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Concept and realization of Kitaev quantum spin liquids

Abstract

The Kitaev model is an exactly solvable S = 1/2 spin model on a 2D honeycomb lattice, in which the spins fractionalize into Majorana fermions and form a topological quantum spin liquid (QSL) in the ground state. Several complex iridium oxides, as well as α-RuCl3, are magnetic insulators with a honeycomb structure, and it was noticed that they accommodate essential ingredients of the Kitaev model owing to the interplay of electron correlation and spin–orbit coupling. This has led to a race to realize the Kitaev QSL and detect signatures of Majorana fermions. We summarize the theoretical background of the Kitaev QSL ground state and its realization using spin–orbital entangled Jeff = 1/2 moments. We provide an overview of candidate materials and their electronic and magnetic properties, including Na2IrO3, α-Li2IrO3, β-Li2IrO3, γ-Li2IrO3, α-RuCl3 and H3LiIr2O6. Finally, we discuss experiments showing that H3LiIr2O6 and α-RuCl3 in an applied magnetic field exhibit signatures of the QSL state and that α-RuCl3 has unusual magnetic excitations and thermal transport properties consistent with spin fractionalization.

Key points

  • The quantum spin liquid is an exotic state of matter in which interacting spins avoid symmetry-breaking phase transitions and form a ground state exhibiting long-range entanglement and topological order.

  • In the exactly soluble Kitaev model, anisotropic spin-pair interactions on different honeycomb lattice bonds conflict, producing strong frustration and a spin-liquid ground state.

  • In some transition-metal-based Mott insulators, unquenched orbital moments and spin–orbit entangled wavefunctions can result in a low-energy Hamiltonian with bond-dependent interactions similar to the Kitaev model.

  • Quantum spin liquid behaviour was recently discovered in the hydrogenated iridate H3LiIr2O6, and signatures of the spin fractionalization and Majorana fermions predicted by the Kitaev model have been detected in α-RuCl3.

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Acknowledgements

The authors thank A. Smerald for his critical reading of this manuscript. H.T., T.T. and G.J. acknowledge support from the Alexander von Humboldt Foundation. The authors thank A. Banerjee, K. Kitagawa and Y. Matsuda for providing figures. H.T. was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI (17H01140, JP15H05852, JP15K21717). S.E.N. was supported by the US Department of Energy, Basic Energy Sciences, Scientific User Facilities Division.

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All authors contributed to the preparation of this manuscript.

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The authors declare no competing interests.

Correspondence to Hidenori Takagi or Tomohiro Takayama or George Jackeli or Giniyat Khaliullin or Stephen E. Nagler.

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Fig. 1: The Kitaev model.
Fig. 2: Local electronic states of octahedrally coordinated Ir4+ and Ru3+ ions and material realization of the Kitaev model.
Fig. 3: Kitaev candidate materials.
Fig. 4: Magnetic ordering in Kitaev candidate materials.
Fig. 5: Magnetic-field-induced paramagnetism and quantum spin liquid behaviour in Kitaev candidate materials.
Fig. 6: Signatures of fractional excitations and non-Kitaev interactions.
Fig. 7: Response functions in extended Kitaev models.