1
|
Loidl A, Lunkenheimer P, Tsurkan V. On the proximate Kitaev quantum-spin liquid α-RuCl 3: thermodynamics, excitations and continua. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:443004. [PMID: 34371492 DOI: 10.1088/1361-648x/ac1bcf] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2021] [Accepted: 08/09/2021] [Indexed: 06/13/2023]
Abstract
This topical review provides an overview over recent thermodynamic, infrared, and THz results on the proximate Kitaev spin-liquid. Quantum-spin liquids are exotic phases characterized by the absence of magnetic ordering even at the lowest temperatures and by the occurrence of fractionalized spin excitations. Among those, Kitaev spin liquids are most fascinating as they belong to the rare class of model systems, that can be solved analytically by decomposing localized spinsS= 1/2 into Majorana fermions. The main aim of this review is to summarize experimental evidence obtained by THz spectroscopy and utilizing heat-capacity experiments, which point to the existence of fractionalized excitations in the spin-liquid state, which in α-RuCl3exists at temperatures just above the onset of magnetic order or at in-plane magnetic fields just beyond the quantum-critical point where antiferromagnetic order becomes suppressed. Thermodynamic and spectroscopic results are compared to theoretical predictions and model calculations. In addition, we document recent progress in elucidating the sub-gap (<1 eV) electronic structure of the 4d5ruthenium electrons to characterize their local electronic configuration. The on-site excitation spectra of thedelectrons below the optical gap can be consistently explained using a spin-orbit coupling constant of ∼170 meV and the concept of multiple spin-orbital excitations. Furthermore, we discuss the phonon spectra of the title compound including rigid-plane shear and compression modes of the single molecular layers. In recent theoretical concepts it has been shown that phonons can couple to Majorana fermions and may play a substantial role in establishing the half-integer thermal quantum Hall effect observed in this material.
Collapse
Affiliation(s)
- A Loidl
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - P Lunkenheimer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - V Tsurkan
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
- Institute of Applied Physics, Chisinau MD-2028, Moldova
| |
Collapse
|
2
|
Yamada MG, Fujimoto S. Electric Probe for the Toric Code Phase in Kitaev Materials through the Hyperfine Interaction. PHYSICAL REVIEW LETTERS 2021; 127:047201. [PMID: 34355932 DOI: 10.1103/physrevlett.127.047201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Accepted: 06/24/2021] [Indexed: 06/13/2023]
Abstract
The Kitaev model is a remarkable spin model with gapped and gapless spin liquid phases, which are potentially realized in iridates and α-RuCl_{3}. In the recent experiment of α-RuCl_{3}, the signature of a nematic transition to the gapped toric code phase, which breaks the C_{3} symmetry of the system, has been observed through the angle dependence of the heat capacity. We here propose a mechanism by which the nematic transition can be detected electrically. This is seemingly impossible because J_{eff}=1/2 spins do not have an electric quadrupole moment (EQM). However, in the second-order perturbation, the virtual state with a nonzero EQM appears, which makes the nematic order parameter detectable by nuclear magnetic resonance and Mössbauer spectroscopy. The purely magnetic origin of the EQM is different from conventional electronic nematic phases, allowing the direct detection of the realization of Kitaev's toric error-correction code.
Collapse
Affiliation(s)
- Masahiko G Yamada
- Department of Materials Engineering Science, Osaka University, Toyonaka 560-8531, Japan
| | - Satoshi Fujimoto
- Department of Materials Engineering Science, Osaka University, Toyonaka 560-8531, Japan
- Center for Quantum Information and Quantum Biology, Osaka University, Toyonaka 560-8531, Japan
| |
Collapse
|
3
|
Suzuki H, Liu H, Bertinshaw J, Ueda K, Kim H, Laha S, Weber D, Yang Z, Wang L, Takahashi H, Fürsich K, Minola M, Lotsch BV, Kim BJ, Yavaş H, Daghofer M, Chaloupka J, Khaliullin G, Gretarsson H, Keimer B. Proximate ferromagnetic state in the Kitaev model material α-RuCl 3. Nat Commun 2021; 12:4512. [PMID: 34301938 PMCID: PMC8302668 DOI: 10.1038/s41467-021-24722-4] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 07/01/2021] [Indexed: 11/27/2022] Open
Abstract
α-RuCl3 is a major candidate for the realization of the Kitaev quantum spin liquid, but its zigzag antiferromagnetic order at low temperatures indicates deviations from the Kitaev model. We have quantified the spin Hamiltonian of α-RuCl3 by a resonant inelastic x-ray scattering study at the Ru L3 absorption edge. In the paramagnetic state, the quasi-elastic intensity of magnetic excitations has a broad maximum around the zone center without any local maxima at the zigzag magnetic Bragg wavevectors. This finding implies that the zigzag order is fragile and readily destabilized by competing ferromagnetic correlations. The classical ground state of the experimentally determined Hamiltonian is actually ferromagnetic. The zigzag state is stabilized by quantum fluctuations, leaving ferromagnetism – along with the Kitaev spin liquid – as energetically proximate metastable states. The three closely competing states and their collective excitations hold the key to the theoretical understanding of the unusual properties of α-RuCl3 in magnetic fields. RuCl3 has stood out as a prime candidate in the search for quantum spin liquids; however, its antiferromagnetic ordering at low temperature suggests deviations from typical QSL models. Here, using resonant inelastic x-ray scattering, the authors provide a comprehensive determination of the low energy effective Hamiltonian.
Collapse
Affiliation(s)
- H Suzuki
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany.
| | - H Liu
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany.
| | - J Bertinshaw
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany
| | - K Ueda
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany.,Department of Applied Physics, University of Tokyo, Tokyo, Japan
| | - H Kim
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany.,Department of Physics, Pohang University of Science and Technology, Pohang, South Korea.,Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang, South Korea
| | - S Laha
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany
| | - D Weber
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany.,Institute of Nanotechnology, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - Z Yang
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany
| | - L Wang
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany
| | - H Takahashi
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany
| | - K Fürsich
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany
| | - M Minola
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany
| | - B V Lotsch
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany.,Department of Chemistry, University of Munich (LMU), München, Germany
| | - B J Kim
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany.,Department of Physics, Pohang University of Science and Technology, Pohang, South Korea.,Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang, South Korea
| | - H Yavaş
- Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany.,SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - M Daghofer
- Institute for Functional Matter and Quantum Technologies, University of Stuttgart, Stuttgart, Germany.,Center for Integrated Quantum Science and Technology, University of Stuttgart, Stuttgart, Germany
| | - J Chaloupka
- Department of Condensed Matter Physics, Faculty of Science, Masaryk University, Brno, Czech Republic.,Central European Institute of Technology, Masaryk University, Brno, Czech Republic
| | - G Khaliullin
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany
| | - H Gretarsson
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany.,Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany
| | - B Keimer
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany.
| |
Collapse
|
4
|
Biasin E, Nascimento DR, Poulter BI, Abraham B, Kunnus K, Garcia-Esparza AT, Nowak SH, Kroll T, Schoenlein RW, Alonso-Mori R, Khalil M, Govind N, Sokaras D. Revealing the bonding of solvated Ru complexes with valence-to-core resonant inelastic X-ray scattering. Chem Sci 2021; 12:3713-3725. [PMID: 34163645 PMCID: PMC8179428 DOI: 10.1039/d0sc06227h] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Accepted: 01/21/2021] [Indexed: 12/27/2022] Open
Abstract
Ru-complexes are widely studied because of their use in biological applications and photoconversion technologies. We reveal novel insights into the chemical bonding of a series of Ru(ii)- and Ru(iii)-complexes by leveraging recent advances in high-energy-resolution tender X-ray spectroscopy and theoretical calculations. We perform Ru 2p4d resonant inelastic X-ray scattering (RIXS) to probe the valence excitations in dilute solvated Ru-complexes. Combining these experiments with a newly developed theoretical approach based on time-dependent density functional theory, we assign the spectral features and quantify the metal-ligand bonding interactions. The valence-to-core RIXS features uniquely identify the metal-centered and charge transfer states and allow extracting the ligand-field splitting for all the complexes. The combined experimental and theoretical approach described here is shown to reliably characterize the ground and excited valence states of Ru complexes, and serve as a basis for future investigations of ruthenium, or other 4d metals active sites, in biological and chemical applications.
Collapse
Affiliation(s)
- Elisa Biasin
- Stanford PULSE Institute, SLAC National Accelerator Laboratory Menlo Park CA 94025 USA
| | - Daniel R Nascimento
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory Richland Washington 99352 USA
| | - Benjamin I Poulter
- Department of Chemistry, University of Washington Seattle Washington 98195 USA
| | - Baxter Abraham
- SSRL, SLAC National Accelerator Laboratory Menlo Park California 94025 USA
| | - Kristjan Kunnus
- Stanford PULSE Institute, SLAC National Accelerator Laboratory Menlo Park CA 94025 USA
- LCLS, SLAC National Accelerator Laboratory Menlo Park CA 94025 USA
| | | | - Stanislaw H Nowak
- SSRL, SLAC National Accelerator Laboratory Menlo Park California 94025 USA
| | - Thomas Kroll
- SSRL, SLAC National Accelerator Laboratory Menlo Park California 94025 USA
| | - Robert W Schoenlein
- Stanford PULSE Institute, SLAC National Accelerator Laboratory Menlo Park CA 94025 USA
- LCLS, SLAC National Accelerator Laboratory Menlo Park CA 94025 USA
| | | | - Munira Khalil
- Department of Chemistry, University of Washington Seattle Washington 98195 USA
| | - Niranjan Govind
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory Richland Washington 99352 USA
| | | |
Collapse
|