A jeff = 1/2 Kitaev material on the triangular lattice: the case of NaRuO2

Razpopov, Aleksandar; Kaib, David A. S.; Backes, Steffen; Balents, Leon; Wilson, Stephen D.; Ferrari, Francesco; Riedl, Kira; Valentí, Roser

doi:10.1038/s41535-023-00567-6

Title: A j_eff = 1/2 Kitaev material on the triangular lattice: the case of NaRuO₂

Journal Article · 13 July 2023 · npj Quantum Materials

DOI: https://doi.org/10.1038/s41535-023-00567-6 · OSTI ID:1989510

^[1];

^[2]; Balents, Leon ^[3];

^[3];

^[1]; Riedl, Kira ^[1];

^[1]

Goethe-Universität, Frankfurt am Main (Germany)
University of Tokyo (Japan); RIKEN, Saitama (Japan); Institut Polytechnique de Paris (France)
University of California, Santa Barbara, CA (United States)

Motivated by recent reports of a quantum-disordered ground state in the triangular lattice compound NaRuO₂, we derive a j_eff = 1/2 magnetic model for this system by means of first-principles calculations. The pseudospin Hamiltonian is dominated by bond-dependent off-diagonal Γ interactions, complemented by a ferromagnetic Heisenberg exchange and a notably antiferromagnetic Kitaev term. In addition to bilinear interactions, we find a sizable four-spin ring exchange contribution with a strongly anisotropic character, which has been so far overlooked when modeling Kitaev materials. The analysis of the magnetic model, based on the minimization of the classical energy and exact diagonalization of the quantum Hamiltonian, points toward the existence of a rather robust easy-plane ferromagnetic order, which cannot be easily destabilized by physically relevant perturbations.

View Journal Article

Cite

Export

Save

Research Organization:: University of California, Santa Barbara, CA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-08ER46524; SC0017752

OSTI ID:: 1989510

Journal Information:: npj Quantum Materials, Journal Name: npj Quantum Materials Journal Issue: 1 Vol. 8; ISSN 2397-4648

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (74)

Ab Initio Approaches for Low‐Energy Spin Hamiltonians Riedl, Kira; Li, Ying; Valentí, Roser physica status solidi (b), Vol. 256, Issue 9 https://doi.org/10.1002/pssb.201800684	journal	March 2019
The ORCA program system: The ORCA program system Neese, Frank Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 1 https://doi.org/10.1002/wcms.81	journal	June 2011
Resonating valence bonds: A new kind of insulator? Anderson, P. W. Materials Research Bulletin, Vol. 8, Issue 2 https://doi.org/10.1016/0025-5408(73)90167-0	journal	February 1973
Anyons in an exactly solved model and beyond Kitaev, Alexei Annals of Physics, Vol. 321, Issue 1 https://doi.org/10.1016/j.aop.2005.10.005	journal	January 2006
FHI-gap: A code based on the all-electron augmented plane wave method Jiang, Hong; Gómez-Abal, Ricardo I.; Li, Xin-Zheng Computer Physics Communications, Vol. 184, Issue 2 https://doi.org/10.1016/j.cpc.2012.09.018	journal	February 2013
Kitaev materials Trebst, Simon; Hickey, Ciarán Physics Reports, Vol. 950 https://doi.org/10.1016/j.physrep.2021.11.003	journal	March 2022
NaRuO ₂ and Na _x RuO ₂ · y H ₂ O: New Oxide and Oxyhydrate with Two Dimensional RuO ₂ Layers Shikano, Masahiro; Delmas, Claude; Darriet, Jacques Inorganic Chemistry, Vol. 43, Issue 4 https://doi.org/10.1021/ic035324d	journal	February 2004
Quantum Calculation of Molecular Energies and Energy Gradients in Solution by a Conductor Solvent Model Barone, Vincenzo; Cossi, Maurizio The Journal of Physical Chemistry A, Vol. 102, Issue 11 https://doi.org/10.1021/jp9716997	journal	March 1998
Spin liquids in frustrated magnets Balents, Leon Nature, Vol. 464, Issue 7286 https://doi.org/10.1038/nature08917	journal	March 2010
Effect of magnetic frustration on nematicity and superconductivity in iron chalcogenides Glasbrenner, J. K.; Mazin, I. I.; Jeschke, Harald O. Nature Physics, Vol. 11, Issue 11 https://doi.org/10.1038/nphys3434	journal	August 2015
Majorana fermions in the Kitaev quantum spin system α-RuCl3 Do, Seung-Hwan; Park, Sang-Youn; Yoshitake, Junki Nature Physics, Vol. 13, Issue 11 https://doi.org/10.1038/nphys4264	journal	September 2017
Breakdown of magnons in a strongly spin-orbital coupled magnet Winter, Stephen M.; Riedl, Kira; Maksimov, Pavel A. Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-01177-0	journal	October 2017
Critical spin liquid versus valence-bond glass in a triangular-lattice organic antiferromagnet Riedl, Kira; Valentí, Roser; Winter, Stephen M. Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-10604-3	journal	June 2019
Spontaneous skyrmionic lattice from anisotropic symmetric exchange in a Ni-halide monolayer Amoroso, Danila; Barone, Paolo; Picozzi, Silvia Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-19535-w	journal	November 2020
Order-by-disorder from bond-dependent exchange and intensity signature of nodal quasiparticles in a honeycomb cobaltate Elliot, M.; McClarty, P. A.; Prabhakaran, D. Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-23851-0	journal	June 2021
Electronic and magnetic properties of the RuX3 (X = Cl, Br, I) family: two siblings—and a cousin? Kaib, David A. S.; Riedl, Kira; Razpopov, Aleksandar npj Quantum Materials, Vol. 7, Issue 1 https://doi.org/10.1038/s41535-022-00481-3	journal	July 2022
Field-tunable quantum disordered ground state in the triangular-lattice antiferromagnet NaYbO2 Bordelon, Mitchell M.; Kenney, Eric; Liu, Chunxiao Nature Physics, Vol. 15, Issue 10 https://doi.org/10.1038/s41567-019-0594-5	journal	July 2019
Quantum disordered ground state in the triangular-lattice magnet NaRuO2 Ortiz, Brenden R.; Sarte, Paul M.; Avidor, Alon Hendler Nature Physics, Vol. 19, Issue 7 https://doi.org/10.1038/s41567-023-02039-x	journal	April 2023
Concept and realization of Kitaev quantum spin liquids Takagi, Hidenori; Takayama, Tomohiro; Jackeli, George Nature Reviews Physics, Vol. 1, Issue 4 https://doi.org/10.1038/s42254-019-0038-2	journal	March 2019
On the ground state properties of the anisotropic triangular antiferromagnet Fazekas, P.; Anderson, P. W. Philosophical Magazine, Vol. 30, Issue 2 https://doi.org/10.1080/14786439808206568	journal	August 1974
Rare-Earth Chalcogenides: A Large Family of Triangular Lattice Spin Liquid Candidates Liu, Weiwei; Zhang, Zheng; Ji, Jianting Chinese Physics Letters, Vol. 35, Issue 11 https://doi.org/10.1088/0256-307X/35/11/117501	journal	October 2018
Exchange in solid ³He and the Heisenberg Hamiltonian Thouless, D. J. Proceedings of the Physical Society, Vol. 86, Issue 5 https://doi.org/10.1088/0370-1328/86/5/301	journal	November 1965
Linear spin wave theory for single-Q incommensurate magnetic structures Toth, S.; Lake, B. Journal of Physics: Condensed Matter, Vol. 27, Issue 16 https://doi.org/10.1088/0953-8984/27/16/166002	journal	March 2015
Models and materials for generalized Kitaev magnetism Winter, Stephen M.; Tsirlin, Alexander A.; Daghofer, Maria Journal of Physics: Condensed Matter, Vol. 29, Issue 49 https://doi.org/10.1088/1361-648X/aa8cf5	journal	November 2017
Heisenberg–Kitaev physics in magnetic fields Janssen, Lukas; Vojta, Matthias Journal of Physics: Condensed Matter, Vol. 31, Issue 42 https://doi.org/10.1088/1361-648X/ab283e	journal	July 2019
Global phase diagram, possible chiral spin liquid, and topological superconductivity in the triangular Kitaev–Heisenberg model Li, Kai; Yu, Shun-Li; Li, Jian-Xin New Journal of Physics, Vol. 17, Issue 4 https://doi.org/10.1088/1367-2630/17/4/043032	journal	April 2015
Quantum spin liquid ground state in the disorder free triangular lattice NaYbS 2 Sarkar, R.; Schlender, Ph.; Grinenko, V. Physical Review B, Vol. 100, Issue 24 https://doi.org/10.1103/PhysRevB.100.241116	journal	December 2019
Comprehensive study of the global phase diagram of the J−K−Γ model on a triangular lattice Wang, Shi; Qi, Zhongyuan; Xi, Bin Physical Review B, Vol. 103, Issue 5 https://doi.org/10.1103/PhysRevB.103.054410	journal	February 2021
Bosonic resonating valence bond theory of the possible chiral spin-liquid state in the triangular-lattice Hubbard model Zhang, Qiu; Li, Tao Physical Review B, Vol. 104, Issue 7 https://doi.org/10.1103/PhysRevB.104.075103	journal	August 2021
Microscopic origin of magnetism in monolayer 3d transition metal dihalides Riedl, Kira; Amoroso, Danila; Backes, Steffen Physical Review B, Vol. 106, Issue 3 https://doi.org/10.1103/PhysRevB.106.035156	journal	July 2022
Combined experimental and theoretical study of hydrostatic He-gas pressure effects in α−RuCl3 Wolf, B.; Kaib, D. A. S.; Razpopov, A. Physical Review B, Vol. 106, Issue 13 https://doi.org/10.1103/PhysRevB.106.134432	journal	October 2022
Computer model of metallic spin-glasses Walker, L. R.; Walstedt, R. E. Physical Review B, Vol. 22, Issue 8 https://doi.org/10.1103/PhysRevB.22.3816	journal	October 1980
Ab initiomolecular dynamics for liquid metals Kresse, G.; Hafner, J. Physical Review B, Vol. 47, Issue 1, p. 558-561 https://doi.org/10.1103/PhysRevB.47.558	journal	January 1993
Density-functional theory and NiO photoemission spectra Anisimov, V. I.; Solovyev, I. V.; Korotin, M. A. Physical Review B, Vol. 48, Issue 23 https://doi.org/10.1103/PhysRevB.48.16929	journal	December 1993
Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J. Physical Review B, Vol. 52, Issue 8 https://doi.org/10.1103/PhysRevB.52.R5467	journal	August 1995
Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y. Physical Review B, Vol. 57, Issue 3, p. 1505-1509 https://doi.org/10.1103/PhysRevB.57.1505	journal	January 1998
Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme Koepernik, Klaus; Eschrig, Helmut Physical Review B, Vol. 59, Issue 3 https://doi.org/10.1103/PhysRevB.59.1743	journal	January 1999
Spin-liquid phase of the multiple-spin exchange Hamiltonian on the triangular lattice Misguich, G.; Lhuillier, C.; Bernu, B. Physical Review B, Vol. 60, Issue 2 https://doi.org/10.1103/PhysRevB.60.1064	journal	July 1999
Frequency-dependent local interactions and low-energy effective models from electronic structure calculations Aryasetiawan, F.; Imada, M.; Georges, A. Physical Review B, Vol. 70, Issue 19 https://doi.org/10.1103/PhysRevB.70.195104	journal	November 2004
Variational study of triangular lattice spin- 1 ∕ 2 model with ring exchanges and spin liquid state in κ − ( ET ) 2 Cu 2 ( CN ) 3 Motrunich, Olexei I. Physical Review B, Vol. 72, Issue 4 https://doi.org/10.1103/PhysRevB.72.045105	journal	July 2005
Calculations of Hubbard U from first-principles Aryasetiawan, F.; Karlsson, K.; Jepsen, O. Physical Review B, Vol. 74, Issue 12 https://doi.org/10.1103/PhysRevB.74.125106	journal	September 2006
Anisotropy and magnetism in the LSDA + U method Ylvisaker, Erik R.; Pickett, Warren E.; Koepernik, Klaus Physical Review B, Vol. 79, Issue 3 https://doi.org/10.1103/PhysRevB.79.035103	journal	January 2009
Spin-liquid behavior in J eff = 1 2 triangular lattice compound Ba 3 IrTi 2 O 9 Dey, Tusharkanti; Mahajan, A. V.; Khuntia, P. Physical Review B, Vol. 86, Issue 14 https://doi.org/10.1103/PhysRevB.86.140405	journal	October 2012
Nonplanar ground states of frustrated antiferromagnets on an octahedral lattice Sklan, Sophia R.; Henley, Christopher L. Physical Review B, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevB.88.024407	journal	July 2013
Kitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices Kimchi, Itamar; Vishwanath, Ashvin Physical Review B, Vol. 89, Issue 1 https://doi.org/10.1103/PhysRevB.89.014414	journal	January 2014
Spin-liquid phase due to competing classical orders in the semiclassical theory of the Heisenberg model with ring exchange on an anisotropic triangular lattice Holt, Michael; Powell, Ben J.; Merino, Jaime Physical Review B, Vol. 89, Issue 17 https://doi.org/10.1103/PhysRevB.89.174415	journal	May 2014
Spin-orbit physics of j = 1 2 Mott insulators on the triangular lattice Becker, Michael; Hermanns, Maria; Bauer, Bela Physical Review B, Vol. 91, Issue 15 https://doi.org/10.1103/PhysRevB.91.155135	journal	April 2015
Magnetic orders proximal to the Kitaev limit in frustrated triangular systems: Application to Ba 3 IrTi 2 O 9 Catuneanu, Andrei; Rau, Jeffrey G.; Kim, Heung-Sik Physical Review B, Vol. 92, Issue 16 https://doi.org/10.1103/PhysRevB.92.165108	journal	October 2015
Quantum order by disorder in the Kitaev model on a triangular lattice Jackeli, George; Avella, Adolfo Physical Review B, Vol. 92, Issue 18 https://doi.org/10.1103/PhysRevB.92.184416	journal	November 2015
Monoclinic crystal structure of α − RuCl 3 and the zigzag antiferromagnetic ground state Johnson, R. D.; Williams, S. C.; Haghighirad, A. A. Physical Review B, Vol. 92, Issue 23 https://doi.org/10.1103/PhysRevB.92.235119	journal	December 2015
Kitaev anisotropy induces mesoscopic Z 2 vortex crystals in frustrated hexagonal antiferromagnets Rousochatzakis, Ioannis; Rössler, Ulrich K.; van den Brink, Jeroen Physical Review B, Vol. 93, Issue 10 https://doi.org/10.1103/PhysRevB.93.104417	journal	March 2016
Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales Winter, Stephen M.; Li, Ying; Jeschke, Harald O. Physical Review B, Vol. 93, Issue 21 https://doi.org/10.1103/PhysRevB.93.214431	journal	June 2016
Magnetic anisotropy in the Kitaev model systems Na 2 IrO 3 and RuCl 3 Chaloupka, Jiří; Khaliullin, Giniyat Physical Review B, Vol. 94, Issue 6 https://doi.org/10.1103/PhysRevB.94.064435	journal	August 2016
Reduction of magnetic interlayer coupling in barlowite through isoelectronic substitution Guterding, Daniel; Valentí, Roser; Jeschke, Harald O. Physical Review B, Vol. 94, Issue 12 https://doi.org/10.1103/PhysRevB.94.125136	journal	September 2016
NaYbS 2 : A planar spin- 1 2 triangular-lattice magnet and putative spin liquid Baenitz, M.; Schlender, Ph.; Sichelschmidt, J. Physical Review B, Vol. 98, Issue 22 https://doi.org/10.1103/PhysRevB.98.220409	journal	December 2018
Novel J eff = 1 / 2 Mott State Induced by Relativistic Spin-Orbit Coupling in Sr 2 IrO 4 Kim, B. J.; Jin, Hosub; Moon, S. J. Physical Review Letters, Vol. 101, Issue 7 https://doi.org/10.1103/PhysRevLett.101.076402	journal	August 2008
Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models Jackeli, G.; Khaliullin, G. Physical Review Letters, Vol. 102, Issue 1 https://doi.org/10.1103/PhysRevLett.102.017205	journal	January 2009
Exotic Gapless Mott Insulators of Bosons on Multileg Ladders Block, Matthew S.; Mishmash, Ryan V.; Kaul, Ribhu K. Physical Review Letters, Vol. 106, Issue 4 https://doi.org/10.1103/PhysRevLett.106.046402	journal	January 2011
Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit Rau, Jeffrey G.; Lee, Eric Kin-Ho; Kee, Hae-Young Physical Review Letters, Vol. 112, Issue 7 https://doi.org/10.1103/PhysRevLett.112.077204	journal	February 2014
Pseudo-Goldstone Gaps and Order-by-Quantum Disorder in Frustrated Magnets Rau, Jeffrey G.; McClarty, Paul A.; Moessner, Roderich Physical Review Letters, Vol. 121, Issue 23 https://doi.org/10.1103/PhysRevLett.121.237201	journal	December 2018
Microscopic Mechanism for a Higher-Spin Kitaev Model Stavropoulos, P. Peter; Pereira, D.; Kee, Hae-Young Physical Review Letters, Vol. 123, Issue 3 https://doi.org/10.1103/PhysRevLett.123.037203	journal	July 2019
Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice Cookmeyer, Tessa; Motruk, Johannes; Moore, Joel E. Physical Review Letters, Vol. 127, Issue 8 https://doi.org/10.1103/PhysRevLett.127.087201	journal	August 2021
Spin Vortex Crystal Order in Organic Triangular Lattice Compound Riedl, Kira; Gati, Elena; Zielke, David Physical Review Letters, Vol. 127, Issue 14 https://doi.org/10.1103/PhysRevLett.127.147204	journal	September 2021
Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)] Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 78, Issue 7 https://doi.org/10.1103/PhysRevLett.78.1396	journal	February 1997
Low Energy Electronic States and Triplet Pairing in Layered Cobaltate Khaliullin, G.; Koshibae, W.; Maekawa, S. Physical Review Letters, Vol. 93, Issue 17 https://doi.org/10.1103/PhysRevLett.93.176401	journal	October 2004
Signatures of a gearwheel quantum spin liquid in a spin- 1 2 pyrochlore molybdate Heisenberg antiferromagnet Iqbal, Yasir; Müller, Tobias; Riedl, Kira Physical Review Materials, Vol. 1, Issue 7 https://doi.org/10.1103/PhysRevMaterials.1.071201	journal	December 2017
Defect control in the Heisenberg-Kitaev candidate material NaRuO2 Ortiz, Brenden R.; Sarte, Paul M.; Avidor, Alon H. Physical Review Materials, Vol. 6, Issue 10 https://doi.org/10.1103/PhysRevMaterials.6.104413	journal	October 2022
Correlated electrons in high-temperature superconductors Dagotto, Elbio Reviews of Modern Physics, Vol. 66, Issue 3 https://doi.org/10.1103/RevModPhys.66.763	journal	July 1994
Neutron scattering in the proximate quantum spin liquid α-RuCl ₃ Banerjee, Arnab; Yan, Jiaqiang; Knolle, Johannes Science, Vol. 356, Issue 6342 https://doi.org/10.1126/science.aah6015	journal	June 2017
Orbital Order and Fluctuations in Mott Insulators Khaliullin, Giniyat Progress of Theoretical Physics Supplement, Vol. 160 https://doi.org/10.1143/PTPS.160.155	journal	January 2005
Ingredients for Generalized Models of κ-Phase Organic Charge-Transfer Salts: A Review Riedl, Kira; Gati, Elena; Valentí, Roser Crystals, Vol. 12, Issue 12 https://doi.org/10.3390/cryst12121689	journal	November 2022
Ring-Exchange Interaction Effects on Magnons in Dirac Magnet CoTiO$_3$ Li, Yufei; Mai, Thuc T.; Karaki, M. arXiv https://doi.org/10.48550/arXiv.2212.05278	preprint	January 2022
NaRuO$_2$: Kitaev-Heisenberg exchange in triangular-lattice setting Bhattacharyya, Pritam; Bogdanov, Nikolay A.; Nishimoto, Satoshi arXiv https://doi.org/10.48550/arXiv.2212.09365	preprint	January 2022
Density-Matrix Renormalization Group Study of Kitaev–Heisenberg Model on a Triangular Lattice Shinjo, Kazuya; Sota, Shigetoshi; Yunoki, Seiji Journal of the Physical Society of Japan, Vol. 85, Issue 11 https://doi.org/10.7566/JPSJ.85.114710	journal	November 2016

Similar Records

NaRuO2: Kitaev-Heisenberg exchange in triangular-lattice setting

Journal Article · 2023 · npj Quantum Materials · OSTI ID:2007242

Bhattacharyya, Pritam; Bogdanov, Nikolay A.; Nishimoto, Satoshi; +2 more

Quantum disordered ground state in the triangular-lattice magnet NaRuO₂

Journal Article · 2023 · Nature Physics · OSTI ID:3015208

Ortiz, Brenden R.; Sarte, Paul M.; Avidor, Alon Hendler; +12 more

Pressure tuning of Kitaev spin liquid candidate Na₃Co₂SbO₆

Journal Article · 2025 · Communications Physics · OSTI ID:2574468

Poldi, E. H. T.; Tartaglia, R.; Fabbris, Gilberto; +17 more

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Magnetic properties and materials
Phase transitions and critical phenomena

Title: A jeff = 1/2 Kitaev material on the triangular lattice: the case of NaRuO2

Citation Formats

References (74)

Similar Records

Related Subjects

Title: A j_eff = 1/2 Kitaev material on the triangular lattice: the case of NaRuO₂