Na2Co2TeO6: Layered Cobalt Honeycomb Oxide
- Na2Co2TeO6 is a layered cobalt honeycomb oxide characterized by quasi-2D structures with partial Na disorder and bond-dependent exchange that favors Kitaev magnetism.
- The material exhibits complex magnetic behavior including zigzag antiferromagnetic order, multiple transition temperatures, and pronounced in-plane versus out-of-plane anisotropy.
- Diverse experimental techniques reveal gapped low-energy excitations, field-induced phase transitions, and ongoing debates over its microscopic Hamiltonian and ground state.
NaCoTeO is a layered cobalt honeycomb oxide that has become a central 3-electron candidate for bond-directional Kitaev magnetism. In the hexagonal material most commonly studied, Co ions in edge-sharing CoO octahedra form quasi-two-dimensional honeycomb layers, while Na disorder in the interlayer galleries weakens interplane coupling and complicates the low-temperature magnetic state. Across neutron scattering, ESR, NMR, SR, thermal transport, torque magnetometry, and Raman studies, NaCoTeO is consistently described as a pseudospin-0 honeycomb magnet with strong spin-orbit entanglement and substantial frustration; the main open issues are the precise zero-field order, the correct microscopic Hamiltonian, and the nature of the field-induced intermediate phase (Songvilay et al., 2020).
1. Crystal chemistry, layering, and polymorphism
Most studies describe Na1Co2TeO3 as a hexagonal layered oxide in which edge-sharing CoO4 octahedra form two-dimensional honeycomb networks in the 5 plane, separated by Na and TeO6 layers. A commonly reported crystallographic description is space group 7 (No. 182), with room-temperature lattice parameters roughly 8 Å and 9 Å, or closely related values 0 Å, 1 Å, 2 Å3 (Lin et al., 2020, Papawassiliou et al., 2024). Earlier neutron refinements in the same structural family gave 4 Å, 5 Å and emphasized that the three Na sites are only partially occupied, producing substantial interlayer disorder (Bera et al., 2016).
The local structural motif is unusually consequential for the magnetism. Co6 ions occupy slightly distorted octahedra and the Co–O–Co geometry is close to 7, a configuration that is repeatedly invoked in the literature as favorable for bond-dependent exchange. Several reports stress that the interlayer Na distribution is disordered: one refinement gave Na occupancies of about 8, 9, and 0 on three partially occupied sites, while a later NMR-oriented refinement described 1 occupancy on 2 and 3 on 4 (Bera et al., 2016, Papawassiliou et al., 2024). These data are consistent with the repeated observation that magnetic correlations are much longer ranged within the honeycomb planes than perpendicular to them.
The structural literature is not fully uniform. Different studies have described the same hexagonal material in 5, 6, or 7 settings, always retaining the essential picture of quasi-two-dimensional Co honeycomb layers separated by Na/Te-based spacers (Yao et al., 2022, Miao et al., 2023, Takeda et al., 2022). In addition, a distinct monoclinic polymorph in 8 has been reported, with room-temperature lattice parameters 9 Å, 0 Å, 1 Å, 2, and 3 Å4 (Dufault et al., 2023).
| Structural variant | Reported setting | Key reported feature |
|---|---|---|
| Hexagonal Na5Co6TeO7 | 8 | Strong Na disorder; quasi-2D honeycomb layers |
| Alternative hexagonal descriptions | 9, 0, 1 | Same layered Co-honeycomb motif |
| Monoclinic polymorph | 2 | Lower 3, single AFM transition, reduced Na/vacancy disorder |
The monoclinic polymorph is not a small perturbation of the hexagonal phase. It shows only one AFM transition at 4 K and no lower-temperature spin reorientation transitions, in contrast to the hexagonal material where ordering near 5 K is often accompanied by additional anomalies near 6–7 K and 8–9 K (Dufault et al., 2023). This suggests that interlayer Na disorder and stacking details are not secondary crystallographic complications but integral control parameters for the magnetic phenomenology.
2. Local electronic structure and effective Hamiltonians
In the hexagonal compound, Co0 is consistently described as high-spin 1 in an approximately octahedral crystal field, with the 2 configuration supporting a low-energy Kramers doublet that behaves as an effective pseudospin-3 or 4 degree of freedom (Songvilay et al., 2020). One neutron study placed the first excited 5 manifold roughly 6–7 meV above the ground doublet, and observed a spin-orbit excitation near 8 meV; a single-crystal INS study reported two crystal-field bands around 9 meV and 0–1 meV; by contrast, an out-of-plane field study described the lowest Kramers doublet as separated from the excited quartet by about 2 meV (Yao et al., 2022, Zhang et al., 2024). The spread in quoted splittings reflects that different analyses emphasize different effective descriptions and energy windows.
The low-energy spin dynamics are usually modeled by a bond-dependent extended Kitaev Hamiltonian on the honeycomb lattice. A representative form is
3
where 4 labels nearest-neighbor 5 bonds, 6 is the Kitaev exchange, 7 are Heisenberg terms, and 8 are symmetry-allowed off-diagonal exchanges (Songvilay et al., 2020). Simpler versions retain only 9, 0, and 1, or omit 2 to reduce over-parameterization (Lin et al., 2020, Sanders et al., 2021).
Parameter extraction remains one of the most contested aspects of the material:
| Source | Model | Reported parameter set for Na3Co4TeO5 |
|---|---|---|
| (Songvilay et al., 2020) | 6–7–8–9–0–1 | 2, 3, 4, 5, 6, 7 meV |
| (Lin et al., 2020) | 8–9–00–01–02 | 03, 04, 05, 06, 07 meV |
| (Sanders et al., 2021) | 08–09–10–11–12 | FM-13: 14, 15, 16, 17, 18 meV; dual AF-19: 20, 21, 22, 23, 24 meV |
| (Lin et al., 2024) | 25–26–27–28–29, VMC | 30, 31, 32, 33, 34 meV |
Despite the disagreement in fitted couplings, several recurring conclusions appear. First, a purely isotropic Heisenberg model is repeatedly found inadequate for the observed spectra (Sanders et al., 2021). Second, many analyses favor a dominant ferromagnetic Kitaev term with subleading 35, 36, and 37 (Songvilay et al., 2020, Sanders et al., 2021). Third, other fits obtain very different balances of 38, 39, and anisotropies from similar classes of powder data (Lin et al., 2020). This suggests that the microscopic Hamiltonian is underdetermined by powder-averaged spectra alone and is highly sensitive to assumptions about the magnetic unit cell and the relevant field regime.
3. Zero-field magnetic order and correlation anisotropy
The most frequently reported zero-field ordered state of the hexagonal compound is zigzag antiferromagnetism with propagation vector 40, or equivalently M-point ordering in the honeycomb Brillouin zone. In this picture, ferromagnetic chains run along one in-plane direction and are coupled antiferromagnetically from chain to chain; early neutron powder refinements placed the ordered moments essentially along the crystallographic 41 axis, with negligible 42-axis component within uncertainty (Lefrançois et al., 2016, Bera et al., 2016). Representative refined moments are 43 and 44 on the two Co sites in one study, and 45 and 46 in another, both below the spin-only 47 expectation for 48 and therefore suggestive of persistent fluctuations (Lefrançois et al., 2016, Bera et al., 2016).
A robust feature of the neutron data is the strong anisotropy of magnetic correlations. The first magnetic reflection is resolution-limited, implying very long in-plane correlation lengths, whereas peaks involving nonzero 49 are Lorentzian broadened, consistent with much shorter correlations perpendicular to the layers. One analysis quoted 50 Å and 51–52 Å, while another obtained 53 Å even at 54 K (Lefrançois et al., 2016, Bera et al., 2016). Above the ordering temperature, diffuse scattering and reverse Monte Carlo analysis showed that short-range correlations are largely confined to the honeycomb planes, with 55 Å at 56 K and a sign structure of positive nearest-neighbor and negative second- and third-neighbor correlations, consistent with the eventual zigzag motif (Bera et al., 2016).
The thermal evolution is more complex than a single transition. Several bulk and diffraction studies place the main ordering temperature near 57–58 K and report additional anomalies around 59–60 K and 61–62 K (Lefrançois et al., 2016, Lin et al., 2020). A single-crystal study further resolved a two-step sequence: a transition at 63 K into a two-dimensional long-range ordered state characterized by Bragg rods at the six M-points, followed by a 64 ordering transition at 65 K where sharp Bragg peaks at integer 66 appear (Chen et al., 2020). In contrast, the linear-spin-wave analysis of one powder INS study discussed zigzag order below 67 K (Songvilay et al., 2020). The literature therefore supports the existence of multiple thermodynamic and magnetic scales rather than a universally agreed single 68.
The detailed microscopic structure is also debated. The conventional assignment is a collinear zigzag state, but single-crystal INS and diffraction arguments have been used to support a triple-69 description in which the three zigzag ordering vectors 70, 71, and 72 superpose, giving a larger magnetic Brillouin zone and preserving 73 in a way not expected for single-domain zigzag order (Chen et al., 2020). A later single-crystal neutron diffraction study described the zero-field order as a triple-74-type zigzag structure with 75 (Bera et al., 2023). By contrast, an out-of-plane field study described the zero-field state as a canonical ferrimagnetic state with canted Co moments along the 76-axis (Zhang et al., 2024). Taken together, these results show that the existence of long-range order is not controversial, but its detailed symmetry content remains unsettled.
4. Excitation spectrum from meV to crystal-field scales
Powder INS first established that the ordered state supports gapped low-energy modes emerging from 77 Å78, a flat band near 79 meV, additional weaker flat bands near 80 and 81 meV, and residual magnetic intensity up to about 82 meV (Songvilay et al., 2020). Another powder study in the 83–84 meV window found dispersive magnons with a minimum gap of about 85 meV at the M point, while high-field ESR observed three AFMR modes 86, 87, and 88 with a zero-field gap 89 meV and an emergent mode 90 above 91 T with slope 92 meV/T and 93 (Lin et al., 2020). A later neutron/ESR study instead described a zero-field gap of about 94 meV, consistent with 95 GHz (Bera et al., 2023).
High-resolution single-crystal INS substantially complicated this picture. At 96 K, at least six non-overlapping spin-wave branches were resolved between 97 and 98 meV, and the lowest mode was reported to have minima of 99 meV at both M and 00, which the authors argued is incompatible with simple nearest-neighbor Kitaev-zigzag scenarios (Yao et al., 2022). In an effective fit restricted to the lowest branch, they obtained 01 meV and 02 meV, promoting the third-neighbor distance as an emergent “soft link” (Yao et al., 2022). This was used to argue that all then-available powder-based HK03 parameterizations fail to reproduce the full branch multiplicity and 04-dependence.
The low-energy magnons coexist with higher-energy orbital and crystal-field excitations. Neutron spectroscopy identified a spin-orbit transition from 05 to 06 near 07 meV in one study and two bands around 08 meV and 09–10 meV in another (Songvilay et al., 2020, Yao et al., 2022). Raman spectroscopy extended this hierarchy to much higher energies, reporting broad features at 11 meV and 12 meV that sharpen and shift below the 13 ordering transition, together with a weaker feature at 14 meV; these were assigned to spin-orbit excitons and multi-phonon processes aided by orbital fluctuations (Chen et al., 2020). A later Raman study further reported low-temperature crystal-field excitations at 15 cm16, 17 cm18, 19 cm20, 21 cm22, and 23 cm24, including a 25 cm26 splitting of a Kramers doublet (Chakkar et al., 6 Feb 2025).
Above 27, the excitation spectrum remains far from featureless. Single-crystal INS found that finite-energy correlations persist up to 28, with dynamic intensity remaining concentrated around the M points and equal-time structure factors describable by a single Co29 hexagon in zigzag-type or noncollinear “tornado-like” arrangements (Yao et al., 2022). This suggests that local hexagonal-cluster correlations survive well into the paramagnetic regime, constraining theories that attempt to identify the material solely through its ordered state.
5. Field-induced phase structure and candidate disordered regimes
The field response is strongly anisotropic. For fields perpendicular to the 30 axis, one thermodynamic/INS/ESR study reported a coexistence regime for 31, a field-induced spin-disordered regime for 32, suppression of long-range zigzag order at 33 T, crossover to a fully polarized state at 34 T, and full saturation near 35 T (Lin et al., 2020). In that regime, heat-capacity anomalies are suppressed, 36 peaks near 37 T, 38 becomes nearly temperature-independent below 39 K, and ESR shows the additional mode 40, all interpreted as hallmarks of a QSL-like intermediate state.
More recent angle-resolved work for 41 sharpened this interpretation. Torque magnetometry, INS, and variational Monte Carlo identified 42 T, 43 T, and 44 T, with a zigzag AFM phase below 45, a coexistence “X-phase” between 46 and 47, a partially polarized quantum spin liquid for 48, and a trivial polarized state above 49 (Lin et al., 2024). Two specific observations were emphasized: the restoration of the honeycomb in-plane point-group symmetry in the torque signal, through the emergence of a dominant sixfold component 50, and an INS spectrum at 51 T showing coexisting low-energy magnon-like bands and a broad 52–53 meV continuum across the Brillouin zone. These were taken as evidence for a field-induced, partially polarized 54 QSL.
Single-crystal neutron diffraction for in-plane fields 55 and 56 yielded a somewhat more conventional sequence. At 57 K, the AFM Bragg intensity at the M points begins to drop sharply near 58 kOe, marking a transition from collinear zigzag to a canted zigzag state in which each Co moment tilts by approximately 59–60 toward the field. Between 61 and 62 kOe, the AFM peaks extrapolate toward zero while the nuclear 63 peak grows only to about half of its expected saturation intensity, leading to a “near-polarized” regime with residual AFM correlations. Above 64 kOe, a fully polarized state with 65 is reached (Bera et al., 2023). The same study also found a distinct 66 transition near 67 kOe through complete softening of one AFMR mode.
Out-of-plane fields reveal still different scales. One high-field study mapped four ordered phases for 68: phase I below 69, a 70-plateau-like phase II below 71 K between 72 and 73 T, a canted phase III up to 74, and a fully polarized phase IV above 75 T at 76 K (Zhang et al., 2024). That work interpreted the data with an XXZ model plus single-ion anisotropy and only small 77 and 78, rather than a dominantly Kitaev model.
Not all local-probe studies support a field-induced disordered phase in the experimentally accessible 79 T regime. A 80Na NMR study explicitly concluded that a spin-disordered phase does not appear up to 81 T: the low-temperature line width grows faster than the bulk magnetization, the hyperfine shift deviates from linear 82-83 scaling, and residual staggered hyperfine fields remain visible, all interpreted as evidence that long-range order persists to at least 84 T (Kikuchi et al., 2022). The present literature therefore contains a genuine controversy: some probes identify a field-induced QSL or QSL-like window, while others find field-evolved but still ordered magnetism over overlapping field ranges.
6. Thermal Hall response, local probes, and competing interpretations of the low-temperature state
Thermal transport has provided two distinct but not identical pictures. In one study of in-plane fields, a finite planar thermal Hall conductivity 85 was observed only below 86, with 87 peaking around 88–89 K and vanishing as 90, behavior identified with bosonic rather than Majorana carriers (Takeda et al., 2022). For 91, 92 changes sign at 93 T and again at 94 T; for 95, a sharp hysteretic negative peak appears at 96 T and 97 remains finite up to the highest measured fields below saturation. This was interpreted as evidence for topological magnons and, for 98, as proof of a magnetically ordered phase that spontaneously breaks the twofold rotation 99, because planar Hall transport would otherwise be symmetry-forbidden.
A later ac-plane field-angle study focused instead on the phonon thermal Hall effect and compared Na00Co01TeO02 with nonmagnetic Na03Zn04TeO05. There, the angular dependence of 06 was found to closely follow the out-of-plane magnetization 07, supporting an extrinsic impurity-induced skew-scattering mechanism rather than a dominant intrinsic phonon-Berry-curvature mechanism (Yan et al., 16 Sep 2025). At 08 K and 09 T, that work reported 10, 11, and a thermal Hall angle 12. The two thermal-Hall interpretations are not formally identical, since one concerns topological magnons in ordered in-plane phases and the other phonon Hall transport in a different geometry, but together they show that both magnonic and phononic Hall channels are actively discussed.
NMR adds another layer of complexity. A 2024 13Na study at 14 T and 15 T found that the center of gravity of the 16 distribution follows the pure-Kitaev form
17
with 18 and 19 K at 20 T, and that the same concave form fits the low-temperature data even at 21 T below the AFM transition (Papawassiliou et al., 2024). Yet below about 22 K, the 23 and 24 distributions broaden dramatically and split into fast and slow components spanning more than 25–26 orders of magnitude. The slow sector shows Arrhenius slowing,
27
with 28 K and 29, and the authors interpret this as a dynamically heterogeneous quantum spin glass rather than a spatially uniform QSL (Papawassiliou et al., 2024).
Muon probes similarly emphasize persistent dynamics inside the ordered regime. One 30SR study found that even well below 31, a dynamic fraction 32–33 remains, with a stretch exponent 34 below 35 and correlation times 36–37 s derived from longitudinal-field decoupling (Miao et al., 2023). A later neutron+38SR work reported a nearly temperature-independent low-39 longitudinal relaxation rate 40, attributed to strong quantum fluctuations and frustrated Kitaev interactions, and showed that an in-plane magnetic field broadens the spin-wave gap at the K point from about 41 meV to about 42 meV between 43 and 44 T (Lin et al., 2023). These observations are difficult to reconcile with a purely static classical zigzag antiferromagnet.
Raman spectroscopy extends the discussion to higher temperatures and additional broken-symmetry channels. A 2025 single-crystal Raman study reported anomalies at 45 K, a spin-reorientation scale 46 K, a ferroelectric transition 47 K, and a crossover near 48 K from a pure paramagnetic phase to a quantum paramagnetic phase, all inferred from phonon self-energies, a low-frequency Fano mode near 49 cm50, quasi-elastic scattering, and a broad magnetic continuum between 51 and 52 cm53 (Chakkar et al., 6 Feb 2025). This suggests that the correlated regime extends to temperatures far above the conventional AFM transition and may involve coupled spin, lattice, and orbital sectors.
Across these probes, a consistent minimal statement is possible. Na54Co55TeO56 supports static magnetic order at low field and low temperature, but that order coexists with unusually strong low-energy dynamics, broad continua, metastability, and pronounced sensitivity to field direction. The unresolved questions are whether the intermediate-field state is best viewed as a partially polarized 57 QSL, a correlated spin-disordered regime, a canted or near-polarized ordered phase, or a dynamically heterogeneous state with quantum-glassy sectors. The present body of work suggests proximity to the Kitaev limit, but not a consensus on how that proximity is realized microscopically.
