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Andriushin ND, Sukhanov AS, Korshunov AN, Pavlovskii MS, Rahn MC, Nikitin SE. Phonon Topology and Winding of Spectral Weight in Graphite. PHYSICAL REVIEW LETTERS 2023; 131:246601. [PMID: 38181154 DOI: 10.1103/physrevlett.131.246601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 10/19/2023] [Indexed: 01/07/2024]
Abstract
The topology of electronic and phonon band structures of graphene is well studied and known to exhibit a Dirac cone at the K point of the Brillouin zone. Here, we applied inelastic x-ray scattering (IXS) along with ab initio calculations to investigate phonon topology in graphite, the 3D analog of graphene. We identified a pair of modes that form a very weakly gapped linear anticrossing at the K point that can be essentially viewed as a Dirac cone approximant. The IXS intensity in the vicinity of the quasi-Dirac point reveals a harmonic modulation of the phonon spectral weight above and below the Dirac energy, which was previously proposed as an experimental fingerprint of the nontrivial topology. We illustrate how the topological winding of IXS intensity can be understood in terms of atomic displacements and highlight that the intensity winding is not in fact sensitive in telling quasi- and true Dirac points apart.
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Affiliation(s)
- N D Andriushin
- Institut für Festkörper- und Materialphysik, Technische Universität Dresden, D-01069 Dresden, Germany
| | - A S Sukhanov
- Institut für Festkörper- und Materialphysik, Technische Universität Dresden, D-01069 Dresden, Germany
| | - A N Korshunov
- Institut für Festkörper- und Materialphysik, Technische Universität Dresden, D-01069 Dresden, Germany
- Kirensky Institute of Physics, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation
- Quantum Criticality and Dynamics Group, Paul Scherrer Institut, CH-5232 Villigen-PSI, Switzerland
- Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, CH-5232 Villigen-PSI, Switzerland
| | - M S Pavlovskii
- Kirensky Institute of Physics, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation
| | - M C Rahn
- Institut für Festkörper- und Materialphysik, Technische Universität Dresden, D-01069 Dresden, Germany
| | - S E Nikitin
- Quantum Criticality and Dynamics Group, Paul Scherrer Institut, CH-5232 Villigen-PSI, Switzerland
- Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, CH-5232 Villigen-PSI, Switzerland
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Dos Santos Dias M, Biniskos N, Dos Santos FJ, Schmalzl K, Persson J, Bourdarot F, Marzari N, Blügel S, Brückel T, Lounis S. Topological magnons driven by the Dzyaloshinskii-Moriya interaction in the centrosymmetric ferromagnet Mn 5Ge 3. Nat Commun 2023; 14:7321. [PMID: 37951946 PMCID: PMC10640582 DOI: 10.1038/s41467-023-43042-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Accepted: 10/31/2023] [Indexed: 11/14/2023] Open
Abstract
The phase of the quantum-mechanical wave function can encode a topological structure with wide-ranging physical consequences, such as anomalous transport effects and the existence of edge states robust against perturbations. While this has been exhaustively demonstrated for electrons, properties associated with the elementary quasiparticles in magnetic materials are still underexplored. Here, we show theoretically and via inelastic neutron scattering experiments that the bulk ferromagnet Mn5Ge3 hosts gapped topological Dirac magnons. Although inversion symmetry prohibits a net Dzyaloshinskii-Moriya interaction in the unit cell, it is locally allowed and is responsible for the gap opening in the magnon spectrum. This gap is predicted and experimentally verified to close by rotating the magnetization away from the c-axis with an applied magnetic field. Hence, Mn5Ge3 realizes a gapped Dirac magnon material in three dimensions. Its tunability by chemical doping or by thin film nanostructuring defines an exciting new platform to explore and design topological magnons. More generally, our experimental route to verify and control the topological character of the magnons is applicable to bulk centrosymmetric hexagonal materials, which calls for systematic investigation.
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Affiliation(s)
- M Dos Santos Dias
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, D-52425, Jülich, Germany.
- Faculty of Physics, University of Duisburg-Essen and CENIDE, D-47053, Duisburg, Germany.
- Scientific Computing Department, STFC Daresbury Laboratory, Warrington, WA4 4AD, UK.
| | - N Biniskos
- Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science at MLZ, Lichtenbergstr. 1, D-85748, Garching, Germany.
- Charles University, Faculty of Mathematics and Physics, Department of Condensed Matter Physics, Ke Karlovu 5, 121 16, Praha, Czech Republic.
| | - F J Dos Santos
- Laboratory for Materials Simulations, Paul Scherrer Institut, 5232, Villigen, PSI, Switzerland.
- Theory and Simulation of Materials (THEOS), and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland.
| | - K Schmalzl
- Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science at ILL, 71 Avenue des Martyrs, F-38000, Grenoble, France
| | - J Persson
- Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science (JCNS-2) and Peter Grünberg Institut (PGI-4), JARA-FIT, D-52425, Jülich, Germany
| | - F Bourdarot
- Université Grenoble Alpes, CEA, IRIG, MEM, MDN, F-38000, Grenoble, France
| | - N Marzari
- Laboratory for Materials Simulations, Paul Scherrer Institut, 5232, Villigen, PSI, Switzerland
- Theory and Simulation of Materials (THEOS), and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland
| | - S Blügel
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, D-52425, Jülich, Germany
| | - T Brückel
- Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science (JCNS-2) and Peter Grünberg Institut (PGI-4), JARA-FIT, D-52425, Jülich, Germany
| | - S Lounis
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, D-52425, Jülich, Germany
- Faculty of Physics, University of Duisburg-Essen and CENIDE, D-47053, Duisburg, Germany
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Gohlke M, Corticelli A, Moessner R, McClarty PA, Mook A. Spurious Symmetry Enhancement in Linear Spin Wave Theory and Interaction-Induced Topology in Magnons. PHYSICAL REVIEW LETTERS 2023; 131:186702. [PMID: 37977642 DOI: 10.1103/physrevlett.131.186702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Revised: 09/06/2023] [Accepted: 10/03/2023] [Indexed: 11/19/2023]
Abstract
Linear spin wave theory (LSWT) is the standard technique to compute the spectra of magnetic excitations in quantum materials. In this Letter, we show that LSWT, even under ordinary circumstances, may fail to implement the symmetries of the underlying ordered magnetic Hamiltonian leading to spurious degeneracies. In common with pseudo-Goldstone modes in cases of quantum order by disorder these degeneracies tend to be lifted by magnon-magnon interactions. We show how, instead, the correct symmetries may be restored at the level of LSWT. In the process we give examples, supported by nonperturbative matrix product based time evolution calculations, where symmetry dictates topological features but where LSWT fails to implement them. We also comment on possible spin split magnons in MnF_{2} and similar rutiles by analogy to recently proposed altermagnets.
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Affiliation(s)
- Matthias Gohlke
- Theory of Quantum Matter Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
| | - Alberto Corticelli
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Roderich Moessner
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Paul A McClarty
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Alexander Mook
- Institute of Physics, Johannes Gutenberg University Mainz, 55128 Mainz, Germany
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Corticelli A, Moessner R, McClarty PA. Identifying and Constructing Complex Magnon Band Topology. PHYSICAL REVIEW LETTERS 2023; 130:206702. [PMID: 37267554 DOI: 10.1103/physrevlett.130.206702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Revised: 12/20/2022] [Accepted: 04/28/2023] [Indexed: 06/04/2023]
Abstract
Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path toward coherent spin transport for spintronics applications. In this work we explore the variety of topological magnon band structures and provide insight into how to efficiently identify topological magnon bands in materials. We do this by adapting the topological quantum chemistry approach that has used constraints imposed by time reversal and crystalline symmetries to enumerate a large class of topological electronic bands. We show how to identify physically relevant models of gapped magnon band topology by using so-called decomposable elementary band representations, and in turn discuss how to use symmetry data to infer the presence of exotic symmetry enforced nodal topology.
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Affiliation(s)
- Alberto Corticelli
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Roderich Moessner
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Paul A McClarty
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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Nikitin SE, Fåk B, Krämer KW, Fennell T, Normand B, Läuchli AM, Rüegg C. Thermal Evolution of Dirac Magnons in the Honeycomb Ferromagnet CrBr_{3}. PHYSICAL REVIEW LETTERS 2022; 129:127201. [PMID: 36179160 DOI: 10.1103/physrevlett.129.127201] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2022] [Accepted: 08/17/2022] [Indexed: 06/16/2023]
Abstract
CrBr_{3} is an excellent realization of the two-dimensional honeycomb ferromagnet, which offers a bosonic equivalent of graphene with Dirac magnons and topological character. We perform inelastic neutron scattering measurements using state-of-the-art instrumentation to update 50-year-old data, thereby enabling a definitive comparison both with recent experimental claims of a significant gap at the Dirac point and with theoretical predictions for thermal magnon renormalization. We demonstrate that CrBr_{3} has next-neighbor J_{2} and J_{3} interactions approximately 5% of J_{1}, an ideal Dirac magnon dispersion at the K point, and the associated signature of isospin winding. The magnon lifetime and the thermal band renormalization show the universal T^{2} evolution expected from an interacting spin-wave treatment, but the measured dispersion lacks the predicted van Hove features, pointing to the need for more sophisticated theoretical analysis.
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Affiliation(s)
- S E Nikitin
- Quantum Criticality and Dynamics Group, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland
| | - B Fåk
- Institut Laue-Langevin, 71 avenue des Martyrs, CS 20156, F-38042 Grenoble Cedex 9, France
| | - K W Krämer
- Department of Chemistry, Biochemistry and Pharmacy, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
| | - T Fennell
- Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, CH-5232 Villigen, Switzerland
| | - B Normand
- Laboratory for Theoretical and Computational Physics, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - A M Läuchli
- Laboratory for Theoretical and Computational Physics, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Ch Rüegg
- Quantum Criticality and Dynamics Group, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- Institute for Quantum Electronics, ETH Zürich, CH-8093 Hönggerberg, Switzerland
- Department of Quantum Matter Physics, University of Geneva, CH-1211 Geneva, Switzerland
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Walker H. Topological Magnetism Turns Elementary. PHYSICS 2022. [DOI: 10.1103/physics.15.30] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
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