentially as T→0. The Z_{2} flux variable associated with each hexagonal plaquette saturates at the value +1 as T→0 in all models except the S=1 antiferromagnet where the mean flux remains zero as T→0. We provide qualitative explanations for these results.
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Affiliation(s)
- Owen Bradley
- Department of Physics, University of California Davis, California 95616, USA
| | - Jaan Oitmaa
- School of Physics, The University of New South Wales, Sydney 2052, Australia
| | - Diptiman Sen
- Center for High Energy Physics and Department of Physics, Indian Institute of Science, Bengaluru 560012, India
| | - Rajiv R P Singh
- Department of Physics, University of California Davis, California 95616, USA
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10
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Abstract
Quantum spin liquids are an exciting playground for exotic physical phenomena and emergent many-body quantum states. The realization and discovery of quantum spin liquid candidate materials and associated phenomena lie at the intersection of solid-state chemistry, condensed matter physics, and materials science and engineering. In this review, we provide the current status of the crystal chemistry, synthetic techniques, physical properties, and research methods in the field of quantum spin liquids. We highlight a number of specific quantum spin liquid candidate materials and their structure-property relationships, elucidating their fascinating behavior and connecting it to the intricacies of their structures. Furthermore, we share our thoughts on defects and their inevitable presence in materials, of which quantum spin liquids are no exception, which can complicate the interpretation of characterization of these materials, and urge the community to extend their attention to materials preparation and data analysis, cognizant of the impact of defects. This review was written with the intention of providing guidance on improving the materials design and growth of quantum spin liquids, and to paint a picture of the beauty of the underlying chemistry of this exciting class of materials.
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Affiliation(s)
- Juan R Chamorro
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States.,Institute for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Tyrel M McQueen
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States.,Institute for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, United States.,Department of Materials Science and Engineering, The Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Thao T Tran
- Department of Chemistry, Clemson University, Clemson, South Carolina 29634, United States
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11
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Kanyolo GM, Masese T, Matsubara N, Chen CY, Rizell J, Huang ZD, Sassa Y, Månsson M, Senoh H, Matsumoto H. Honeycomb layered oxides: structure, energy storage, transport, topology and relevant insights. Chem Soc Rev 2021; 50:3990-4030. [PMID: 33576756 DOI: 10.1039/d0cs00320d] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
The advent of nanotechnology has hurtled the discovery and development of nanostructured materials with stellar chemical and physical functionalities in a bid to address issues in energy, environment, telecommunications and healthcare. In this quest, a class of two-dimensional layered materials consisting of alkali or coinage metal atoms sandwiched between slabs exclusively made of transition metal and chalcogen (or pnictogen) atoms arranged in a honeycomb fashion have emerged as materials exhibiting fascinatingly rich crystal chemistry, high-voltage electrochemistry, fast cation diffusion besides playing host to varied exotic electromagnetic and topological phenomena. Currently, with a niche application in energy storage as high-voltage materials, this class of honeycomb layered oxides serves as ideal pedagogical exemplars of the innumerable capabilities of nanomaterials drawing immense interest in multiple fields ranging from materials science, solid-state chemistry, electrochemistry and condensed matter physics. In this review, we delineate the relevant chemistry and physics of honeycomb layered oxides, and discuss their functionalities for tunable electrochemistry, superfast ionic conduction, electromagnetism and topology. Moreover, we elucidate the unexplored albeit vastly promising crystal chemistry space whilst outlining effective ways to identify regions within this compositional space, particularly where interesting electromagnetic and topological properties could be lurking within the aforementioned alkali and coinage-metal honeycomb layered oxide structures. We conclude by pointing towards possible future research directions, particularly the prospective realisation of Kitaev-Heisenberg-Dzyaloshinskii-Moriya interactions with single crystals and Floquet theory in closely-related honeycomb layered oxide materials.
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Affiliation(s)
- Godwill Mbiti Kanyolo
- Department of Engineering Science, The University of Electro-Communications, 1-5-1, Chofugaoka, Chofu, Tokyo 182-8585, Japan.
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12
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Bergeron H, Lebedev D, Hersam MC. Polymorphism in Post-Dichalcogenide Two-Dimensional Materials. Chem Rev 2021; 121:2713-2775. [PMID: 33555868 DOI: 10.1021/acs.chemrev.0c00933] [Citation(s) in RCA: 40] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Two-dimensional (2D) materials exhibit a wide range of atomic structures, compositions, and associated versatility of properties. Furthermore, for a given composition, a variety of different crystal structures (i.e., polymorphs) can be observed. Polymorphism in 2D materials presents a fertile landscape for designing novel architectures and imparting new functionalities. The objective of this Review is to identify the polymorphs of emerging 2D materials, describe their polymorph-dependent properties, and outline methods used for polymorph control. Since traditional 2D materials (e.g., graphene, hexagonal boron nitride, and transition metal dichalcogenides) have already been studied extensively, the focus here is on polymorphism in post-dichalcogenide 2D materials including group III, IV, and V elemental 2D materials, layered group III, IV, and V metal chalcogenides, and 2D transition metal halides. In addition to providing a comprehensive survey of recent experimental and theoretical literature, this Review identifies the most promising opportunities for future research including how 2D polymorph engineering can provide a pathway to materials by design.
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Affiliation(s)
- Hadallia Bergeron
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Dmitry Lebedev
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Mark C Hersam
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States.,Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States.,Department of Electrical and Computer Engineering, Northwestern University, Evanston, Illinois 60208, United States
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13
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Yang S, Zhang T, Jiang C. van der Waals Magnets: Material Family, Detection and Modulation of Magnetism, and Perspective in Spintronics. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2021; 8:2002488. [PMID: 33511010 PMCID: PMC7816723 DOI: 10.1002/advs.202002488] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Revised: 09/09/2020] [Indexed: 06/02/2023]
Abstract
van der Waals (vdW) materials exhibit great potential in spintronics, arising from their excellent spin transportation, large spin-orbit coupling, and high-quality interfaces. The recent discovery of intrinsic vdW antiferromagnets and ferromagnets has laid the foundation for the construction of all-vdW spintronic devices, and enables the study of low-dimensional magnetism, which is of both technical and scientific significance. In this review, several representative families of vdW magnets are introduced, followed by a comprehensive summary of the methods utilized in reading out the magnetic states of vdW magnets. Thereafter, it is shown that various electrical, mechanical, and chemical approaches are employed to modulate the magnetism of vdW magnets. Finally, the perspective of vdW magnets in spintronics is discussed and an outlook of future development direction in this field is also proposed.
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Affiliation(s)
- Shengxue Yang
- School of Materials Science and EngineeringBeihang UniversityBeijing100191P. R. China
| | - Tianle Zhang
- School of Materials Science and EngineeringBeihang UniversityBeijing100191P. R. China
| | - Chengbao Jiang
- School of Materials Science and EngineeringBeihang UniversityBeijing100191P. R. China
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14
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Natori WMH, Knolle J. Dynamics of a Two-Dimensional Quantum Spin-Orbital Liquid: Spectroscopic Signatures of Fermionic Magnons. PHYSICAL REVIEW LETTERS 2020; 125:067201. [PMID: 32845662 DOI: 10.1103/physrevlett.125.067201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2020] [Accepted: 07/16/2020] [Indexed: 06/11/2023]
Abstract
We provide an exact study of dynamical correlations for the quantum spin-orbital liquid phases of an SU(2)-symmetric Kitaev honeycomb lattice model. We show that the spin dynamics in this Kugel-Khomskii type model is exactly the density-density correlation function of S=1 fermionic magnons, which could be probed in resonant inelastic x-ray scattering experiments. We predict the characteristic signatures of spin-orbital fractionalization in inelastic scattering experiments and compare them to the ones of the spin-anisotropic Kitaev honeycomb spin liquid. In particular, the resonant inelastic x-ray scattering response shows a characteristic momentum dependence directly related to the dispersion of fermionic excitations. The neutron scattering cross section displays a mixed response of fermionic magnons as well as spin-orbital excitations. The latter has a bandwidth of broad excitations and a vison gap that is three times larger than that of the spin-1=2 Kitaev model.
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Affiliation(s)
- Willian M H Natori
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Johannes Knolle
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
- Department of Physics, TQM, Technische Universität Munchen, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
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15
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Xu C, Feng J, Kawamura M, Yamaji Y, Nahas Y, Prokhorenko S, Qi Y, Xiang H, Bellaiche L. Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2. PHYSICAL REVIEW LETTERS 2020; 124:087205. [PMID: 32167315 DOI: 10.1103/physrevlett.124.087205] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2019] [Accepted: 02/07/2020] [Indexed: 06/10/2023]
Abstract
Quantum spin liquids (QSLs) form an extremely unusual magnetic state in which the spins are highly correlated and fluctuate coherently down to the lowest temperatures, but without symmetry breaking and without the formation of any static long-range-ordered magnetism. Such intriguing phenomena are not only of great fundamental relevance in themselves, but also hold promise for quantum computing and quantum information. Among different types of QSLs, the exactly solvable Kitaev model is attracting much attention, with most proposed candidate materials, e.g., RuCl_{3} and Na_{2}IrO_{3}, having an effective S=1/2 spin value. Here, via extensive first-principles-based simulations, we report the investigation of the Kitaev physics and possible Kitaev QSL state in epitaxially strained Cr-based monolayers, such as CrSiTe_{3}, that rather possess a S=3/2 spin value. Our study thus extends the playground of Kitaev physics and QSLs to 3d transition metal compounds.
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Affiliation(s)
- Changsong Xu
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Junsheng Feng
- Key Laboratory of Computational Physical Sciences (Ministry of Education), State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
- School of Physics and Materials Engineering, Hefei Normal University, Hefei 230601, People's Republic of China
| | - Mitsuaki Kawamura
- The Institute for Solid State Physics, The University of Tokyo, Kashiwa-shi, Chiba 277-8581, Japan
| | - Youhei Yamaji
- Department of Applied Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Yousra Nahas
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Sergei Prokhorenko
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Yang Qi
- Key Laboratory of Computational Physical Sciences (Ministry of Education), State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, People's Republic of China
| | - Hongjun Xiang
- Key Laboratory of Computational Physical Sciences (Ministry of Education), State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, People's Republic of China
| | - L Bellaiche
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
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16
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Lee I, Utermohlen FG, Weber D, Hwang K, Zhang C, van Tol J, Goldberger JE, Trivedi N, Hammel PC. Fundamental Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet CrI_{3}. PHYSICAL REVIEW LETTERS 2020; 124:017201. [PMID: 31976706 DOI: 10.1103/physrevlett.124.017201] [Citation(s) in RCA: 39] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Indexed: 06/10/2023]
Abstract
We lay the foundation for determining the microscopic spin interactions in two-dimensional (2D) ferromagnets by combining angle-dependent ferromagnetic resonance (FMR) experiments on high quality CrI_{3} single crystals with theoretical modeling based on symmetries. We discover that the Kitaev interaction is the strongest in this material with K∼-5.2 meV, 25 times larger than the Heisenberg exchange J∼-0.2 meV, and responsible for opening the ∼5 meV gap at the Dirac points in the spin-wave dispersion. Furthermore, we find that the symmetric off-diagonal anisotropy Γ∼-67.5 μeV, though small, is crucial for opening a ∼0.3 meV gap in the magnon spectrum at the zone center and stabilizing ferromagnetism in the 2D limit. The high resolution of the FMR data further reveals a μeV-scale quadrupolar contribution to the S=3/2 magnetism. Our identification of the underlying exchange anisotropies opens paths toward 2D ferromagnets with higher T_{C} as well as magnetically frustrated quantum spin liquids based on Kitaev physics.
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Affiliation(s)
- Inhee Lee
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - Franz G Utermohlen
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - Daniel Weber
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Kyusung Hwang
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
- School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea
| | - Chi Zhang
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - Johan van Tol
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
| | - Joshua E Goldberger
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Nandini Trivedi
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - P Chris Hammel
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
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