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Simeth W, Rahn MC, Bauer A, Meven M, Pfleiderer C. Topological aspects of multi- kantiferromagnetism in cubic rare-earth compounds. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:215602. [PMID: 38295434 DOI: 10.1088/1361-648x/ad24bb] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Accepted: 01/31/2024] [Indexed: 02/02/2024]
Abstract
We advertise rare-earth intermetallics with high-symmetry crystal structures and competing interactions as a possible materials platform hosting spin structures with non-trivial topological properties. Focusing on the series of cubicRCu compounds, whereR= Ho, Er, Tm, the bulk properties of these systems display exceptionally rich magnetic phase diagrams hosting an abundance of different phase pockets characteristic of antiferromagnetic order in the presence of delicately balanced interactions. The electrical transport properties exhibit large anomalous contributions suggestive of topologically non-trivial winding in the electronic and magnetic structures. Neutron diffraction identifies spontaneous long-range magnetic order in terms of commensurate and incommensurate variations of(ππ0)antiferromagnetism with the possibility for various multi-kconfigurations. Motivated by general trends in these materials, we discuss the possible existence of topologically non-trivial winding in real and reciprocal space in the class ofRCu compounds including antiferromagnetic skyrmion lattices. Putatively bringing together different limits of non-trivial topological winding in the same material, the combination of properties inRCu systems promises access to advanced functionalities.
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Affiliation(s)
- W Simeth
- Physik-Department, Technical University of Munich, D-85748 Garching, Germany
- Paul Scherrer Institut, Forschungsstrasse 111, CH-5232 Villigen, Switzerland
| | - M C Rahn
- Physik-Department, Technical University of Munich, D-85748 Garching, Germany
- Institute for Solid State and Materials Physics, Technical University of Dresden, D-01062 Dresden, Germany
| | - A Bauer
- Physik-Department, Technical University of Munich, D-85748 Garching, Germany
- Centre for Quantum Engineering (ZQE), Technical University of Munich, D-85748 Garching, Germany
| | - M Meven
- Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science (JCNS) at Heinz Maier-Leibnitz Zentrum (MLZ), D-85748 Garching, Germany
- Institut für Kristallographie, RWTH Aachen, D-52056 Aachen, Germany
| | - C Pfleiderer
- Physik-Department, Technical University of Munich, D-85748 Garching, Germany
- Centre for Quantum Engineering (ZQE), Technical University of Munich, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Technical University of Munich, D-85748 Garching, Germany
- Heinz Maier-Leibnitz Zentrum (MLZ), Technical University of Munich, D-85748 Garching, Germany
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Huber N, Leeb V, Bauer A, Benka G, Knolle J, Pfleiderer C, Wilde MA. Quantum oscillations of the quasiparticle lifetime in a metal. Nature 2023; 621:276-281. [PMID: 37532938 DOI: 10.1038/s41586-023-06330-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2022] [Accepted: 06/15/2023] [Indexed: 08/04/2023]
Abstract
Following nearly a century of research, it remains a puzzle that the low-lying excitations of metals are remarkably well explained by effective single-particle theories of non-interacting bands1-4. The abundance of interactions in real materials raises the question of direct spectroscopic signatures of phenomena beyond effective single-particle, single-band behaviour. Here we report the identification of quantum oscillations (QOs) in the three-dimensional topological semimetal CoSi, which defy the standard description in two fundamental aspects. First, the oscillation frequency corresponds to the difference of semiclassical quasiparticle (QP) orbits of two bands, which are forbidden as half of the trajectory would oppose the Lorentz force. Second, the oscillations exist up to above 50 K, in strong contrast to all other oscillatory components, which vanish below a few kelvin. Our findings are in excellent agreement with generic model calculations of QOs of the QP lifetime (QPL). Because the only precondition for their existence is a nonlinear coupling of at least two electronic orbits, for example, owing to QP scattering on defects or collective excitations, such QOs of the QPL are generic for any metal featuring Landau quantization with several orbits. They are consistent with certain frequencies in topological semimetals5-9, unconventional superconductors10,11, rare-earth compounds12-14 and Rashba systems15, and permit to identify and gauge correlation phenomena, for example, in two-dimensional materials16,17 and multiband metals18.
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Affiliation(s)
- Nico Huber
- TUM School of Natural Sciences, Department of Physics, Technical University of Munich, Garching, Germany
| | - Valentin Leeb
- TUM School of Natural Sciences, Department of Physics, Technical University of Munich, Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Munich, Germany
| | - Andreas Bauer
- TUM School of Natural Sciences, Department of Physics, Technical University of Munich, Garching, Germany
- Centre for Quantum Engineering (ZQE), Technical University of Munich, Garching, Germany
| | - Georg Benka
- TUM School of Natural Sciences, Department of Physics, Technical University of Munich, Garching, Germany
| | - Johannes Knolle
- TUM School of Natural Sciences, Department of Physics, Technical University of Munich, Garching, Germany.
- Munich Center for Quantum Science and Technology (MCQST), Munich, Germany.
- Blackett Laboratory, Imperial College London, London, UK.
| | - Christian Pfleiderer
- TUM School of Natural Sciences, Department of Physics, Technical University of Munich, Garching, Germany.
- Munich Center for Quantum Science and Technology (MCQST), Munich, Germany.
- Centre for Quantum Engineering (ZQE), Technical University of Munich, Garching, Germany.
| | - Marc A Wilde
- TUM School of Natural Sciences, Department of Physics, Technical University of Munich, Garching, Germany.
- Centre for Quantum Engineering (ZQE), Technical University of Munich, Garching, Germany.
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Simeth W, Bauer A, Franz C, Aqeel A, Bereciartua PJ, Sears JA, Francoual S, Back CH, Pfleiderer C. Resonant Elastic X-Ray Scattering of Antiferromagnetic Superstructures in EuPtSi_{3}. PHYSICAL REVIEW LETTERS 2023; 130:266701. [PMID: 37450805 DOI: 10.1103/physrevlett.130.266701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Revised: 04/06/2023] [Accepted: 05/11/2023] [Indexed: 07/18/2023]
Abstract
We report resonant elastic x-ray scattering of long-range magnetic order in EuPtSi_{3}, combining different scattering geometries with full linear polarization analysis to unambiguously identify magnetic scattering contributions. At low temperatures, EuPtSi_{3} stabilizes type A antiferromagnetism featuring various long-wavelength modulations. For magnetic fields applied in the hard magnetic basal plane, well-defined regimes of cycloidal, conical, and fanlike superstructures may be distinguished that encompass a pocket of commensurate type A order without superstructure. For magnetic field applied along the easy axis, the phase diagram comprises the cycloidal and conical superstructures only. Highlighting the power of polarized resonant elastic x-ray scattering, our results reveal a combination of magnetic phases that suggest a highly unusual competition between antiferromagnetic exchange interactions with Dzyaloshinsky-Moriya spin-orbit coupling of similar strength.
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Affiliation(s)
- Wolfgang Simeth
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
- Laboratory for Neutron and Muon Instrumentation, Paul Scherrer Institute, CH-5232 Villigen, Switzerland
| | - Andreas Bauer
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
- Zentrum für QuantumEngineering (ZQE), Technische Universität München, D-85748 Garching, Germany
| | - Christian Franz
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
- Jülich Centre for Neutron Science (JCNS) at Heinz Maier-Leibnitz Zentrum (MLZ), D-85748 Garching, Germany
| | - Aisha Aqeel
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Technische Universität München, D-85748 Garching, Germany
| | | | - Jennifer A Sears
- Deutsches Elektronen-Synchrotron (DESY), D-22607 Hamburg, Germany
| | - Sonia Francoual
- Deutsches Elektronen-Synchrotron (DESY), D-22607 Hamburg, Germany
| | - Christian H Back
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
- Zentrum für QuantumEngineering (ZQE), Technische Universität München, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Technische Universität München, D-85748 Garching, Germany
| | - Christian Pfleiderer
- Physik-Department, Technische Universität München, D-85748 Garching, Germany
- Zentrum für QuantumEngineering (ZQE), Technische Universität München, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Technische Universität München, D-85748 Garching, Germany
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Huber N, Alpin K, Causer GL, Worch L, Bauer A, Benka G, Hirschmann MM, Schnyder AP, Pfleiderer C, Wilde MA. Network of Topological Nodal Planes, Multifold Degeneracies, and Weyl Points in CoSi. PHYSICAL REVIEW LETTERS 2022; 129:026401. [PMID: 35867447 DOI: 10.1103/physrevlett.129.026401] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Revised: 01/26/2022] [Accepted: 05/24/2022] [Indexed: 06/15/2023]
Abstract
We showcase the importance of global band topology in a study of the Weyl semimetal CoSi as a representative of chiral space group (SG) 198. We identify a network of band crossings comprising topological nodal planes, multifold degeneracies, and Weyl points consistent with the fermion doubling theorem. To confirm these findings, we combined the general analysis of the band topology of SG 198 with Shubnikov-de Haas oscillations and material-specific calculations of the electronic structure and Berry curvature. The observation of two nearly dispersionless Shubnikov-de Haas frequency branches provides unambiguous evidence of four Fermi surface sheets at the R point that reflect the symmetry-enforced orthogonality of the underlying wave functions at the intersections with the nodal planes. Hence, irrespective of the spin-orbit coupling strength, SG 198 features always six- and fourfold degenerate crossings at R and Γ that are intimately connected to the topological charges distributed across the network.
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Affiliation(s)
- Nico Huber
- Physik Department, Technische Universität München, D-85748 Garching, Germany
| | - Kirill Alpin
- Max-Planck-Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Grace L Causer
- Physik Department, Technische Universität München, D-85748 Garching, Germany
| | - Lukas Worch
- Physik Department, Technische Universität München, D-85748 Garching, Germany
| | - Andreas Bauer
- Physik Department, Technische Universität München, D-85748 Garching, Germany
| | - Georg Benka
- Physik Department, Technische Universität München, D-85748 Garching, Germany
| | - Moritz M Hirschmann
- Max-Planck-Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Andreas P Schnyder
- Max-Planck-Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Christian Pfleiderer
- Physik Department, Technische Universität München, D-85748 Garching, Germany
- MCQST, Technische Universität München, D-85748 Garching, Germany
- Centre for Quantum Engineering (ZQE), Technische Universität München, D-85748 Garching, Germany
| | - Marc A Wilde
- Physik Department, Technische Universität München, D-85748 Garching, Germany
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Čermák P, Schneidewind A, Liu B, Koza MM, Franz C, Schönmann R, Sobolev O, Pfleiderer C. Magnetoelastic hybrid excitations in CeAuAl 3. Proc Natl Acad Sci U S A 2019; 116:6695-6700. [PMID: 30894488 PMCID: PMC6452737 DOI: 10.1073/pnas.1819664116] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
Nearly a century of research has established the Born-Oppenheimer approximation as a cornerstone of condensed-matter systems, stating that the motion of the atomic nuclei and electrons may be treated separately. Interactions beyond the Born-Oppenheimer approximation are at the heart of magneto-elastic functionalities and instabilities. We report comprehensive neutron spectroscopy and ab initio phonon calculations of the coupling between phonons, CEF-split localized 4f electron states, and conduction electrons in the paramagnetic regime of [Formula: see text], an archetypal Kondo lattice compound. We identify two distinct magneto-elastic hybrid excitations that form even though all coupling constants are small. First, we find a CEF-phonon bound state reminiscent of the vibronic bound state (VBS) observed in other materials. However, in contrast to an abundance of optical phonons, so far believed to be essential for a VBS, the VBS in [Formula: see text] arises from a comparatively low density of states of acoustic phonons. Second, we find a pronounced anticrossing of the CEF excitations with acoustic phonons at zero magnetic field not observed before. Remarkably, both magneto-elastic excitations are well developed despite considerable damping of the CEFs that arises dominantly by the conduction electrons. Taking together the weak coupling with the simultaneous existence of a distinct VBS and anticrossing in the same material in the presence of damping suggests strongly that similarly well-developed magneto-elastic hybrid excitations must be abundant in a wide range of materials. In turn, our study of the excitation spectra of [Formula: see text] identifies a tractable point of reference in the search for magneto-elastic functionalities and instabilities.
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Affiliation(s)
- Petr Čermák
- Faculty of Mathematics and Physics, Department of Condensed Matter Physics, Charles University, 121 16 Praha, Czech Republic;
- Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science at Heinz Maier-Leibnitz Zentrum, 85748 Garching, Germany
| | - Astrid Schneidewind
- Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science at Heinz Maier-Leibnitz Zentrum, 85748 Garching, Germany
| | - Benqiong Liu
- Key Laboratory of Neutron Physics, Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900, People's Republic of China
| | | | - Christian Franz
- Heinz Maier-Leibnitz Zentrum, Technische Universität München, 85748 Garching, Germany
- Physik-Department, Technische Universität München, 85748 Garching, Germany
| | - Rudolf Schönmann
- Physik-Department, Technische Universität München, 85748 Garching, Germany
| | - Oleg Sobolev
- Institute for Physical Chemistry, Georg-August-University of Göttingen, D-37077 Göttingen, Germany
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Wild J, Meier TNG, Pöllath S, Kronseder M, Bauer A, Chacon A, Halder M, Schowalter M, Rosenauer A, Zweck J, Müller J, Rosch A, Pfleiderer C, Back CH. Entropy-limited topological protection of skyrmions. SCIENCE ADVANCES 2017; 3:e1701704. [PMID: 28975152 PMCID: PMC5621974 DOI: 10.1126/sciadv.1701704] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Accepted: 09/07/2017] [Indexed: 05/27/2023]
Abstract
Magnetic skyrmions are topologically protected whirls that decay through singular magnetic configurations known as Bloch points. We used Lorentz transmission electron microscopy to infer the energetics associated with the topological decay of magnetic skyrmions far from equilibrium in the chiral magnet Fe1-x Co x Si. We observed that the lifetime τ of the skyrmions depends exponentially on temperature, [Formula: see text]. The prefactor τ0 of this Arrhenius law changes by more than 30 orders of magnitude for small changes of the magnetic field, reflecting a substantial reduction of the lifetime of skyrmions by entropic effects and, thus, an extreme case of enthalpy-entropy compensation. Such compensation effects, being well known across many different scientific disciplines, affect topological transitions and, thus, topological protection on an unprecedented level.
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Affiliation(s)
- Johannes Wild
- Institut für Experimentelle Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Thomas N. G. Meier
- Institut für Experimentelle Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Simon Pöllath
- Institut für Experimentelle Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Matthias Kronseder
- Institut für Experimentelle Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Andreas Bauer
- Physik Department, Technische Universität Bremen, D-85748 Garching, Germany
| | - Alfonso Chacon
- Physik Department, Technische Universität Bremen, D-85748 Garching, Germany
| | - Marco Halder
- Physik Department, Technische Universität Bremen, D-85748 Garching, Germany
| | - Marco Schowalter
- Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, D-28359 Bremen, Germany
| | - Andreas Rosenauer
- Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, D-28359 Bremen, Germany
| | - Josef Zweck
- Institut für Experimentelle Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Jan Müller
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Köln, Germany
| | - Achim Rosch
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Köln, Germany
| | | | - Christian H. Back
- Institut für Experimentelle Physik, Universität Regensburg, D-93040 Regensburg, Germany
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