Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3

Hwan Chun, Sae; Kim, Jong-Woo; Kim, Jungho; Zheng, H.; Stoumpos, Constantinos C.; Malliakas, C. D.; Mitchell, J. F.; Mehlawat, Kavita; Singh, Yogesh; Choi, Y.; Gog, T.; Al-Zein, A.; Sala, M. Moretti; Krisch, M.; Chaloupka, J.; Jackeli, G.; Khaliullin, G.; Kim, B. J.

doi:10.1038/nphys3322

Title: Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na₂IrO₃

Abstract

We show that heisenberg interactions are ubiquitous in magnetic materials and play a central role in modelling and designing quantum magnets. Bond-directional interactions offer a novel alternative to Heisenberg exchange and provide the building blocks of the Kitaev model, which has a quantum spin liquid as its exact ground state. Honeycomb iridates, A₂IrO₃ (A = Na, Li), offer potential realizations of the Kitaev magnetic exchange coupling, and their reported magnetic behaviour may be interpreted within the Kitaev framework. However, the extent of their relevance to the Kitaev model remains unclear, as evidence for bond-directional interactions has so far been indirect. Here we present direct evidence for dominant bond-directional interactions in antiferromagnetic Na₂IrO₃ and show that they lead to strong magnetic frustration. Diffuse magnetic X-ray scattering reveals broken spin-rotational symmetry even above the Néel temperature, with the three spin components exhibiting short-range correlations along distinct crystallographic directions. Lastly, this spin- and real-space entanglement directly uncovers the bond-directional nature of these interactions, thus providing a direct connection between honeycomb iridates and Kitaev physics.

Authors:

Hwan Chun, Sae ^[1]; Kim, Jong-Woo ^[2]; Kim, Jungho ^[2]; Zheng, H. ^[1]; Stoumpos, Constantinos C. ^[1]; Malliakas, C. D. ^[1]; Mitchell, J. F. ^[1]; Mehlawat, Kavita ^[3]; Singh, Yogesh ^[3]; Choi, Y. ^[2]; Gog, T. ^[2]; Al-Zein, A. ^[4]; Sala, M. Moretti ^[4]; Krisch, M. ^[4]; Chaloupka, J. ^[5]; Jackeli, G. ^[6]; Khaliullin, G. ^[7]; Kim, B. J. ^[7]

Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division
Argonne National Lab. (ANL), Argonne, IL (United States). Advanced Photon Source (APS)
Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City (India)
European Synchrotron Radiation Facility (France)
Masaryk University (Czech Republic). Central European Institute of Technology
Max Planck Institute for Solid State Research (Germany); University of Stuttgart (Germany). Institute for Functional Matter and Quantum Technologies
Max Planck Institute for Solid State Research (Germany)

Publication Date:: Mon May 11 00:00:00 EDT 2015

Research Org.:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1355347

Grant/Contract Number:: AC02-06CH11357

Resource Type:: Accepted Manuscript

Journal Name:: Nature Physics

Additional Journal Information:: Journal Volume: 11; Journal Issue: 6; Journal ID: ISSN 1745-2473

Publisher:: Nature Publishing Group (NPG)

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Magnetic properties and materials

Citation Formats


                    Hwan Chun, Sae, Kim, Jong-Woo, Kim, Jungho, Zheng, H., Stoumpos, Constantinos C., Malliakas, C. D., Mitchell, J. F., Mehlawat, Kavita, Singh, Yogesh, Choi, Y., Gog, T., Al-Zein, A., Sala, M. Moretti, Krisch, M., Chaloupka, J., Jackeli, G., Khaliullin, G., and Kim, B. J. Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3.  United States: N. p., 2015. 
Web.  doi:10.1038/nphys3322.

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                    Hwan Chun, Sae, Kim, Jong-Woo, Kim, Jungho, Zheng, H., Stoumpos, Constantinos C., Malliakas, C. D., Mitchell, J. F., Mehlawat, Kavita, Singh, Yogesh, Choi, Y., Gog, T., Al-Zein, A., Sala, M. Moretti, Krisch, M., Chaloupka, J., Jackeli, G., Khaliullin, G., & Kim, B. J. Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3.  United States.  https://doi.org/10.1038/nphys3322

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                    Hwan Chun, Sae, Kim, Jong-Woo, Kim, Jungho, Zheng, H., Stoumpos, Constantinos C., Malliakas, C. D., Mitchell, J. F., Mehlawat, Kavita, Singh, Yogesh, Choi, Y., Gog, T., Al-Zein, A., Sala, M. Moretti, Krisch, M., Chaloupka, J., Jackeli, G., Khaliullin, G., and Kim, B. J. Mon .  
"Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3".  United States.  https://doi.org/10.1038/nphys3322.  https://www.osti.gov/servlets/purl/1355347.

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@article{osti_1355347,

  title        = {Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3},

  author       = {Hwan Chun, Sae and Kim, Jong-Woo and Kim, Jungho and Zheng, H. and Stoumpos, Constantinos C. and Malliakas, C. D. and Mitchell, J. F. and Mehlawat, Kavita and Singh, Yogesh and Choi, Y. and Gog, T. and Al-Zein, A. and Sala, M. Moretti and Krisch, M. and Chaloupka, J. and Jackeli, G. and Khaliullin, G. and Kim, B. J.},

  abstractNote = {We show that heisenberg interactions are ubiquitous in magnetic materials and play a central role in modelling and designing quantum magnets. Bond-directional interactions offer a novel alternative to Heisenberg exchange and provide the building blocks of the Kitaev model, which has a quantum spin liquid as its exact ground state. Honeycomb iridates, A2IrO3 (A = Na, Li), offer potential realizations of the Kitaev magnetic exchange coupling, and their reported magnetic behaviour may be interpreted within the Kitaev framework. However, the extent of their relevance to the Kitaev model remains unclear, as evidence for bond-directional interactions has so far been indirect. Here we present direct evidence for dominant bond-directional interactions in antiferromagnetic Na2IrO3 and show that they lead to strong magnetic frustration. Diffuse magnetic X-ray scattering reveals broken spin-rotational symmetry even above the Néel temperature, with the three spin components exhibiting short-range correlations along distinct crystallographic directions. Lastly, this spin- and real-space entanglement directly uncovers the bond-directional nature of these interactions, thus providing a direct connection between honeycomb iridates and Kitaev physics.},

  doi          = {10.1038/nphys3322},

  journal      = {Nature Physics},

  number       = 6,

  volume       = 11,

  place        = {United States},

  year         = {Mon May 11 00:00:00 EDT 2015},

  month        = {Mon May 11 00:00:00 EDT 2015}

}

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DOI: 10.1107/s1600577518001200

Excitations in the field-induced quantum spin liquid state of α-RuCl3
text, January 2018

Banerjee, A.; Lampen-Kelley, P.; Knolle, Johannes
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Magnetic anisotropy of the alkali iridate Na2IrO3 at high magnetic fields: Evidence for strong ferromagnetic Kitaev correlations
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DOI: 10.1073/pnas.1821406116

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Sarkar, R.; Mei, Z.; Ruiz, A.
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DOI: 10.1103/physrevb.101.081101

Quantum spin liquids
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Science, Vol. 367, Issue 6475
DOI: 10.1126/science.aay0668

Neutron scattering in the proximate quantum spin liquid α-RuCl3.
text, January 2017

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Superconducting quantum simulator for topological order and the toric code
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DOI: 10.3929/ethz-b-000196764

Observation of a $d$-wave gap in electron-doped Sr$_2$IrO$_4$
text, January 2015

Kim, Y. K.; Sung, N. H.; Denlinger, J. D.
arXiv
DOI: 10.48550/arxiv.1506.06639

Challenges in Design of Kitaev Materials: Magnetic Interactions from Competing Energy Scales
text, January 2016

Winter, Stephen M.; Li, Ying; Jeschke, Harald O.
arXiv
DOI: 10.48550/arxiv.1603.02548

Honeycomb-lattice Heisenberg-Kitaev model in a magnetic field: Spin canting, metamagnetism, and vortex crystals
text, January 2016

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arXiv
DOI: 10.48550/arxiv.1607.04640

Spin Liquid versus Spin Orbit Coupling on the Triangular Lattice
text, January 2017

Iaconis, Jason; Liu, Chunxiao; Halász, Gábor B.
arXiv
DOI: 10.48550/arxiv.1708.07856

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text, January 2018

Paramekanti, Arun; Singh, David J.; Yuan, Bo
arXiv
DOI: 10.48550/arxiv.1804.02006

Quantization of the thermal Hall conductivity at small Hall angles
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Ye, Mengxing; Halász, Gábor B.; Savary, Lucile
arXiv
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text, January 2018

Liu, Peitao; Kim, Bongjae; Chen, Xing-Qiu
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DOI: 10.48550/arxiv.1806.07280

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DOI: 10.48550/arxiv.1806.08215

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text, January 2018

Halász, Gábor B.; Kourtis, Stefanos; Knolle, Johannes
arXiv
DOI: 10.48550/arxiv.1811.04951

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text, January 2019

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arXiv
DOI: 10.48550/arxiv.1902.07451

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arXiv
DOI: 10.48550/arxiv.1905.07040

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Title: Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3

Abstract

Citation Formats

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

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Li 2 RhO 3 : A spin-glassy relativistic Mott insulator journal, April 2013

Quantum Spin Hall Effect in a Transition Metal Oxide Na 2 IrO 3 journal, June 2009

Na 2 IrO 3 as a Molecular Orbital Crystal journal, November 2012

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Emergent quantum phases in a frustrated J 1 − J 2 Heisenberg model on the hyperhoneycomb lattice journal, October 2014

First-Principles Study of the Honeycomb-Lattice Iridates Na 2 IrO 3 in the Presence of Strong Spin-Orbit Interaction and Electron Correlations journal, September 2014

Generic spin model for the honeycomb iridates beyond the Kitaev limit text, January 2013

Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations text, January 2013

Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates text, January 2014

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Electronic Structure of the Kitaev Material α-RuCl3 Probed by Photoemission and Inverse Photoemission Spectroscopies journal, December 2016

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A high-energy-resolution resonant inelastic X-ray scattering spectrometer at ID20 of the European Synchrotron Radiation Facility journal, February 2018

Title: Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na₂IrO₃

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

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

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

Hyperhoneycomb Iridate $β − {Li}_{2} {IrO}_{3}$ as a Platform for Kitaev Magnetism
journal, February 2015

Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice
journal, June 2014

Topological Quantum Phase Transition in $5 d$ Transition Metal Oxide ${Na}_{2} {IrO}_{3}$
journal, March 2012

Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in $β − {Li}_{2} {IrO}_{3}$ : Full solution via magnetic resonant x-ray diffraction
journal, November 2014

Spiral order in the honeycomb iridate ${Li}_{2} {IrO}_{3}$
journal, September 2014

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

Kitaev interactions between j = 1/2 moments in honeycomb Na ₂ IrO ₃ are large and ferromagnetic: insights from ab initio quantum chemistry calculations
journal, January 2014

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

Theory of magnetic phase diagrams in hyperhoneycomb and harmonic-honeycomb iridates
journal, February 2015

Noncoplanar and Counterrotating Incommensurate Magnetic Order Stabilized by Kitaev Interactions in $γ − {Li}_{2} {IrO}_{3}$
journal, November 2014

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

Kitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices
journal, January 2014

Two-Dimensional Heisenberg Behavior of $J_{eff} = 1 / 2$ Isospins in the Paramagnetic State of the Spin-Orbital Mott Insulator ${Sr}_{2} {IrO}_{4}$
journal, June 2012

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

Phase-Sensitive Observation of a Spin-Orbital Mott State in Sr2IrO4
journal, March 2009

Direct evidence of a zigzag spin-chain structure in the honeycomb lattice: A neutron and x-ray diffraction investigation of single-crystal Na $_{2}$ IrO $_{3}$
journal, May 2012

Antiferromagnetic Mott insulating state in single crystals of the honeycomb lattice material ${Na}_{2} {IrO}_{3}$
journal, August 2010

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

Realization of a three-dimensional spin–anisotropic harmonic honeycomb iridate
journal, June 2014

Finite-temperature phase diagram of the classical Kitaev-Heisenberg model
journal, July 2013

Magnetic excitation spectrum of Na $_{2}$ IrO $_{3}$ probed with resonant inelastic x-ray scattering
journal, June 2013

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

Li $_{2}$ RhO $_{3}$ : A spin-glassy relativistic Mott insulator
journal, April 2013

Quantum Spin Hall Effect in a Transition Metal Oxide ${Na}_{2} {IrO}_{3}$
journal, June 2009

${Na}_{2} {IrO}_{3}$ as a Molecular Orbital Crystal
journal, November 2012

Long-range magnetic ordering in Na $_{2}$ IrO $_{3}$
journal, June 2011

Emergent quantum phases in a frustrated $J_{1} − J_{2}$ Heisenberg model on the hyperhoneycomb lattice
journal, October 2014

First-Principles Study of the Honeycomb-Lattice Iridates ${Na}_{2} {IrO}_{3}$ in the Presence of Strong Spin-Orbit Interaction and Electron Correlations
journal, September 2014

Generic spin model for the honeycomb iridates beyond the Kitaev limit
text, January 2013

Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
text, January 2013

Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates
text, January 2014

A spin–orbital-entangled quantum liquid on a honeycomb lattice
journal, February 2018

Iridates from the molecular side
journal, July 2016

Raman spectroscopic signature of fractionalized excitations in the harmonic-honeycomb iridates β- and γ-Li2IrO3
journal, July 2016

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

Observation of a d-wave gap in electron-doped Sr2IrO4
journal, October 2015

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

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

Two-dimensional spin liquid behaviour in the triangular-honeycomb antiferromagnet TbInO3
journal, January 2019

Single crystal growth from separated educts and its application to lithium transition-metal oxides
journal, October 2016

Synergism and aggregation behaviour in an aqueous binary mixture of cationic–zwitterionic surfactants: physico-chemical characterization with molecular simulation approach
journal, January 2018

Spin orientations of the spin-half Ir ⁴⁺ ions in Sr ₃ NiIrO ₆ , Sr ₂ IrO ₄ , and Na ₂ IrO ₃ : Density functional, perturbation theory, and Madelung potential analyses
journal, March 2016

The 2016 oxide electronic materials and oxide interfaces roadmap
journal, October 2016

Recent progress on correlated electron systems with strong spin–orbit coupling
journal, August 2016

Quantum spin liquids: a review
journal, November 2016

The challenge of spin–orbit-tuned ground states in iridates: a key issues review
journal, February 2018

Frustration and quantum criticality
journal, May 2018

Emergent ultrafast phenomena in correlated oxides and heterostructures
journal, January 2017

Large off-diagonal exchange couplings and spin liquid states in $C_{3}$ -symmetric iridates
journal, October 2019

Chemical tuning between triangular and honeycomb structures in a $5 d$ spin-orbit Mott insulator
journal, December 2019

Counterrotating magnetic order in the honeycomb layers of ${NaNi}_{2} {BiO}_{6 - δ}$
journal, December 2019

Lattice dynamics and structural transition of the hyperhoneycomb iridate $β - {Li}_{2} {IrO}_{3}$ investigated by high-pressure Raman scattering
journal, February 2020

Fragile magnetic order in the honeycomb lattice Iridate ${Na}_{2} {IrO}_{3}$ revealed by magnetic impurity doping
journal, October 2015

Selection of direction of the ordered moments in ${Na}_{2} {IrO}_{3}$ and $α - {RuCl}_{3}$
journal, August 2016

Magnetic dynamics and spin-phonon coupling in the antiferromagnet ${Ni}_{2} {NbBO}_{6}$
journal, September 2018

Spin dynamics and field-induced magnetic phase transition in the honeycomb Kitaev magnet $α − {Li}_{2} {IrO}_{3}$
journal, February 2019

Magnetic anisotropy of the alkali iridate ${Na}_{2} {IrO}_{3}$ at high magnetic fields: Evidence for strong ferromagnetic Kitaev correlations
journal, February 2019

First-Principles Study of the Magnetic Structure of ${Na}_{2} {IrO}_{3}$
journal, October 2015

Hidden Plaquette Order in a Classical Spin Liquid Stabilized by Strong Off-Diagonal Exchange
journal, June 2019

Field-induced ${QCD}_{3}$ -Chern-Simons quantum criticalities in Kitaev materials
journal, January 2020

X-ray magnetic diffraction under high pressure
journal, June 2019

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

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

The physics of quantum materials
journal, October 2017

Direct experimental observation of the molecular J eff = 3/2 ground state in the lacunar spinel GaTa4Se8
journal, October 2017

Correlated states in β-Li2IrO3 driven by applied magnetic fields
journal, October 2017

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

Electronic Structure of the Kitaev Material α-RuCl3 Probed by Photoemission and Inverse Photoemission Spectroscopies
journal, December 2016

Field evolution of magnons in $α − {RuCl}_{3}$ by high-resolution polarized terahertz spectroscopy
journal, September 2018

Ground state and low-energy excitations of the Kitaev-Heisenberg two-leg ladder
journal, June 2019

Low-Energy Spin Dynamics of the Honeycomb Spin Liquid Beyond the Kitaev Limit
journal, July 2016

Steplike metamagnetic transitions in a honeycomb lattice antiferromagnet ${Tb}_{2} {Ir}_{3} {Ga}_{9}$
journal, November 2019

A high-energy-resolution resonant inelastic X-ray scattering spectrometer at ID20 of the European Synchrotron Radiation Facility
journal, February 2018

Excitations in the field-induced quantum spin liquid state of α-RuCl3
text, January 2018

Magnetic anisotropy of the alkali iridate Na2IrO3 at high magnetic fields: Evidence for strong ferromagnetic Kitaev correlations
text, January 2019