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npj Quantum Materials

Kitaev-derived spin liquid in the frustrated quantum magnet Na2Co2TeO6

Han Li, Xu-Guang Zhou, Gang Su, Wei Li

Published May 29, 2026• 1 citation
Publisher

Abstract

Abstract The pursuit of the quantum spin liquid (QSL) predicted by the Kitaev honeycomb model remains a central yet challenging goal in quantum magnetism. Realistic candidate materials inevitably host non-Kitaev interactions that often lead to antiferromagnetic (AFM) order at low temperature. While magnetic fields can suppress such AFM order and may stabilize a QSL phase, conclusive evidence for a field-induced Kitaev QSL has remained elusive despite a decade of research. Here, we establish an effective K - J -Γ- $${\Gamma }^{{\prime} }$$ Γ ′ model with a dominant AFM Kitaev interaction for Na 2 Co 2 TeO 6 , which quantitatively explains its key experimental measurements. Using high-precision tensor-network calculations, we reveal a QSL phase under intermediate [111] magnetic fields, which is possibly gapless, and find it can be adiabatically connected to the intensively studied intermediate-field QSL in the pure AFM Kitaev model. This correspondence confirms that the Kitaev model as the origin of the intermediate-field QSL in cobalt-based magnet Na 2 Co 2 TeO 6 , thus offering a concrete platform for exploring Kitaev-derived QSL in realistic materials.

DOI
10.1038/s41535-026-00903-6

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Abstract The pursuit of the quantum spin liquid (QSL) predicted by the Kitaev honeycomb model remains a central yet challenging goal in quantum magnetism. Realistic candidate materials inevitably host non-Kitaev interactions that often lead to antiferromagnetic (AFM) order at low temperature. While magnetic fields can suppress such AFM order and may stabilize a QSL phase, conclusive evidence for a field-induced Kitaev QSL has remained elusive despite a decade of research. Here, we establish an effective K - J -Γ- Γ′{\Gamma }^{{\prime} }Γ′ Γ ′ model with a dominant AFM Kitaev interaction for Na 2 Co 2 TeO 6 , which quantitatively explains its key experimental measurements. Using high-precision tensor-network calculations, we reveal a QSL phase under intermediate [111] magnetic fields, which is possibly gapless, and find it can be adiabatically connected to the intensively studied intermediate-field QSL in the pure AFM Kitaev model. This correspondence confirms that the Kitaev model as the origin of the intermediate-field QSL in cobalt-based magnet Na 2 Co 2 TeO 6 , thus offering a concrete platform for exploring Kitaev-derived QSL in realistic materials.
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In- and out-of-plane field induced quantum spin-liquid states in a more ideal Kitaev material: BaCo2_22​(AsO4_44​)2_22​
Kitaev quantum spin liquids (QSLs) are exotic states of matter that are predicted to host Majorana fermions and gauge flux excitations. However, so far all known Kitaev QSL candidates are known to have appreciable non-Kitaev interactions that pushes these systems far from the QSL regime. Using time-domain terahertz spectroscopy (TDTS) we show that the honeycomb cobalt-based Kitaev QSL candidate, BaCo2_22​(AsO4_44​)2_22​, has dominant Kitaev interactions. Due to only small non-Kitaev terms a magnetic continuum consistent with Majorana fermions and the existence of a Kitaev QSL can be induced by a small 4 T out-of-plane-magnetic field. Applying an even smaller in-plane magnetic field ∼\sim∼ 0.5 T suppresses the effects of the non-Kitaev interactions and gives rise to a field induced intermediate state also consistent with a QSL. These results may have fundamental impact for realizing quantum computation. Our results demonstrate BaCo2_22​(AsO4_44​)2_22​ as a far more ideal version of Kitaev QSL compared with other candidates.
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The possible existence of a quantum spin liquid (QSL) phase, an exotic state of matter with long-range quantum entanglement and fractionalized excitations, in ααα-RuCl3_33​ has sparked widespread interests in exploring QSLs in various Kitaev models under magnetic fields. Recently, a KKK-JJJ-ΓΓΓ-Γ′Γ'Γ′ model has been proposed to accurately describe the compound by fitting the measured thermodynamic data, where JJJ is Heisenberg interaction, and ΓΓΓ, Γ′Γ'Γ′ are off-diagonal exchanges on top of the dominant Kitaev coupling KKK. Based on this effective model, an intermediate QSL phase in presence of an out-of-plane fields along the [111][1 1 1][111] direction, between the low-field zigzag order and high-field polarized phase, has been predicted. By combining density matrix renormalization group (DMRG), exponential tensor renormalization group (XTRG), and variational Monte Carlo (VMC) calculations, we address the nature of this QSL phase in the honeycomb KKK-JJJ-ΓΓΓ-Γ′Γ'Γ′ model under the [111][1 1 1][111]-direction field. Our DMRG calculations find the algebraic-like decay of spin correlation function, the finite spin scalar chiral order, and lattice nematic order. Together with the XTRG results of power-law specific heat at low temperature, our findings naturally suggest a gapless nematic chiral spin liquid. On the other hand, our VMC study finds a gapped nematic chiral spin liquid with the variational energy very close to that obtained in DMRG. As VMC finds a very small gap that is beyond the current resolution of both ground-state DMRG and finite-temperature XTRG calculations on finite-width cylinders, we resort the full clarification for the nature of the intermediate QSL to future studies. Lastly, we discuss the implications of our results to the recent experiment on ααα-RuCl3_33​ and the QSL-like phase in a similar KKK-ΓΓΓ-Γ′Γ'Γ′ model.