Dirac Magnons in a Honeycomb Lattice Quantum XY Magnet CoTiO 3

Yuan, Bo; Khait, Ilia; Shu, Guo-Jiun; Chou, F. C.; Stone, M. B.; Clancy, J. P.; Paramekanti, Arun; Kim, Young-June

doi:10.1103/PhysRevX.10.011062

Title: Dirac Magnons in a Honeycomb Lattice Quantum $XY$ Magnet ${CoTiO}_{3}$

Abstract

The discovery of massless Dirac electrons in graphene and topological Dirac-Weyl materials has prompted a broad search for bosonic analogues of such Dirac particles. Recent experiments have found evidence for Dirac magnons above an Ising-like ferromagnetic ground state in a two-dimensional (2D) kagome lattice magnet and in the van der Waals layered honeycomb crystal CrI₃, and in a 3D Heisenberg magnet Cu₃TeO₆. Here, we report our inelastic neutron scattering investigation on a large single crystal of a stacked honeycomb lattice magnet CoTiO₃, which is part of a broad family of ilmenite materials. The magnetically ordered ground state of CoTiO₃ features ferromagnetic layers of Co²⁺, stacked antiferromagnetically along the c axis. The magnon dispersion relation is described very well with a simple magnetic Hamiltonian with strong easy-plane exchange anisotropy. Importantly, a magnon Dirac cone is found along the edge of the 3D Brillouin zone. Our results establish CoTiO₃ as a model pseudospin-1/2 material to study interacting Dirac bosons in a 3D quantum XY magnet.

Authors:

; Khait, Ilia; Shu, Guo-Jiun;

;

; Paramekanti, Arun;

Publication Date:: 2020-03-12

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE Office of Science (SC); Ministry of Education in Taiwan; Natural Science and Engineering Research Council (NSERC); Ministry of Science and Technology (MOST)

OSTI Identifier:: 1604508

Alternate Identifier(s):: OSTI ID: 1666019

Grant/Contract Number:: AC05-00OR22725; 8-2622-8-002-016; 06-2119-M-002-035-MY3; 108L900903

Resource Type:: Published Article

Journal Name:: Physical Review. X

Additional Journal Information:: Journal Name: Physical Review. X Journal Volume: 10 Journal Issue: 1; Journal ID: ISSN 2160-3308

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Magnons; symmetry protected topological states; magnetic insulators; inelastic neutron scattering

Citation Formats


                    Yuan, Bo, Khait, Ilia, Shu, Guo-Jiun, Chou, F. C., Stone, M. B., Clancy, J. P., Paramekanti, Arun, and Kim, Young-June. Dirac Magnons in a Honeycomb Lattice Quantum XY Magnet CoTiO 3.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevX.10.011062.

Copy to clipboard


                    Yuan, Bo, Khait, Ilia, Shu, Guo-Jiun, Chou, F. C., Stone, M. B., Clancy, J. P., Paramekanti, Arun, & Kim, Young-June. Dirac Magnons in a Honeycomb Lattice Quantum XY Magnet CoTiO 3.  United States.  https://doi.org/10.1103/PhysRevX.10.011062

Copy to clipboard


                    Yuan, Bo, Khait, Ilia, Shu, Guo-Jiun, Chou, F. C., Stone, M. B., Clancy, J. P., Paramekanti, Arun, and Kim, Young-June. Thu .  
"Dirac Magnons in a Honeycomb Lattice Quantum XY Magnet CoTiO 3".  United States.  https://doi.org/10.1103/PhysRevX.10.011062.

Copy to clipboard


                    
@article{osti_1604508,

  title        = {Dirac Magnons in a Honeycomb Lattice Quantum XY Magnet CoTiO 3},

  author       = {Yuan, Bo and Khait, Ilia and Shu, Guo-Jiun and Chou, F. C. and Stone, M. B. and Clancy, J. P. and Paramekanti, Arun and Kim, Young-June},

  abstractNote = {The discovery of massless Dirac electrons in graphene and topological Dirac-Weyl materials has prompted a broad search for bosonic analogues of such Dirac particles. Recent experiments have found evidence for Dirac magnons above an Ising-like ferromagnetic ground state in a two-dimensional (2D) kagome lattice magnet and in the van der Waals layered honeycomb crystal CrI3, and in a 3D Heisenberg magnet Cu3TeO6. Here, we report our inelastic neutron scattering investigation on a large single crystal of a stacked honeycomb lattice magnet CoTiO3, which is part of a broad family of ilmenite materials. The magnetically ordered ground state of CoTiO3 features ferromagnetic layers of Co2+, stacked antiferromagnetically along the c axis. The magnon dispersion relation is described very well with a simple magnetic Hamiltonian with strong easy-plane exchange anisotropy. Importantly, a magnon Dirac cone is found along the edge of the 3D Brillouin zone. Our results establish CoTiO3 as a model pseudospin-1/2 material to study interacting Dirac bosons in a 3D quantum XY magnet.},

  doi          = {10.1103/PhysRevX.10.011062},

  journal      = {Physical Review. X},

  number       = 1,

  volume       = 10,

  place        = {United States},

  year         = {2020},

  month        = {3}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record
https://doi.org/10.1103/PhysRevX.10.011062

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 53 works

Citation information provided by
Web of Science

Figures / Tables:

FIG. 1: (a) Structure of CoTiO₃. A nonprimitive hexagonal unit cell, which is used to describe our data, is indicated by solid black lines. (b) Magnetic structure of the Co²⁺ sublattice. The Co²⁺ magnetic moments (shown by green arrows) order ferromagnetically within each honeycomb plane and antiferromagnetically along the cmore »

All figures and tables (7 total)

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Topological magnon insulator in insulating ferromagnet
journal, April 2013

Zhang, Lifa; Ren, Jie; Wang, Jian-Sheng
Physical Review B, Vol. 87, Issue 14
DOI: 10.1103/PhysRevB.87.144101

Experimental observation of the quantum Hall effect and Berry's phase in graphene
journal, November 2005

Zhang, Yuanbo; Tan, Yan-Wen; Stormer, Horst L.
Nature, Vol. 438, Issue 7065, p. 201-204
DOI: 10.1038/nature04235

Substrate-induced bandgap opening in epitaxial graphene
journal, September 2007

Zhou, S. Y.; Gweon, G. -H.; Fedorov, A. V.
Nature Materials, Vol. 6, Issue 10
DOI: 10.1038/nmat2003

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

Liu, Huimei; Khaliullin, Giniyat
Physical Review B, Vol. 97, Issue 1
DOI: 10.1103/PhysRevB.97.014407

Dirac materials
journal, January 2014

Wehling, T. O.; Black-Schaffer, A. M.; Balatsky, A. V.
Advances in Physics, Vol. 63, Issue 1
DOI: 10.1080/00018732.2014.927109

Electronic properties of graphene in a strong magnetic field
journal, November 2011

Goerbig, M. O.
Reviews of Modern Physics, Vol. 83, Issue 4
DOI: 10.1103/RevModPhys.83.1193

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

Sano, Ryoya; Kato, Yasuyuki; Motome, Yukitoshi
Physical Review B, Vol. 97, Issue 1
DOI: 10.1103/PhysRevB.97.014408

Topological photonics
journal, March 2019

Ozawa, Tomoki; Price, Hannah M.; Amo, Alberto
Reviews of Modern Physics, Vol. 91, Issue 1
DOI: 10.1103/RevModPhys.91.015006

Electric and magnetic properties of titanium-cobalt-oxide single crystals produced by floating zone melting with light heating
journal, August 2017

Balbashov, A. M.; Mukhin, A. A.; Ivanov, V. Yu.
Low Temperature Physics, Vol. 43, Issue 8
DOI: 10.1063/1.5001297

Unconventional superconductivity in magic-angle graphene superlattices
journal, March 2018

Cao, Yuan; Fatemi, Valla; Fang, Shiang
Nature, Vol. 556, Issue 7699
DOI: 10.1038/nature26160

Discovery of coexisting Dirac and triply degenerate magnons in a three-dimensional antiferromagnet
journal, July 2018

Bao, Song; Wang, Jinghui; Wang, Wei
Nature Communications, Vol. 9, Issue 1
DOI: 10.1038/s41467-018-05054-2

Neutron scattering study of magnetic excitations in oblique easy-axis antiferromagnet FeTiO ₃
journal, December 1986

Kato, H.; Yamaguchi, Y.; Yamada, M.
Journal of Physics C: Solid State Physics, Vol. 19, Issue 35
DOI: 10.1088/0022-3719/19/35/013

Weyl magnons in breathing pyrochlore antiferromagnets
journal, September 2016

Li, Fei-Ye; Li, Yao-Dong; Kim, Yong Baek
Nature Communications, Vol. 7, Issue 1
DOI: 10.1038/ncomms12691

Coherent and incoherent coupling dynamics in a two-dimensional atomic crystal embedded in a plasmon-induced magnetic resonator
journal, January 2020

Xie, Peng; Liang, Zhengchen; Li, Zhoujun
Physical Review B, Vol. 101, Issue 4
DOI: 10.1103/PhysRevB.101.045403

Two Topologically Distinct Dirac-Line Semimetal Phases and Topological Phase Transitions in Rhombohedrally Stacked Honeycomb Lattices
journal, January 2018

Hyart, T.; Ojajärvi, R.; Heikkilä, T. T.
Journal of Low Temperature Physics, Vol. 191, Issue 1-2
DOI: 10.1007/s10909-017-1846-3

Defect Scattering in Graphene
journal, June 2009

Chen, Jian-Hao; Cullen, W. G.; Jang, C.
Physical Review Letters, Vol. 102, Issue 23
DOI: 10.1103/PhysRevLett.102.236805

Excitations in KCoF ₃ . II. Theoretical
journal, October 1971

Buyers, W. J. L.; Holden, T. M.; Svensson, E. C.
Journal of Physics C: Solid State Physics, Vol. 4, Issue 14
DOI: 10.1088/0022-3719/4/14/028

Magnetic anisotropies in MTiO3 (M = Co, Ni)
journal, January 1980

Watanabe, H.; Yamauchi, H.; Takei, H.
Journal of Magnetism and Magnetic Materials, Vol. 15-18
DOI: 10.1016/0304-8853(80)90658-7

Double-Weyl Phonons in Transition-Metal Monosilicides
journal, January 2018

Zhang, Tiantian; Song, Zhida; Alexandradinata, A.
Physical Review Letters, Vol. 120, Issue 1
DOI: 10.1103/PhysRevLett.120.016401

Observation of Double Weyl Phonons in Parity-Breaking FeSi
journal, July 2018

Miao, H.; Zhang, T. T.; Wang, L.
Physical Review Letters, Vol. 121, Issue 3
DOI: 10.1103/PhysRevLett.121.035302

Edge states in topological magnon insulators
journal, July 2014

Mook, Alexander; Henk, Jürgen; Mertig, Ingrid
Physical Review B, Vol. 90, Issue 2
DOI: 10.1103/PhysRevB.90.024412

Topological Magnon Bands in a Kagome Lattice Ferromagnet
journal, September 2015

Chisnell, R.; Helton, J. S.; Freedman, D. E.
Physical Review Letters, Vol. 115, Issue 14
DOI: 10.1103/PhysRevLett.115.147201

A first theoretical realization of honeycomb topological magnon insulator
journal, July 2016

Owerre, S. A.
Journal of Physics: Condensed Matter, Vol. 28, Issue 38
DOI: 10.1088/0953-8984/28/38/386001

Strain Engineering of Graphene’s Electronic Structure
journal, July 2009

Pereira, Vitor M.; Castro Neto, A. H.
Physical Review Letters, Vol. 103, Issue 4
DOI: 10.1103/PhysRevLett.103.046801

Classification of topological quantum matter with symmetries
journal, August 2016

Chiu, Ching-Kai; Teo, Jeffrey C. Y.; Schnyder, Andreas P.
Reviews of Modern Physics, Vol. 88, Issue 3
DOI: 10.1103/RevModPhys.88.035005

Recipe for Dirac Phonon States with a Quantized Valley Berry Phase in Two-Dimensional Hexagonal Lattices
journal, November 2018

Jin, Yuanjun; Wang, Rui; Xu, Hu
Nano Letters, Vol. 18, Issue 12
DOI: 10.1021/acs.nanolett.8b03492

Topological photonics
journal, October 2014

Lu, Ling; Joannopoulos, John D.; Soljačić, Marin
Nature Photonics, Vol. 8, Issue 11
DOI: 10.1038/nphoton.2014.248

Evolution of magnetic Dirac bosons in a honeycomb lattice
journal, January 2018

Boyko, D.; Balatsky, A. V.; Haraldsen, J. T.
Physical Review B, Vol. 97, Issue 1
DOI: 10.1103/PhysRevB.97.014433

Single-ion properties of the $S_{eff}$ = $\frac{1}{2}$ XY antiferromagnetic pyrochlores $Na A^{'} {Co}_{2} F_{7}$ ( $A^{'} = {Ca}^{2 +}, {Sr}^{2 +}$ )
journal, April 2017

Ross, K. A.; Brown, J. M.; Cava, R. J.
Physical Review B, Vol. 95, Issue 14
DOI: 10.1103/PhysRevB.95.144414

Crystal structure and magnetic properties of CoTiO3
journal, March 1964

Newnham, R. E.; Fang, J. H.; Santoro, R. P.
Acta Crystallographica, Vol. 17, Issue 3
DOI: 10.1107/S0365110X64000615

The electronic properties of graphene
journal, January 2009

Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.
Reviews of Modern Physics, Vol. 81, Issue 1, p. 109-162
DOI: 10.1103/RevModPhys.81.109

Metal to Insulator Transition in Epitaxial Graphene Induced by Molecular Doping
journal, August 2008

Zhou, S. Y.; Siegel, D. A.; Fedorov, A. V.
Physical Review Letters, Vol. 101, Issue 8
DOI: 10.1103/PhysRevLett.101.086402

Linear spin wave theory for single-Q incommensurate magnetic structures
journal, March 2015

Toth, S.; Lake, B.
Journal of Physics: Condensed Matter, Vol. 27, Issue 16
DOI: 10.1088/0953-8984/27/16/166002

Chiral tunnelling and the Klein paradox in graphene
journal, August 2006

Katsnelson, M. I.; Novoselov, K. S.; Geim, A. K.
Nature Physics, Vol. 2, Issue 9
DOI: 10.1038/nphys384

Modeling disorder in graphene
journal, March 2008

Pereira, Vitor M.; Lopes dos Santos, J. M. B.; Castro Neto, A. H.
Physical Review B, Vol. 77, Issue 11
DOI: 10.1103/PhysRevB.77.115109

Topological spin excitations in a three-dimensional antiferromagnet
journal, July 2018

Yao, Weiliang; Li, Chenyuan; Wang, Lichen
Nature Physics, Vol. 14, Issue 10
DOI: 10.1038/s41567-018-0213-x

Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering
journal, September 2009

Guinea, F.; Katsnelson, M. I.; Geim, A. K.
Nature Physics, Vol. 6, Issue 1
DOI: 10.1038/nphys1420

Magnon Dirac materials
journal, August 2016

Fransson, J.; Black-Schaffer, A. M.; Balatsky, A. V.
Physical Review B, Vol. 94, Issue 7
DOI: 10.1103/PhysRevB.94.075401

Epitaxial growth of NiTiO3 with a distorted ilmenite structure
journal, June 2012

Varga, Tamas; Droubay, Timothy C.; Bowden, Mark E.
Thin Solid Films, Vol. 520, Issue 17
DOI: 10.1016/j.tsf.2012.04.060

Two-dimensional gas of massless Dirac fermions in graphene
journal, November 2005

Novoselov, K. S.; Geim, A. K.; Morozov, S. V.
Nature, Vol. 438, Issue 7065, p. 197-200
DOI: 10.1038/nature04233

Figures / Tables found in this record:

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

Similar Records in DOE PAGES and OSTI.GOV collections:

Topological Spin Excitations in Honeycomb Ferromagnet ${CrI}_{3}$

Journal Article Chen, Lebing ; Chung, Jae-Ho ; Gao, Bin ; ... - Physical Review. X

In two-dimensional honeycomb ferromagnets, bosonic magnon quasiparticles (spin waves) may either behave as massless Dirac fermions or form topologically protected edge states. The key ingredient defining their nature is the next-nearest-neighbor Dzyaloshinskii-Moriya interaction that breaks the inversion symmetry of the lattice and discriminates chirality of the associated spin-wave excitations. Using inelastic neutron scattering, we find that spin waves of the insulating honeycomb ferromagnet CrI₃ (T_C=61 K) have two distinctive bands of ferromagnetic excitations separated by a ∼4 meV gap at the Dirac points. These results can only be understood by considering a Heisenberg Hamiltonian with Dzyaloshinskii-Moriya interaction, thus providing experimentalmore »« less
Cited by 188
https://doi.org/10.1103/PhysRevX.8.041028
Spin-orbit exciton in a honeycomb lattice magnet CoTiO₃: Revealing a link between magnetism in d- and f-electron systems

Journal Article Yuan, Bo ; Stone, M. B. ; Shu, Guo-Jiun ; ... - Physical Review B

We carried out inelastic neutron scattering to study the spin-orbital (SO) exciton in a single crystal sample of CoTiO₃ as a function of temperature. CoTiO₃ is a honeycomb magnet with dominant XY-type magnetic interaction and an A-type antiferromagnetic order below T_N ≈ 38 K. We found that the SO exciton becomes softer, but acquires a larger bandwidth in the paramagnetic phase, compared to that in the magnetically ordered phase. Moreover, an additional mode is only observed in the intermediate temperature range, as the sample is warmed up above the lowest accessible temperature below T_N. Such an unusual temperature dependence observedmore »« less
https://doi.org/10.1103/physrevb.102.134404

Full Text Available
Magnetic Field Effect on Topological Spin Excitations in ${CrI}_{3}$

Journal Article Chen, Lebing ; Chung, Jae-Ho ; Stone, Matthew B. ; ... - Physical Review. X

The search for topological spin excitations in recently discovered two-dimensional (2D) van der Waals (vdW) magnetic materials is important because of their potential applications in dissipationless spintronics. In the 2D vdW ferromagnetic (FM) honeycomb lattice CrI₃ (T_C=61 K), acoustic and optical spin waves are found to be separated by a gap at the Dirac points. The presence of such a gap is a signature of topological spin excitations if it arises from the next-nearest-neighbor (NNN) Dzyaloshinskii-Moriya (DM) or bond-angle-dependent Kitaev interactions within the Cr honeycomb lattice. Alternatively, the gap is suggested to arise from an electron correlation effect not associatedmore »« less
https://doi.org/10.1103/PhysRevX.11.031047
Dynamic Spin Correlations in the Honeycomb Lattice ${Na}_{2} {IrO}_{3}$ Measured by Resonant Inelastic x-Ray Scattering

Journal Article Kim, Jungho ; Chaloupka, Jiří ; Singh, Yogesh ; ... - Physical Review. X

Kitaev quantum spin liquid is a prime example of novel quantum magnetism of spin-orbit entangled pseudospin-1/2 moments in a honeycomb lattice. Most candidate materials such as Na₂IrO₃ have many competing exchange interactions beyond the minimal Kitaev-Heisenberg model whose small variations in the strength of the interactions produce huge differences in low energy dynamics. An incomplete knowledge of dynamic spin correlations hampers identification of a minimal model and quantification of the proximity to the Kitaev quantum spin-liquid phase. Here, we report fully momentum- and energy-resolved magnetic excitation spectra in a honeycomb lattice Na₂IrO₃ measured using resonant inelastic x-ray scattering. The state-of-the-artmore »« less
Cited by 21
https://doi.org/10.1103/PhysRevX.10.021034
Hyperhoneycomb Iridate $β - {Li}_{2} {IrO}_{3}$ as a Platform for Kitaev Magnetism

Journal Article Takayama, T. ; Kato, A. ; Dinnebier, R. ; ... - Physical Review Letters

A complex iridium oxide β-Li₂IrO₃ crystallizes in a hyperhoneycomb structure, a three-dimensional analogue of honeycomb lattice, and is found to be a spin-orbital Mott insulator with J_eff = 1/2 moment. Ir ions are connected to the three neighboring Ir ions via Ir-O₂-Ir bonding planes, which very likely gives rise to bond-dependent ferromagnetic interactions between the J_eff = 1/2 moments, an essential ingredient of Kitaev model with a spin liquid ground state. Dominant ferromagnetic interaction between J(eff) = 1/2 moments is indeed confirmed by the temperature dependence of magnetic susceptibility chi(T) which shows a positive Curie-Weiss temperaturemore »« less
https://doi.org/10.1103/PhysRevLett.114.077202

Similar Records

Title: Dirac Magnons in a Honeycomb Lattice Quantum XY Magnet CoTiO 3

Abstract

Citation Formats

Figures / Tables:

Topological magnon insulator in insulating ferromagnet journal, April 2013

Experimental observation of the quantum Hall effect and Berry's phase in graphene journal, November 2005

Substrate-induced bandgap opening in epitaxial graphene journal, September 2007

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

Dirac materials journal, January 2014

Electronic properties of graphene in a strong magnetic field journal, November 2011

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

Topological photonics journal, March 2019

Electric and magnetic properties of titanium-cobalt-oxide single crystals produced by floating zone melting with light heating journal, August 2017

Unconventional superconductivity in magic-angle graphene superlattices journal, March 2018

Discovery of coexisting Dirac and triply degenerate magnons in a three-dimensional antiferromagnet journal, July 2018

Neutron scattering study of magnetic excitations in oblique easy-axis antiferromagnet FeTiO 3 journal, December 1986

Weyl magnons in breathing pyrochlore antiferromagnets journal, September 2016

Coherent and incoherent coupling dynamics in a two-dimensional atomic crystal embedded in a plasmon-induced magnetic resonator journal, January 2020

Two Topologically Distinct Dirac-Line Semimetal Phases and Topological Phase Transitions in Rhombohedrally Stacked Honeycomb Lattices journal, January 2018

Defect Scattering in Graphene journal, June 2009

Excitations in KCoF 3 . II. Theoretical journal, October 1971

Magnetic anisotropies in MTiO3 (M = Co, Ni) journal, January 1980

Double-Weyl Phonons in Transition-Metal Monosilicides journal, January 2018

Observation of Double Weyl Phonons in Parity-Breaking FeSi journal, July 2018

Edge states in topological magnon insulators journal, July 2014

Topological Magnon Bands in a Kagome Lattice Ferromagnet journal, September 2015

A first theoretical realization of honeycomb topological magnon insulator journal, July 2016

Strain Engineering of Graphene’s Electronic Structure journal, July 2009

Classification of topological quantum matter with symmetries journal, August 2016

Recipe for Dirac Phonon States with a Quantized Valley Berry Phase in Two-Dimensional Hexagonal Lattices journal, November 2018

Topological photonics journal, October 2014

Evolution of magnetic Dirac bosons in a honeycomb lattice journal, January 2018

Single-ion properties of the S eff = 1 2 XY antiferromagnetic pyrochlores Na A ′ Co 2 F 7 ( A ′ = Ca 2 + , Sr 2 + ) journal, April 2017

Crystal structure and magnetic properties of CoTiO3 journal, March 1964

The electronic properties of graphene journal, January 2009

Metal to Insulator Transition in Epitaxial Graphene Induced by Molecular Doping journal, August 2008

Linear spin wave theory for single-Q incommensurate magnetic structures journal, March 2015

Chiral tunnelling and the Klein paradox in graphene journal, August 2006

Modeling disorder in graphene journal, March 2008

Topological spin excitations in a three-dimensional antiferromagnet journal, July 2018

Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering journal, September 2009

Magnon Dirac materials journal, August 2016

Epitaxial growth of NiTiO3 with a distorted ilmenite structure journal, June 2012

Two-dimensional gas of massless Dirac fermions in graphene journal, November 2005

Title: Dirac Magnons in a Honeycomb Lattice Quantum $XY$ Magnet ${CoTiO}_{3}$

Topological magnon insulator in insulating ferromagnet
journal, April 2013

Experimental observation of the quantum Hall effect and Berry's phase in graphene
journal, November 2005

Substrate-induced bandgap opening in epitaxial graphene
journal, September 2007

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

Dirac materials
journal, January 2014

Electronic properties of graphene in a strong magnetic field
journal, November 2011

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

Topological photonics
journal, March 2019

Electric and magnetic properties of titanium-cobalt-oxide single crystals produced by floating zone melting with light heating
journal, August 2017

Unconventional superconductivity in magic-angle graphene superlattices
journal, March 2018

Discovery of coexisting Dirac and triply degenerate magnons in a three-dimensional antiferromagnet
journal, July 2018

Neutron scattering study of magnetic excitations in oblique easy-axis antiferromagnet FeTiO ₃
journal, December 1986

Weyl magnons in breathing pyrochlore antiferromagnets
journal, September 2016

Coherent and incoherent coupling dynamics in a two-dimensional atomic crystal embedded in a plasmon-induced magnetic resonator
journal, January 2020

Two Topologically Distinct Dirac-Line Semimetal Phases and Topological Phase Transitions in Rhombohedrally Stacked Honeycomb Lattices
journal, January 2018

Defect Scattering in Graphene
journal, June 2009

Excitations in KCoF ₃ . II. Theoretical
journal, October 1971

Magnetic anisotropies in MTiO3 (M = Co, Ni)
journal, January 1980

Double-Weyl Phonons in Transition-Metal Monosilicides
journal, January 2018

Observation of Double Weyl Phonons in Parity-Breaking FeSi
journal, July 2018

Edge states in topological magnon insulators
journal, July 2014

Topological Magnon Bands in a Kagome Lattice Ferromagnet
journal, September 2015

A first theoretical realization of honeycomb topological magnon insulator
journal, July 2016

Strain Engineering of Graphene’s Electronic Structure
journal, July 2009

Classification of topological quantum matter with symmetries
journal, August 2016

Recipe for Dirac Phonon States with a Quantized Valley Berry Phase in Two-Dimensional Hexagonal Lattices
journal, November 2018

Topological photonics
journal, October 2014

Evolution of magnetic Dirac bosons in a honeycomb lattice
journal, January 2018

Single-ion properties of the $S_{eff}$ = $\frac{1}{2}$ XY antiferromagnetic pyrochlores $Na A^{'} {Co}_{2} F_{7}$ ( $A^{'} = {Ca}^{2 +}, {Sr}^{2 +}$ )
journal, April 2017

Crystal structure and magnetic properties of CoTiO3
journal, March 1964

The electronic properties of graphene
journal, January 2009

Metal to Insulator Transition in Epitaxial Graphene Induced by Molecular Doping
journal, August 2008

Linear spin wave theory for single-Q incommensurate magnetic structures
journal, March 2015

Chiral tunnelling and the Klein paradox in graphene
journal, August 2006

Modeling disorder in graphene
journal, March 2008

Topological spin excitations in a three-dimensional antiferromagnet
journal, July 2018

Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering
journal, September 2009

Magnon Dirac materials
journal, August 2016

Epitaxial growth of NiTiO3 with a distorted ilmenite structure
journal, June 2012

Two-dimensional gas of massless Dirac fermions in graphene
journal, November 2005