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, BaCo$_2$(AsO$_4$)$_2$, 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 BaCo$_2$(AsO$_4$)$_2$ as a far more ideal version of Kitaev QSL compared with other candidates.
In- and out-of-plane field induced quantum spin-liquid states in a more ideal Kitaev material: BaCo2(AsO4)2
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(AsO4)2, 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 ∼ 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(AsO4)2 as a far more ideal version of Kitaev QSL compared with other candidates.
Kitaev-derived Gapless Spin Liquid in the K-J-Γ-Γ′ Quantum Magnet Na2Co2TeO6
The realization of quantum spin liquids (QSLs) in Kitaev magnets represents an intriguing topic in frustrated quantum magnetism. Despite prediction in the pure Kitaev honeycomb model, realization of QSLs in realistic systems and materials remain scarce. The recent discovery of cobalt-based compound Na2Co2TeO6 has raised significant research interest. By establishing a realistic K-J-Γ-Γ′ model for Na2Co2TeO6 -- with a dominant antiferromagnetic (AFM) Kitaev interaction (K>0) that quantitatively explains its thermodynamics measurements -- we reveal an intermediate gapless QSL phase under [111] magnetic fields with tensor-network calculations. We confirm the QSL nature of this phase by demonstrating its adiabatic connection to the intensively studied intermediate QSL of the pure AFM Kitaev model under out-of-plane fields. Our results show excellent agreement with recent high-field experiments, thereby explaining the intermediate-field phase in Na2Co2TeO6. These findings bridge the gap between theoretical proposals for a Kitaev-derived QSL and experimental realization, opening new avenues for exploring exotic quantum states of matter in realistic Kitaev materials.
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′ 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.
Quantum spin liquids (QSLs) host a variety of fractionalized particles. In Kitaev's paradigmatic honeycomb model a spin-fractionalizes intoflux due to emergentgauge field and matter Majorana fermions. Although these excitations have well-defined dynamics in the integrable limit, their direct experimental identification is notoriously challenging: realistic materials inevitably host additional symmetry-allowed interactions that break integrability and hybridize gauge and matter sectors, while magnetic fields, which are often required to suppress competing order and stabilize a putative QSL regime, further entangle the responses of different fractionalized quasiparticles and may even drive the system into field-induced spin-liquid phases that are not adiabatically connected to the integrable limit. A prominent example is the quantum Majorana metal, in which the distinct dynamics of fractionalized Majorana fermions can become directly visible in scattering. This review highlights recent progress on these related questions: in which field-stabilized QSL regimes and nearby emergent phases, and under what conditions, can the response of a specific fractionalized quasiparticle be isolated and positively understood, thereby clarifying the existence and the experimental scope of putative spin liquids? We review the progress on these questions across Abelian, non-Abelian, and emergent quantum phases under magnetic field that are not perturbatively connected to the integrable limit. We connect these field-induced dynamical phenomena to concrete experimental observables, relevant for neutron scattering, resonant inelastic x-ray scattering, and pump-probe spectroscopy, techniques that are capable of identifying the nature of different magnetic-field-induced phases and resolving specific types of fractionalized particles, including Majoranas andfluxes.
Can we realize Kitaev quantum spin liquids in the Jeff=1/2 honeycomb cobaltates?
The quest for Kitaev quantum spin liquids has led to great interest in honeycomb quantum magnets with strong spin-orbit coupling. It has been recently proposed that even Mott insulators with 3d transition metal ions, having nominally weak spin-orbit coupling, can realize such exotic physics. Motivated by this, we study the rhombohedral honeycomb cobaltates CoTiO3, BaCo2(PO4)2, and BaCo2(AsO4)2, using ab initio density functional theory, which takes into account realistic crystal field distortions and chemical information, in conjunction with exact diagonalization numerics. We show that these Co2+ magnets host jeff=1/2 local moments with highly anisotropic g-factors, and we extract their full spin Hamiltonians including longer-range and anisotropic exchange couplings. For CoTiO3, we find a nearest-neighbor easy-plane ferromagnetic XXZ model with additional bond-dependent anisotropies and interlayer exchange, which supports three-dimensional (3D) Dirac nodal line magnons. In contrast, for BaCo2(PO4)2 and BaCo2(AsO4)2, we find a strongly suppressed interlayer coupling, and significant frustration from additional third-neighbor antiferromagnetic exchange mediated by P/As. Such bond-anisotropic J1-J3 spin models can support collinear zig-zag or coplanar spiral ground states; we discuss their dynamical spin correlations which reveal a gapped Goldstone mode, and argue that the effective parameters of these pseudospin-1/2 models may be strongly renormalized by coupling to a low energy spin-exciton. Our results call for re-examining proposals for realizing Kitaev spin liquids in the honeycomb cobaltates.
We develop a gauge-invariant renormalized mean-field theory (RMFT) to reliably find the quantum spin liquid (QSL) states and their field response for realistic Kitaev materials under strong magnetic fields and described by the generalized Kitaev J-K-Γ- Γ′ model. Remarkably, while our RMFT reproduces previous results based on using more complicated numerical methods, it also predicts several new stable QSL states. In particular, since Kitaev spin liquid (KSL) is no longer a saddle point solution, a new exotic 2-cone state distinct from the KSL is found to describe experimental observations well, and hence should be the candidate state realized in the Kitaev material, α-RuCl3. We further explore the mechanism for the suppression of the observed thermal Hall conductivity at low temperatures within the fermionic framework, and show that the polar-angle dependence of the fermionic gap can distinguish the found 2-cone state from the KSL state in further experiments.
High-field fate of the Kitaev quantum spin liquid in α-RuCl3
Kitaev quantum spin liquids (KQSLs) host fractionalized excitations described by itinerant Majorana quasiparticles and gapped Z2 fluxes (visons), providing a platform for emergent topological matter. Whether such a state survives under strong magnetic fields, however, remains an open question. The layered honeycomb magnet α-RuCl3 is a leading candidate material: an in-plane field of ∼ 7 T suppresses antiferromagnetic order and induces a quantum-disordered phase exhibiting signatures consistent with Majorana excitations, including an anomalous thermal Hall effect and field-angle-dependent specific heat. At higher fields, the magnetization approaches saturation, suggesting a transition to a spin-polarized state, yet the microscopic evolution between these limits remains unresolved. Here we report high-field specific heat measurements up to 24 T that reveal a distinct crossover at $μ_0H^*\approx$15 T, beyond which the perturbative Kitaev description breaks down. Above H∗, the characteristic six-fold angular modulation of the specific heat collapses and the excitation gap deviates from the predicted H3 scaling. Meanwhile, the gap decreases with increasing field and the in-plane magnetization anisotropy persists up to ∼ 24 T, both in sharp contrast to a trivial spin-polarized state, indicating that KQSL signatures are preserved even at ∼ 90 % of magnetization saturation. These results reveal that the KQSL in α-RuCl3 extends well beyond the perturbative window, persisting as a nonperturbative regime in which the Majorana and vison energy scales merge, before eventually giving way to spin polarization. This thermodynamic roadmap provides a basis for understanding how fractionalized phases evolve under strong magnetic fields.