Proximate ferromagnetic state in the Kitaev model material α-RuCl3

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, B. V.; Kim, B. J.; Yavaş, H.; Daghofer, M.; Chaloupka, J.; Khaliullin, G.; Gretarsson, H.; Keimer, B.

doi:10.1038/s41467-021-24722-4

Title: Proximate ferromagnetic state in the Kitaev model material α-RuCl₃

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.

Authors:

^[1];

^[2]; Bertinshaw, J. ^[2]; Ueda, K. ^[3]; Kim, H. ^[4];

^[2];

^[5]; Yang, Z. ^[2]; Wang, L. ^[2];

^[2];

^[6];

^[4]; Yavaş, H. ^[7]; Daghofer, M. ^[8]; Chaloupka, J. ^[9];

^[2]; Gretarsson, H. ^[10];

^[2]

Max-Planck-Institut für Festkörperforschung, Stuttgart (Germany)
Max-Planck-Institut für Festkörperforschung, Stuttgart (Germany)
Max-Planck-Institut für Festkörperforschung, Stuttgart (Germany); Univ. of Tokyo (Japan)
Max-Planck-Institut für Festkörperforschung, Stuttgart (Germany); Pohang Univ. of Science and Technology (POSTECH) (Korea, Republic of); Institute for Basic Science (IBS), Pohang (Korea, Republic of)
Max-Planck-Institut für Festkörperforschung, Stuttgart (Germany); Karlsruhe Inst. of Technology (KIT) (Germany)
Max-Planck-Institut für Festkörperforschung, Stuttgart (Germany); University of Munich (LMU), München (Germany)
Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Univ. of Stuttgart (Germany)
Masaryk University, Brno (Czech Republic)
Max-Planck-Institut für Festkörperforschung, Stuttgart (Germany); Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

Publication Date:: Fri Jul 23 00:00:00 EDT 2021

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); European Research Council (ERC); Japan Society for the Promotion of Science (JSPS); Alexander von Humboldt Foundation

OSTI Identifier:: 1819717

Grant/Contract Number:: AC02-76SF00515; 669550

Resource Type:: Accepted Manuscript

Journal Name:: Nature Communications

Additional Journal Information:: Journal Volume: 12; Journal Issue: 1; Journal ID: ISSN 2041-1723

Publisher:: Nature Publishing Group

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE

Citation Formats


                    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, B. V., Kim, B. J., Yavaş, H., Daghofer, M., Chaloupka, J., Khaliullin, G., Gretarsson, H., and Keimer, B. Proximate ferromagnetic state in the Kitaev model material α-RuCl3.  United States: N. p., 2021. 
Web.  doi:10.1038/s41467-021-24722-4.

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                    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, B. V., Kim, B. J., Yavaş, H., Daghofer, M., Chaloupka, J., Khaliullin, G., Gretarsson, H., & Keimer, B. Proximate ferromagnetic state in the Kitaev model material α-RuCl3.  United States.  https://doi.org/10.1038/s41467-021-24722-4

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                    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, B. V., Kim, B. J., Yavaş, H., Daghofer, M., Chaloupka, J., Khaliullin, G., Gretarsson, H., and Keimer, B. Fri .  
"Proximate ferromagnetic state in the Kitaev model material α-RuCl3".  United States.  https://doi.org/10.1038/s41467-021-24722-4.  https://www.osti.gov/servlets/purl/1819717.

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@article{osti_1819717,

  title        = {Proximate ferromagnetic state in the Kitaev model material α-RuCl3},

  author       = {Suzuki, H. and Liu, H. and Bertinshaw, J. and Ueda, K. and Kim, H. and Laha, S. and Weber, D. and Yang, Z. and Wang, L. and Takahashi, H. and Fürsich, K. and Minola, M. and Lotsch, B. V. and Kim, B. J. and Yavaş, H. and Daghofer, M. and Chaloupka, J. and Khaliullin, G. and Gretarsson, H. and Keimer, B.},

  abstractNote = {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.},

  doi          = {10.1038/s41467-021-24722-4},

  journal      = {Nature Communications},

  number       = 1,

  volume       = 12,

  place        = {United States},

  year         = {Fri Jul 23 00:00:00 EDT 2021},

  month        = {Fri Jul 23 00:00:00 EDT 2021}

}

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text, January 2018

Liu, Huimei; Khaliullin, Giniyat
arXiv
DOI: 10.48550/arxiv.1808.06919

Spin waves and spin-state transitions in a ruthenate high-temperature antiferromagnet
text, January 2019

Suzuki, H.; Gretarsson, H.; Ishikawa, H.
arXiv
DOI: 10.48550/arxiv.1904.01930

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Title: Proximate ferromagnetic state in the Kitaev model material α-RuCl3

Abstract

Citation Formats

Breakdown of magnons in a strongly spin-orbital coupled magnet journal, October 2017

Dynamics of a Two-Dimensional Quantum Spin Liquid: Signatures of Emergent Majorana Fermions and Fluxes journal, May 2014

Ab initio analysis of the tight-binding parameters and magnetic interactions in Na 2 IrO 3 journal, July 2013

Crystal-Field Splitting and Correlation Effect on the Electronic Structure of A 2 IrO 3 journal, February 2013

Magnetoelastic coupling and effects of uniaxial strain in α − RuCl 3 from first principles journal, April 2021

Excitations in the field-induced quantum spin liquid state of α-RuCl3 journal, February 2018

Observation of spin-orbit excitations and Hund's multiplets in Ca 2 RuO 4 journal, July 2019

Phase diagram of α − RuCl 3 in an in-plane magnetic field journal, May 2017

Ferromagnetic Kitaev interaction and the origin of large magnetic anisotropy in α-RuCl3 journal, April 2020

Quantum spin liquids: a review journal, November 2016

Electronically highly cubic conditions for Ru in α − RuCl 3 journal, October 2017

Collective Nature of Spin Excitations in Superconducting Cuprates Probed by Resonant Inelastic X-Ray Scattering journal, May 2015

Weak-field induced nonmagnetic state in a Co-based honeycomb journal, January 2020

Models and materials for generalized Kitaev magnetism journal, November 2017

Resonant inelastic x-ray scattering studies of elementary excitations journal, June 2011

Resonant inelastic x-ray scattering operators for t 2 g orbital systems journal, August 2017

Probing α − RuCl 3 Beyond Magnetic Order: Effects of Temperature and Magnetic Field journal, February 2018

Topological excitations in the ferromagnetic Kitaev-Heisenberg model journal, August 2018

Canonical Thermal Pure Quantum State journal, July 2013

Topological magnons in Kitaev magnets at high fields journal, August 2018

Successive magnetic phase transitions in α − RuCl 3 : XY-like frustrated magnet on the honeycomb lattice journal, March 2015

Kitaev-Heisenberg- J 2 - J 3 model for the iridates A 2 IrO 3 journal, November 2011

Scattering Continuum and Possible Fractionalized Excitations in α − RuCl 3 journal, April 2015

Spin waves and spin-state transitions in a ruthenate high-temperature antiferromagnet journal, March 2019

α − RuCl 3 : A spin-orbit assisted Mott insulator on a honeycomb lattice journal, July 2014

Resonant inelastic x-ray scattering spectra for electrons in solids journal, February 2001

Dynamical and thermal magnetic properties of the Kitaev spin liquid candidate α-RuCl3 journal, January 2020

Magnetic Excitations and Continuum of a Possibly Field-Induced Quantum Spin Liquid in α − RuCl 3 journal, November 2017

Exact Results for Spin Dynamics and Fractionalization in the Kitaev Model journal, June 2007

Thermal Pure Quantum States at Finite Temperature journal, June 2012

Kitaev-Heisenberg Model on a Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides A 2 IrO 3 journal, July 2010

Resonant inelastic x-ray scattering study of $\alpha$ -RuCl 3 : a progress report journal, January 2020

IRIXS: a resonant inelastic X-ray scattering instrument dedicated to X-rays in the intermediate energy range journal, February 2020

Pseudo-Jahn-Teller Effect and Magnetoelastic Coupling in Spin-Orbit Mott Insulators journal, February 2019

Low-temperature crystal and magnetic structure of α − RuCl 3 journal, April 2016

Zigzag Magnetic Order in the Iridium Oxide Na 2 IrO 3 journal, February 2013

Rethinking α − RuCl 3 journal, July 2020

Pseudospin exchange interactions in d 7 cobalt compounds: Possible realization of the Kitaev model journal, January 2018

Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet journal, April 2016

Spin liquids in frustrated magnets journal, March 2010

Anyons in an exactly solved model and beyond journal, January 2006

Concept and realization of Kitaev quantum spin liquids journal, March 2019

Kitaev-Heisenberg Hamiltonian for high-spin d 7 Mott insulators journal, January 2018

Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials journal, March 2016

Pseudospin-lattice coupling in the spin-orbit Mott insulator Sr 2 IrO 4 journal, February 2019

Magnetic order in α − RuCl 3 : A honeycomb-lattice quantum magnet with strong spin-orbit coupling journal, April 2015

Orbital Order and Fluctuations in Mott Insulators journal, January 2005

Novel J eff = 1 / 2 Mott State Induced by Relativistic Spin-Orbit Coupling in Sr 2 IrO 4 journal, August 2008

Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections journal, March 2018

Neutron scattering in the proximate quantum spin liquid α-RuCl 3 journal, June 2017

Kitaev Spin Liquid in 3 d Transition Metal Compounds journal, July 2020

Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit journal, February 2014

Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid journal, July 2018

Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models journal, February 2019

Electronic excitations in the edge-shared relativistic Mott insulator: Na 2 IrO 3 journal, February 2014

Spin Waves and Revised Crystal Structure of Honeycomb Iridate Na 2 IrO 3 journal, March 2012

Majorana fermions in the Kitaev quantum spin system α-RuCl3 journal, September 2017

Jahn-Teller Effect in Systems with Strong On-Site Spin-Orbit Coupling journal, March 2016

Magnetic anisotropy in the Kitaev model systems Na 2 IrO 3 and RuCl 3 journal, August 2016

Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for α − RuCl 3 and Na 2 IrO 3 journal, August 2017

Magnetism in two-dimensional van der Waals materials journal, October 2018

Magnon dispersion and dynamic spin response in three-dimensional spin models for α − RuCl 3 journal, May 2020

Spin-orbit excitations and electronic structure of the putative Kitaev magnet α − RuCl 3 journal, February 2016

Magnetic Properties of Restacked 2D Spin 1/2 honeycomb RuCl 3 Nanosheets journal, May 2016

Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models journal, January 2009

J eff Description of the Honeycomb Mott Insulator α − RuCl 3 journal, September 2016

Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3 journal, May 2015

High-field quantum disordered state in α − RuCl 3 : Spin flips, bound states, and multiparticle continuum journal, April 2020

Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for the honeycomb-lattice iridates A 2 IrO 3 journal, July 2015

Finite field regime for a quantum spin liquid in α − RuCl 3 journal, August 2019

Full correction of the self-absorption in soft-fluorescence extended x-ray-absorption fine structure journal, August 1992

Fractional Spin Fluctuations as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model journal, October 2016

Ab initio analysis of the tight-binding parameters and magnetic interactions in Na2IrO3 text, January 2013

Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3 text, January 2015

Jahn-Teller effect in systems with strong on-site spin-orbit coupling text, January 2016

Fermionic response from fractionalization in an insulating two-dimensional magnet text, January 2016

Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3 text, January 2016

Title: Proximate ferromagnetic state in the Kitaev model material α-RuCl₃

Breakdown of magnons in a strongly spin-orbital coupled magnet
journal, October 2017

Dynamics of a Two-Dimensional Quantum Spin Liquid: Signatures of Emergent Majorana Fermions and Fluxes
journal, May 2014

Ab initio analysis of the tight-binding parameters and magnetic interactions in Na $_{2}$ IrO $_{3}$
journal, July 2013

Crystal-Field Splitting and Correlation Effect on the Electronic Structure of $A_{2} {IrO}_{3}$
journal, February 2013

Magnetoelastic coupling and effects of uniaxial strain in $α - {RuCl}_{3}$ from first principles
journal, April 2021

Excitations in the field-induced quantum spin liquid state of α-RuCl3
journal, February 2018

Observation of spin-orbit excitations and Hund's multiplets in ${Ca}_{2} {RuO}_{4}$
journal, July 2019

Phase diagram of $α - {RuCl}_{3}$ in an in-plane magnetic field
journal, May 2017

Ferromagnetic Kitaev interaction and the origin of large magnetic anisotropy in α-RuCl3
journal, April 2020

Quantum spin liquids: a review
journal, November 2016

Electronically highly cubic conditions for Ru in $α - {RuCl}_{3}$
journal, October 2017

Collective Nature of Spin Excitations in Superconducting Cuprates Probed by Resonant Inelastic X-Ray Scattering
journal, May 2015

Weak-field induced nonmagnetic state in a Co-based honeycomb
journal, January 2020

Models and materials for generalized Kitaev magnetism
journal, November 2017

Resonant inelastic x-ray scattering studies of elementary excitations
journal, June 2011

Resonant inelastic x-ray scattering operators for $t_{2 g}$ orbital systems
journal, August 2017

Probing $α - {RuCl}_{3}$ Beyond Magnetic Order: Effects of Temperature and Magnetic Field
journal, February 2018

Topological excitations in the ferromagnetic Kitaev-Heisenberg model
journal, August 2018

Canonical Thermal Pure Quantum State
journal, July 2013

Topological magnons in Kitaev magnets at high fields
journal, August 2018

Successive magnetic phase transitions in $α - {RuCl}_{3}$ : XY-like frustrated magnet on the honeycomb lattice
journal, March 2015

Kitaev-Heisenberg- $J_{2}$ - $J_{3}$ model for the iridates $A_{2}$ IrO $_{3}$
journal, November 2011

Scattering Continuum and Possible Fractionalized Excitations in $α − {RuCl}_{3}$
journal, April 2015

Spin waves and spin-state transitions in a ruthenate high-temperature antiferromagnet
journal, March 2019

$α - {RuCl}_{3}$ : A spin-orbit assisted Mott insulator on a honeycomb lattice
journal, July 2014

Resonant inelastic x-ray scattering spectra for electrons in solids
journal, February 2001

Dynamical and thermal magnetic properties of the Kitaev spin liquid candidate α-RuCl3
journal, January 2020

Magnetic Excitations and Continuum of a Possibly Field-Induced Quantum Spin Liquid in $α − {RuCl}_{3}$
journal, November 2017

Exact Results for Spin Dynamics and Fractionalization in the Kitaev Model
journal, June 2007

Thermal Pure Quantum States at Finite Temperature
journal, June 2012

Kitaev-Heisenberg Model on a Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_{2} {IrO}_{3}$
journal, July 2010

Resonant inelastic x-ray scattering study of $\alpha$ -RuCl ₃ : a progress report
journal, January 2020

IRIXS: a resonant inelastic X-ray scattering instrument dedicated to X-rays in the intermediate energy range
journal, February 2020

Pseudo-Jahn-Teller Effect and Magnetoelastic Coupling in Spin-Orbit Mott Insulators
journal, February 2019

Low-temperature crystal and magnetic structure of $α - {RuCl}_{3}$
journal, April 2016

Zigzag Magnetic Order in the Iridium Oxide ${Na}_{2} {IrO}_{3}$
journal, February 2013

Rethinking $α − {RuCl}_{3}$
journal, July 2020

Pseudospin exchange interactions in $d^{7}$ cobalt compounds: Possible realization of the Kitaev model
journal, January 2018

Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet
journal, April 2016

Spin liquids in frustrated magnets
journal, March 2010

Anyons in an exactly solved model and beyond
journal, January 2006

Concept and realization of Kitaev quantum spin liquids
journal, March 2019

Kitaev-Heisenberg Hamiltonian for high-spin $d^{7}$ Mott insulators
journal, January 2018

Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials
journal, March 2016

Pseudospin-lattice coupling in the spin-orbit Mott insulator ${Sr}_{2} {IrO}_{4}$
journal, February 2019

Magnetic order in $α - {RuCl}_{3}$ : A honeycomb-lattice quantum magnet with strong spin-orbit coupling
journal, April 2015

Orbital Order and Fluctuations in Mott Insulators
journal, January 2005

Novel $J_{eff} = 1 / 2$ Mott State Induced by Relativistic Spin-Orbit Coupling in ${Sr}_{2} {IrO}_{4}$
journal, August 2008

Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections
journal, March 2018

Neutron scattering in the proximate quantum spin liquid α-RuCl ₃
journal, June 2017

Kitaev Spin Liquid in $3 d$ Transition Metal Compounds
journal, July 2020

Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit
journal, February 2014

Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
journal, July 2018

Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
journal, February 2019

Electronic excitations in the edge-shared relativistic Mott insulator: ${Na}_{2}$ ${IrO}_{3}$
journal, February 2014

Spin Waves and Revised Crystal Structure of Honeycomb Iridate ${Na}_{2} {IrO}_{3}$
journal, March 2012

Majorana fermions in the Kitaev quantum spin system α-RuCl3
journal, September 2017

Jahn-Teller Effect in Systems with Strong On-Site Spin-Orbit Coupling
journal, March 2016

Magnetic anisotropy in the Kitaev model systems ${Na}_{2} {IrO}_{3}$ and ${RuCl}_{3}$
journal, August 2016

Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for $α − {RuCl}_{3}$ and ${Na}_{2} {IrO}_{3}$
journal, August 2017

Magnetism in two-dimensional van der Waals materials
journal, October 2018

Magnon dispersion and dynamic spin response in three-dimensional spin models for $α − {RuCl}_{3}$
journal, May 2020

Spin-orbit excitations and electronic structure of the putative Kitaev magnet $α - {RuCl}_{3}$
journal, February 2016

Magnetic Properties of Restacked 2D Spin 1/2 honeycomb RuCl ₃ Nanosheets
journal, May 2016

Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
journal, January 2009

$J_{eff}$ Description of the Honeycomb Mott Insulator $α − {RuCl}_{3}$
journal, September 2016

Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3
journal, May 2015

High-field quantum disordered state in $α - {RuCl}_{3}$ : Spin flips, bound states, and multiparticle continuum
journal, April 2020

Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for the honeycomb-lattice iridates $A_{2} {IrO}_{3}$
journal, July 2015

Finite field regime for a quantum spin liquid in $α − {RuCl}_{3}$
journal, August 2019

Full correction of the self-absorption in soft-fluorescence extended x-ray-absorption fine structure
journal, August 1992

Fractional Spin Fluctuations as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model
journal, October 2016

Ab initio analysis of the tight-binding parameters and magnetic interactions in Na2IrO3
text, January 2013

Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3
text, January 2015

Jahn-Teller effect in systems with strong on-site spin-orbit coupling
text, January 2016

Fermionic response from fractionalization in an insulating two-dimensional magnet
text, January 2016

Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3
text, January 2016

Pseudospin exchange interactions in d^7 cobalt compounds: Possible realization of the Kitaev model
text, January 2017

Pseudo Jahn-Teller Effect and Magnetoelastic Coupling in Spin-Orbit Mott Insulators
text, January 2018