First-principles study of the magnetic interactions in honeycomb Na2IrO3

doi:10.1103/PhysRevB.98.094401

Title: First-principles study of the magnetic interactions in honeycomb $N a_{2} Ir O_{3}$

Abstract

Honeycomb iridate Na2IrO3, a Jeff=1/2 magnet, is a potential platform for realizing quantum spin liquid. Many experiments have shown that its magnetic ground state is a zigzag antiferromagnetic order. However, there is still a lack of consensus on the theoretical model explaining such order, since its second-nearest-neighbor (NN) and long-range third-NN magnetic interactions are highly unclear. By properly considering the orbital moments achieved through constraining their directions in first-principles calculations, we obtain that the relative angle between orbital and spin moments is fairly small and in the order of several degrees, which thus validates the Jeff=1/2 state in Na2IrO3. Surprisingly, we find that the long-range third-NN Heisenberg interactions are sizable, whereas the second-NN magnetic interactions are negligible. Furthermore, we show that sizable long-range third-NN Heisenberg interactions closely correlate with the appreciable distribution of Wannier orbitals of Jeff=1/2 states over the three NN Ir atoms. Based on our study, we propose a minimal J1-K1-G1-J3 model in which the magnetic excitations have an intensity peak at 5.6 meV, consistent with the inelastic neutron-scattering experiment [Phys. Rev. Lett. 108, 127204 (2012)10.1103/PhysRevLett.108.127204]. The present work demonstrates again that constraining orbital moments in first-principles calculations is a powerful way to investigate the intriguing magnetism inmore »« less

Authors:: Hou, Y. S.; Yang, J. H.; Xiang, H. J.; Gong, X. G.

Publication Date:: 2018-09-01

Research Org.:: National Renewable Energy Lab. (NREL), Golden, CO (United States)

Sponsoring Org.:: USDOE Office of Energy Efficiency and Renewable Energy (EERE)

OSTI Identifier:: 1475530

Report Number(s):: NREL/JA-5K00-72528
Journal ID: ISSN 2469-9950; PRBMDO

DOE Contract Number:: AC36-08GO28308

Resource Type:: Journal Article

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 98; Journal Issue: 9; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; magnetism; iridates; density functional theory

Citation Formats


                    Hou, Y. S., Yang, J. H., Xiang, H. J., and Gong, X. G. First-principles study of the magnetic interactions in honeycomb Na2IrO3.  United States: N. p., 2018. 
        Web.  doi:10.1103/PhysRevB.98.094401.

Copy to clipboard


                    Hou, Y. S., Yang, J. H., Xiang, H. J., & Gong, X. G. First-principles study of the magnetic interactions in honeycomb Na2IrO3.  United States.  doi:10.1103/PhysRevB.98.094401.

Copy to clipboard


                    Hou, Y. S., Yang, J. H., Xiang, H. J., and Gong, X. G. Sat .  
        "First-principles study of the magnetic interactions in honeycomb Na2IrO3".  United States.  doi:10.1103/PhysRevB.98.094401.

Copy to clipboard


                    
@article{osti_1475530,

  title        = {First-principles study of the magnetic interactions in honeycomb Na2IrO3},

  author       = {Hou, Y. S. and Yang, J. H. and Xiang, H. J. and Gong, X. G.},

  abstractNote = {Honeycomb iridate Na2IrO3, a Jeff=1/2 magnet, is a potential platform for realizing quantum spin liquid. Many experiments have shown that its magnetic ground state is a zigzag antiferromagnetic order. However, there is still a lack of consensus on the theoretical model explaining such order, since its second-nearest-neighbor (NN) and long-range third-NN magnetic interactions are highly unclear. By properly considering the orbital moments achieved through constraining their directions in first-principles calculations, we obtain that the relative angle between orbital and spin moments is fairly small and in the order of several degrees, which thus validates the Jeff=1/2 state in Na2IrO3. Surprisingly, we find that the long-range third-NN Heisenberg interactions are sizable, whereas the second-NN magnetic interactions are negligible. Furthermore, we show that sizable long-range third-NN Heisenberg interactions closely correlate with the appreciable distribution of Wannier orbitals of Jeff=1/2 states over the three NN Ir atoms. Based on our study, we propose a minimal J1-K1-G1-J3 model in which the magnetic excitations have an intensity peak at 5.6 meV, consistent with the inelastic neutron-scattering experiment [Phys. Rev. Lett. 108, 127204 (2012)10.1103/PhysRevLett.108.127204]. The present work demonstrates again that constraining orbital moments in first-principles calculations is a powerful way to investigate the intriguing magnetism in Jeff=1/2 magnets, and it paves the way toward gaining a deep insight into the novel magnetism discovered in the honeycomb Jeff=1/2 magnets},

  doi          = {10.1103/PhysRevB.98.094401},

  journal      = {Physical Review B},

  issn         = {2469-9950},

  number       = 9,

  volume       = 98,

  place        = {United States},

  year         = {2018},

  month        = {9}

}

Copy to clipboard

Journal Article:

DOI: 10.1103/PhysRevB.98.094401

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

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

Winter, Stephen M.; Riedl, Kira; Maksimov, Pavel A.
Nature Communications, Vol. 8, Issue 1
DOI: 10.1038/s41467-017-01177-0

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

Chaloupka, Jiří; Jackeli, George; Khaliullin, Giniyat
Physical Review Letters, Vol. 110, Issue 9
DOI: 10.1103/PhysRevLett.110.097204

Generalized Gradient Approximation Made Simple
journal, October 1996

Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
DOI: 10.1103/PhysRevLett.77.3865

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

Kitaev, Alexei
Annals of Physics, Vol. 321, Issue 1
DOI: 10.1016/j.aop.2005.10.005

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

Foyevtsova, Kateryna; Jeschke, Harald O.; Mazin, I. I.
Physical Review B, Vol. 88, Issue 3
DOI: 10.1103/PhysRevB.88.035107

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

Rau, Jeffrey G.; Lee, Eric Kin-Ho; Kee, Hae-Young
Annual Review of Condensed Matter Physics, Vol. 7, Issue 1
DOI: 10.1146/annurev-conmatphys-031115-011319

Projector augmented-wave method
journal, December 1994

Blöchl, P. E.
Physical Review B, Vol. 50, Issue 24, p. 17953-17979
DOI: 10.1103/PhysRevB.50.17953

Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales
journal, June 2016

Winter, Stephen M.; Li, Ying; Jeschke, Harald O.
Physical Review B, Vol. 93, Issue 21
DOI: 10.1103/PhysRevB.93.214431

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

Kim, B. J.; Jin, Hosub; Moon, S. J.
Physical Review Letters, Vol. 101, Issue 7
DOI: 10.1103/PhysRevLett.101.076402

Mott physics and band topology in materials with strong spin–orbit interaction
journal, March 2010

Pesin, Dmytro; Balents, Leon
Nature Physics, Vol. 6, Issue 5
DOI: 10.1038/nphys1606

${Na}_{2} {IrO}_{3}$ as a Novel Relativistic Mott Insulator with a 340-meV Gap
journal, December 2012

Comin, R.; Levy, G.; Ludbrook, B.
Physical Review Letters, Vol. 109, Issue 26
DOI: 10.1103/PhysRevLett.109.266406

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

Takayama, T.; Kato, A.; Dinnebier, R.
Physical Review Letters, Vol. 114, Issue 7
DOI: 10.1103/PhysRevLett.114.077202

wannier90: A tool for obtaining maximally-localised Wannier functions
journal, May 2008

Mostofi, Arash A.; Yates, Jonathan R.; Lee, Young-Su
Computer Physics Communications, Vol. 178, Issue 9
DOI: 10.1016/j.cpc.2007.11.016

Spin Hamiltonian of hyper-kagome ${Na}_{4} {Ir}_{3} O_{8}$
journal, May 2010

Micklitz, T.; Norman, M. R.
Physical Review B, Vol. 81, Issue 17
DOI: 10.1103/PhysRevB.81.174417

Dynamical properties of the honeycomb-lattice iridates ${Na}_{2} {IrO}_{3}$
journal, November 2015

Suzuki, Takafumi; Yamada, Takuto; Yamaji, Youhei
Physical Review B, Vol. 92, Issue 18
DOI: 10.1103/PhysRevB.92.184411

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

Rau, Jeffrey G.; Lee, Eric Kin-Ho; Kee, Hae-Young
Physical Review Letters, Vol. 112, Issue 7
DOI: 10.1103/PhysRevLett.112.077204

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

Katukuri, Vamshi M.; Nishimoto, S.; Yushankhai, V.
New Journal of Physics, Vol. 16, Issue 1
DOI: 10.1088/1367-2630/16/1/013056

Relevance of the Heisenberg-Kitaev Model for the Honeycomb Lattice Iridates $A_{2} {IrO}_{3}$
journal, March 2012

Singh, Yogesh; Manni, S.; Reuther, J.
Physical Review Letters, Vol. 108, Issue 12
DOI: 10.1103/PhysRevLett.108.127203

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

Hu, Kaige; Wang, Fa; Feng, Ji
Physical Review Letters, Vol. 115, Issue 16
DOI: 10.1103/PhysRevLett.115.167204

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

Choi, S. K.; Coldea, R.; Kolmogorov, A. N.
Physical Review Letters, Vol. 108, Issue 12
DOI: 10.1103/PhysRevLett.108.127204

Maximally localized generalized Wannier functions for composite energy bands
journal, November 1997

Marzari, Nicola; Vanderbilt, David
Physical Review B, Vol. 56, Issue 20
DOI: 10.1103/PhysRevB.56.12847

Correlated electrons in high-temperature superconductors
journal, July 1994

Dagotto, Elbio
Reviews of Modern Physics, Vol. 66, Issue 3
DOI: 10.1103/RevModPhys.66.763

Kitaev magnetism in honeycomb ${RuCl}_{3}$ with intermediate spin-orbit coupling
journal, June 2015

Kim, Heung-Sik; V., Vijay Shankar; Catuneanu, Andrei
Physical Review B, Vol. 91, Issue 24
DOI: 10.1103/PhysRevB.91.241110

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

Mehlawat, Kavita; Sharma, G.; Singh, Yogesh
Physical Review B, Vol. 92, Issue 13
DOI: 10.1103/PhysRevB.92.134412

Importance of anisotropic exchange interactions in honeycomb iridates: Minimal model for zigzag antiferromagnetic order in ${Na}_{2} {IrO}_{3}$
journal, October 2014

Sizyuk, Yuriy; Price, Craig; Wölfle, Peter
Physical Review B, Vol. 90, Issue 15
DOI: 10.1103/PhysRevB.90.155126

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

Biffin, A.; Johnson, R. D.; Kimchi, I.
Physical Review Letters, Vol. 113, Issue 19
DOI: 10.1103/PhysRevLett.113.197201

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

Kimchi, Itamar; You, Yi-Zhuang
Physical Review B, Vol. 84, Issue 18
DOI: 10.1103/PhysRevB.84.180407

Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators
journal, August 1995

Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J.
Physical Review B, Vol. 52, Issue 8
DOI: 10.1103/PhysRevB.52.R5467

Dynamical Properties of Quantum Many-Body Systems at Zero Temperature
journal, December 1987

Gagliano, E. R.; Balseiro, C. A.
Physical Review Letters, Vol. 59, Issue 26
DOI: 10.1103/PhysRevLett.59.2999

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

Kimchi, Itamar; Vishwanath, Ashvin
Physical Review B, Vol. 89, Issue 1
DOI: 10.1103/PhysRevB.89.014414

From a Quasimolecular Band Insulator to a Relativistic Mott Insulator in $t_{2 g}^{5}$ Systems with a Honeycomb Lattice Structure
journal, October 2016

Kim, Beom Hyun; Shirakawa, Tomonori; Yunoki, Seiji
Physical Review Letters, Vol. 117, Issue 18
DOI: 10.1103/PhysRevLett.117.187201

Exchange Monte Carlo Method and Application to Spin Glass Simulations
journal, June 1996

Hukushima, Koji; Nemoto, Koji
Journal of the Physical Society of Japan, Vol. 65, Issue 6
DOI: 10.1143/JPSJ.65.1604

Unveiling magnetic interactions of ruthenium trichloride via constraining direction of orbital moments: Potential routes to realize a quantum spin liquid
journal, August 2017

Hou, Y. S.; Xiang, H. J.; Gong, X. G.
Physical Review B, Vol. 96, Issue 5
DOI: 10.1103/PhysRevB.96.054410

Strain-induced topological insulator phase and effective magnetic interactions in Li $_{2}$ IrO $_{3}$
journal, April 2013

Kim, Heung-Sik; Kim, Choong H.; Jeong, Hogyun
Physical Review B, Vol. 87, Issue 16
DOI: 10.1103/PhysRevB.87.165117

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

Ye, Feng; Chi, Songxue; Cao, Huibo
Physical Review B, Vol. 85, Issue 18
DOI: 10.1103/PhysRevB.85.180403

Ground-state properties of ${Na}_{2} {IrO}_{3}$ determined from an ab initio Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions
journal, August 2017

Okubo, Tsuyoshi; Shinjo, Kazuya; Yamaji, Youhei
Physical Review B, Vol. 96, Issue 5
DOI: 10.1103/PhysRevB.96.054434

Electron-Doped ${Sr}_{2} {IrO}_{4}$ : An Analogue of Hole-Doped Cuprate Superconductors Demonstrated by Scanning Tunneling Microscopy
journal, November 2015

Yan, Y. J.; Ren, M. Q.; Xu, H. C.
Physical Review X, Vol. 5, Issue 4
DOI: 10.1103/PhysRevX.5.041018

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

Chaloupka, Jiří; Jackeli, George; Khaliullin, Giniyat
Physical Review Letters, Vol. 105, Issue 2
DOI: 10.1103/PhysRevLett.105.027204

Predicting the spin-lattice order of frustrated systems from first principles
journal, December 2011

Xiang, H. J.; Kan, E. J.; Wei, Su-Huai
Physical Review B, Vol. 84, Issue 22
DOI: 10.1103/PhysRevB.84.224429

Monte Carlo Study of an Unconventional Superconducting Phase in Iridium Oxide $J_{eff} = 1 / 2$ Mott Insulators Induced by Carrier Doping
journal, January 2013

Watanabe, Hiroshi; Shirakawa, Tomonori; Yunoki, Seiji
Physical Review Letters, Vol. 110, Issue 2
DOI: 10.1103/PhysRevLett.110.027002

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

Jackeli, G.; Khaliullin, G.
Physical Review Letters, Vol. 102, Issue 1
DOI: 10.1103/PhysRevLett.102.017205

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

Hwan Chun, Sae; Kim, Jong-Woo; Kim, Jungho
Nature Physics, Vol. 11, Issue 6
DOI: 10.1038/nphys3322

Unveiling the origin of the basal-plane antiferromagnetism in the spin–orbit Mott insulator Ba ₂ IrO ₄ : a density functional and model Hamiltonian study
journal, April 2016

Hou, Y. S.; Xiang, H. J.; Gong, X. G.
New Journal of Physics, Vol. 18, Issue 4
DOI: 10.1088/1367-2630/18/4/043007

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

Liu, X.; Berlijn, T.; Yin, W. -G.
Physical Review B, Vol. 83, Issue 22
DOI: 10.1103/PhysRevB.83.220403

Maximally localized Wannier functions for entangled energy bands
journal, December 2001

Souza, Ivo; Marzari, Nicola; Vanderbilt, David
Physical Review B, Vol. 65, Issue 3
DOI: 10.1103/PhysRevB.65.035109

Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates
journal, May 2011

Wan, Xiangang; Turner, Ari M.; Vishwanath, Ashvin
Physical Review B, Vol. 83, Issue 20
DOI: 10.1103/PhysRevB.83.205101

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

Yamaji, Youhei; Nomura, Yusuke; Kurita, Moyuru
Physical Review Letters, Vol. 113, Issue 10
DOI: 10.1103/PhysRevLett.113.107201

Predicting a Ferrimagnetic Phase of ${Zn}_{2} {FeOsO}_{6}$ with Strong Magnetoelectric Coupling
journal, April 2015

Wang, P. S.; Ren, W.; Bellaiche, L.
Physical Review Letters, Vol. 114, Issue 14
DOI: 10.1103/PhysRevLett.114.147204

Similar records in OSTI.GOV collections:

Strong anisotropy within a Heisenberg model in the $J_{eff} = \frac{1}{2}$ insulating state of ${Sr}_{2} {Ir}_{0.8} {Ru}_{0.2} O_{4}$

Journal Article Calder, S. ; Kim, J. W. ; Taylor, A. E. ; ... - Physical Review B

The dispersive magnetic excitations in Sr2IrO4 have previously been well described within an isospin-1/2 Heisenberg model on a square lattice that revealed parallels with La2CuO4. Here we investigate the inelastic spectra of Sr2Ir0.8Ru0.2O4 with resonant inelastic x-ray scattering (RIXS) at the Ir L3 edge. The results are well described using linear spin-wave theory within a similar Heisenberg model applicable to Sr2IrO4; however, the disorder induced by the substitution of 20%Ir4+ ions for Ru4+ removes longer range exchange interactions. A large spin gap (40 meV) is measured indicating strong anisotropy from spin-orbit coupling that is manifest due to the altered magneticmore »« less
Cited by 1
DOI: 10.1103/PhysRevB.94.220407

Full Text Available
Spin order and dynamics in the diamond-lattice Heisenberg antiferromagnets ${CuRh}_{2} O_{4}$ and ${CoRh}_{2} O_{4}$

Journal Article Ge, L. ; Flynn, J. ; Paddison, Joseph A. M. ; ... - Physical Review B

Here, antiferromagnetic insulators on a diamond lattice are candidate materials to host exotic magnetic phenomena ranging from spin-orbital entanglement to degenerate spiral ground states and topological paramagnetism. Compared to other three-dimensional networks of magnetic ions, such as the geometrically frustrated pyrochlore lattice, the investigation of diamond-lattice magnetism in real materials is less mature. In this work, we characterize the magnetic properties of model A-site spinels CoRh ₂O ₄ (cobalt rhodite) and CuRh ₂O ₄ (copper rhodite) by means of thermomagnetic and neutron-scattering measurements, and we perform group theory analysis, Rietveld refinement, mean-field theory, and spin-wave theory calculations to analyze themore »« less
Cited by 6
DOI: 10.1103/PhysRevB.96.064413

Full Text Available
Frustrated magnetic interactions in an $S = 3 / 2$ bilayer honeycomb lattice compound ${Bi}_{3} {Mn}_{4} O_{12}$ ( ${NO}_{3}$ )

Journal Article Matsuda, Masaaki ; Dissanayake, Sachith E. ; Abernathy, Douglas L. ; ... - Physical Review B

An inelmore »« less
DOI: 10.1103/PhysRevB.100.134430
Strong anisotropy within a Heisenberg model in the $J_{eff} = \frac{1}{2}$ insulating state of ${Sr}_{2} {Ir}_{0.8} {Ru}_{0.2} O_{4}$

Journal Article Calder, Stuart A. ; Kim, J. W. ; Taylor, Alice E. ; ... - Physical Review B

The dispersive magnetic excitations in Sr ₂IrO ₄ have previously been well described within an isospin-1/2 Heisenberg model on a square lattice that revealed parallels with La ₂CuO ₄. In this paper, we investigate the inelastic spectra of Sr ₂Ir _0.8Ru _0.2O ₄ with resonant inelastic x-ray scattering (RIXS) at the Ir L ₃ edge. The results are well described using linear spin-wave theory within a similar Heisenberg model applicable to Sr ₂IrO ₄; however, the disorder induced by the substitution of 20% Ir ⁴⁺ ions for Ru ⁴⁺ removes longer range exchange interactions. A large spin gap (40 meV)more »« less
Cited by 1
DOI: 10.1103/PhysRevB.94.220407

Full Text Available
Spin gaps in the ordered states of ${La}_{2} Li X O_{6} (X = Ru, Os)$ and their relation to the distortion of the cubic double perovskite structure in $4 d^{3}$ and $5 d^{3}$ magnets

Journal Article Maharaj, D. D. ; Sala, G. ; Marjerrison, C. A. ; ... - Physical Review B

Time-of-flight inelastic neutron scattering measurements have been carried out on polycrystalline samples of the 4d ³ and 5d ³ double pervoskite antiferromagnets La ₂LiRuO ₆ and La ₂LiOsO ₆. These reveal the development of an inelastic spin gap in La ₂LiRuO ₆ and La ₂LiOsO ₆ of ~1.8(8) and 6(1) meV, below their respective ordering temperatures TN, ~23.8 and 30 K. The bandwidths of the spin excitations are shown to be ~5.7(9)and12(1)meV, respectively, at low temperatures. Spin gaps are surprising in such magnets as the t _2g levels of Ru ⁵⁺ or Os ⁵⁺ are expected to be half-filled, resultingmore »« less
Cited by 2
DOI: 10.1103/PhysRevB.98.104434

Full Text Available

Similar Records

Title: First-principles study of the magnetic interactions in honeycomb N a 2 Ir O 3

Abstract

Citation Formats

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

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

Generalized Gradient Approximation Made Simple journal, October 1996

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

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

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

Projector augmented-wave method journal, December 1994

Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales journal, June 2016

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

Mott physics and band topology in materials with strong spin–orbit interaction journal, March 2010

Na 2 IrO 3 as a Novel Relativistic Mott Insulator with a 340-meV Gap journal, December 2012

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

wannier90: A tool for obtaining maximally-localised Wannier functions journal, May 2008

Spin Hamiltonian of hyper-kagome Na 4 Ir 3 O 8 journal, May 2010

Dynamical properties of the honeycomb-lattice iridates Na 2 IrO 3 journal, November 2015

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

Relevance of the Heisenberg-Kitaev Model for the Honeycomb Lattice Iridates A 2 IrO 3 journal, March 2012

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

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

Maximally localized generalized Wannier functions for composite energy bands journal, November 1997

Correlated electrons in high-temperature superconductors journal, July 1994

Kitaev magnetism in honeycomb RuCl 3 with intermediate spin-orbit coupling journal, June 2015

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

Importance of anisotropic exchange interactions in honeycomb iridates: Minimal model for zigzag antiferromagnetic order in Na 2 IrO 3 journal, October 2014

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

Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators journal, August 1995

Dynamical Properties of Quantum Many-Body Systems at Zero Temperature journal, December 1987

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

From a Quasimolecular Band Insulator to a Relativistic Mott Insulator in t 2 g 5 Systems with a Honeycomb Lattice Structure journal, October 2016

Exchange Monte Carlo Method and Application to Spin Glass Simulations journal, June 1996

Unveiling magnetic interactions of ruthenium trichloride via constraining direction of orbital moments: Potential routes to realize a quantum spin liquid journal, August 2017

Strain-induced topological insulator phase and effective magnetic interactions in Li 2 IrO 3 journal, April 2013

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

Ground-state properties of Na 2 IrO 3 determined from an ab initio Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions journal, August 2017

Electron-Doped Sr 2 IrO 4 : An Analogue of Hole-Doped Cuprate Superconductors Demonstrated by Scanning Tunneling Microscopy journal, November 2015

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

Predicting the spin-lattice order of frustrated systems from first principles journal, December 2011

Monte Carlo Study of an Unconventional Superconducting Phase in Iridium Oxide J eff = 1 / 2 Mott Insulators Induced by Carrier Doping journal, January 2013

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

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

Unveiling the origin of the basal-plane antiferromagnetism in the spin–orbit Mott insulator Ba 2 IrO 4 : a density functional and model Hamiltonian study journal, April 2016

Long-range magnetic ordering in Na 2 IrO 3 journal, June 2011

Maximally localized Wannier functions for entangled energy bands journal, December 2001

Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates journal, May 2011

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

Predicting a Ferrimagnetic Phase of Zn 2 FeOsO 6 with Strong Magnetoelectric Coupling journal, April 2015

Title: First-principles study of the magnetic interactions in honeycomb $N a_{2} Ir O_{3}$

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

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

Generalized Gradient Approximation Made Simple
journal, October 1996

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

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

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

Projector augmented-wave method
journal, December 1994

Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales
journal, June 2016

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

Mott physics and band topology in materials with strong spin–orbit interaction
journal, March 2010

${Na}_{2} {IrO}_{3}$ as a Novel Relativistic Mott Insulator with a 340-meV Gap
journal, December 2012

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

wannier90: A tool for obtaining maximally-localised Wannier functions
journal, May 2008

Spin Hamiltonian of hyper-kagome ${Na}_{4} {Ir}_{3} O_{8}$
journal, May 2010

Dynamical properties of the honeycomb-lattice iridates ${Na}_{2} {IrO}_{3}$
journal, November 2015

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

Relevance of the Heisenberg-Kitaev Model for the Honeycomb Lattice Iridates $A_{2} {IrO}_{3}$
journal, March 2012

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

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

Maximally localized generalized Wannier functions for composite energy bands
journal, November 1997

Correlated electrons in high-temperature superconductors
journal, July 1994

Kitaev magnetism in honeycomb ${RuCl}_{3}$ with intermediate spin-orbit coupling
journal, June 2015

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

Importance of anisotropic exchange interactions in honeycomb iridates: Minimal model for zigzag antiferromagnetic order in ${Na}_{2} {IrO}_{3}$
journal, October 2014

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

Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators
journal, August 1995

Dynamical Properties of Quantum Many-Body Systems at Zero Temperature
journal, December 1987

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

From a Quasimolecular Band Insulator to a Relativistic Mott Insulator in $t_{2 g}^{5}$ Systems with a Honeycomb Lattice Structure
journal, October 2016

Exchange Monte Carlo Method and Application to Spin Glass Simulations
journal, June 1996

Unveiling magnetic interactions of ruthenium trichloride via constraining direction of orbital moments: Potential routes to realize a quantum spin liquid
journal, August 2017

Strain-induced topological insulator phase and effective magnetic interactions in Li $_{2}$ IrO $_{3}$
journal, April 2013

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

Ground-state properties of ${Na}_{2} {IrO}_{3}$ determined from an ab initio Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions
journal, August 2017

Electron-Doped ${Sr}_{2} {IrO}_{4}$ : An Analogue of Hole-Doped Cuprate Superconductors Demonstrated by Scanning Tunneling Microscopy
journal, November 2015

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

Predicting the spin-lattice order of frustrated systems from first principles
journal, December 2011

Monte Carlo Study of an Unconventional Superconducting Phase in Iridium Oxide $J_{eff} = 1 / 2$ Mott Insulators Induced by Carrier Doping
journal, January 2013

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

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

Unveiling the origin of the basal-plane antiferromagnetism in the spin–orbit Mott insulator Ba ₂ IrO ₄ : a density functional and model Hamiltonian study
journal, April 2016

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

Maximally localized Wannier functions for entangled energy bands
journal, December 2001

Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates
journal, May 2011

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

Predicting a Ferrimagnetic Phase of ${Zn}_{2} {FeOsO}_{6}$ with Strong Magnetoelectric Coupling
journal, April 2015