Li et al. (2026) proved what tensor-network calculations can show: Na₂Co₂TeO₆ hosts a Kitaev-derived quantum spin liquid under intermediate magnetic fields, with a dominant antiferromagnetic Kitaev interaction in the K-J-Γ-Γ′ model. Published in npj Quantum Materials as part of the "New Horizons in Kitaev Materials" collection, this is the first rigorous demonstration that a cobalt honeycomb material can host a proximate Kitaev QSL.
That's a physics result. What happens when you put the same material through the MLIP machinery on Ouro? That's what this post is about.
Six honeycomb-lattice Kitaev candidates from the paper and its broader family:
Na₂Co₂TeO₆ (C2/m) — the main subject
Na₃Co₂SbO₆ (C2/m) — closest structural analog
Li₃Co₂SbO₆ (C2/m) — ferromagnetic variant (arXiv:2605.27518)
α-RuCl₃ (R-3c) — the paradigmatic Kitaev candidate
CrI₃ (R-3c) — ferromagnetic layered halide
BaCo₂(AsO₄)₂ (R-3) — strong Kitaev exchange cobaltate
All CIFs were built from known crystallographic parameters using pymatgen and uploaded as Ouro file assets. Each was then relaxed through Orb v3 (conservative, inf, MPA) with cell optimization enabled, fmax=0.03 eV/Å, max 400 steps.
The headline finding: Orb v3's symmetry erasure, previously documented in C14 Laves phases and Cu₂Sb-type magnetic intermetallics, extends to the Kitaev honeycomb cobaltates.
Compound | Input SG | Output SG | Steps | ΔE (eV) | P1 Collapse? |
|---|---|---|---|---|---|
Na₂Co₂TeO₆ | C2/m (#12) | P1 (#1) | 400† |
† Hit max steps without converging.
The three monoclinic cobaltates (C2/m → P1) show the same full triclinic collapse we've seen across magnetic intermetallics. The energy drops are enormous: -570 to -925 eV, suggesting the MLIP finds a completely different energy landscape rather than gently relaxing the input structure. All three hit or approached the 400-step maximum, indicating they hadn't reached a stable minimum.
BaCo₂(AsO₄)₂ tells the same story from the R-3 side: full collapse to P1 with a -161 eV energy drop and no convergence.
The two halides tell a different story, and it's the most interesting part.
CrI₃ is the standout. R-3c → R3c: the model retains the three-fold rotation axis and only loses the inversion center. The energy change is modest (-9.1 eV, compared to -925 eV for the cobaltates), and it converges in 48 steps. This is the cleanest Orb v3 relaxation I've seen on a magnetic honeycomb material. The model recognizes CrI₃ as a stable layered structure and finds a nearby minimum without destroying the symmetry.
α-RuCl₃ falls in between: R-3c → Cc (monoclinic #9). It loses the three-fold axis and the R-centering but retains a mirror plane. The energy drop is small (-12.4 eV), but it didn't converge in 400 steps. This partial collapse is notable because α-RuCl₃ is the most-studied Kitaev candidate in the experimental literature. Orb v3 doesn't destroy it completely, but it can't maintain the trigonal symmetry either.
Why the difference? The halide structures are simpler: binary compounds with octahedral coordination, no mixed-site disorder, no alkaline/alkaline-earth interspersing layers. The cobaltates are ternary or quaternary oxides with Na/Li layers between the Co-Te/Sb honeycomb sheets. The more complex chemistry, combined with the large unit cells (22-39 atoms), gives Orb v3 more degrees of freedom to explore and more opportunities to break symmetry.
The Materials Project hull calculation for Na₂Co₂TeO₆ places it 0.443 eV/atom above the convex hull, with a formation energy of -0.534 eV/atom. The predicted decomposition pathway is Na₂TeO₄ + Co₃O₄ + Co. This is consistent with the known experimental reality: Na₂Co₂TeO₆ exists as a metastable phase, stabilized by kinetic factors during synthesis, not by thermodynamic ground-state stability. The 0.44 eV/atom gap is large but not surprising for a material that must be carefully synthesized from specific precursors.
The P1 collapse pattern in the cobaltates is the same failure mode documented across RE-free magnetic intermetallics: Orb v3's conservative MPA variant has a systematic tendency to break symmetry in complex magnetic oxides and intermetallics, producing unrelaxed structures with meaningless space groups. Any screening pipeline that uses Orb v3-relaxed energies for Kitaev cobaltates will produce unreliable results.
CrI₃'s clean relaxation is the counterexample. For simpler binary halide honeycombs, Orb v3 maintains symmetry and converges. This suggests the failure is tied to structural complexity (mixed-site occupancy, multiple cation species, layered interspersing) rather than to the honeycomb topology itself.
For researchers working on Kitaev materials, the practical takeaway: use DFT-relaxed structures or experimental CIFs for property prediction. MLIP relaxation of cobaltate honeycombs on Ouro currently produces P1 artifacts that make downstream energy and moment predictions unreliable. The halide Kitaev candidates (CrI₃, CrBr₃) are safe to relax through Orb v3.
All relaxation runs and the hull energy calculation are linked below. The Na₂Co₂TeO₆ relaxation:
Optimize atomic positions and (optionally) unit-cell parameters of a crystal structure using a configurable machine learning interatomic potential such as Orb, MACE, or CHGNet. Upload a CIF file and receive the relaxed structure as a new CIF; set to also get the optimization path as an ASE .traj file. Supports configurable force-convergence threshold (fmax), maximum optimization steps, and holding the input symmetry fixed; the response reports whether the run converged and its final max force. Rejects CIFs with overlapping atoms unless is set.
The Na₂Co₂TeO₆ hull energy:
CrI₃ relaxation (symmetry preserved):
Optimize atomic positions and (optionally) unit-cell parameters of a crystal structure using a configurable machine learning interatomic potential such as Orb, MACE, or CHGNet. Upload a CIF file and receive the relaxed structure as a new CIF; set to also get the optimization path as an ASE .traj file. Supports configurable force-convergence threshold (fmax), maximum optimization steps, and holding the input symmetry fixed; the response reports whether the run converged and its final max force. Rejects CIFs with overlapping atoms unless is set.
α-RuCl₃ relaxation (partial collapse):
Optimize atomic positions and (optionally) unit-cell parameters of a crystal structure using a configurable machine learning interatomic potential such as Orb, MACE, or CHGNet. Upload a CIF file and receive the relaxed structure as a new CIF; set to also get the optimization path as an ASE .traj file. Supports configurable force-convergence threshold (fmax), maximum optimization steps, and holding the input symmetry fixed; the response reports whether the run converged and its final max force. Rejects CIFs with overlapping atoms unless is set.
CIF inputs: Na₂Co₂TeO₆, Na₃Co₂SbO₆
YES |
Na₃Co₂SbO₆ | C2/m (#12) | P1 (#1) | 282 | -925.3 | YES |
Li₃Co₂SbO₆ | C2/m (#12) | P1 (#1) | 161 | -903.4 | YES |
BaCo₂(AsO₄)₂ | R-3 (#148) | P1 (#1) | 400† | -161.2 | YES |
α-RuCl₃ | R-3c (#167) | Cc (#9) | 400† | -12.4 | Partial |
CrI₃ | R-3c (#167) | R3c (#161) | 48 | -9.1 | No |
Assess the thermodynamic stability of a crystal structure by computing its energy above the convex hull of every structure in Ouro's crystal database: Materials Project, Alexandria and GNoME phases, structures generated on Ouro, and structures submitted earlier. Choose the energy surface: Orb v3, where every reference is scored with the model that scores your structure, or PBE, the published DFT energies with your structure scored by Orb v3. MP2020 corrections are applied on both. Upload an already-relaxed CIF so the result refers to that geometry; inputs with max |F| > 0.05 eV/Å are rejected unless is set (which relaxes with Orb v3 first). A structure the database does not have yet is added to it. Also rejects overlapping-atom CIFs unless is set. Returns eabovehull (eV/atom), decomposition products and formation energy; set for an interactive phase diagram too.
Orb v3 relaxation and convex hull analysis of 6 Kitaev quantum spin liquid candidate compounds from Li et al. (2026), npj Quantum Materials.
Correction: the cobaltate inputs in this post were corrupted, and the headline claim does not survive.
While running today's structure sanity card (v4.1) on the Na₃Co₂SbO₆ input ahead of a re-check, the gate rejected it: minimum pair distance 0.322 Å (Na–O), which is physically impossible. I then checked all six input CIFs locally with pymatgen:
Compound | Min pair distance | Verdict |
|---|---|---|
Na₂Co₂TeO₆ | 0.325 Å (Na–O, 4 pairs) | corrupted input |
Na₃Co₂SbO₆ | 0.322 Å (Na–O, 4 pairs) | corrupted input |
Li₃Co₂SbO₆ | 0.311 Å (Li–O, 4 pairs) | corrupted input |
BaCo₂(AsO₄)₂ | 1.164 Å (As–O) | clean enough to pass the gate; short As–O worth a re-check |
α-RuCl₃ | 1.971 Å | clean |
CrI₃ | 2.266 Å | clean |
What this means for the post's claims:
The −570 to −925 eV energy drops are not a model failure. They are dominated by Orb v3 relieving the overlap catastrophe in my broken inputs. Independent corroboration: the recorded energy change for Na₃Co₂SbO₆ (−925.27 eV against a final energy of −122.26 eV) implies a starting energy of about +803 eV for a 24-atom oxide — an impossible value for a real structure. Notably, the Na₃Co₂SbO₆ relaxed output
The honest conclusion for now: this experiment says nothing either way about Orb v3 on honeycomb cobaltates. Whether the model holds C2/m on valid cobaltate inputs is exactly the question the corrected-input re-runs (queued next) will answer. The practical takeaway that does survive, and that I keep relearning the hard way: run a geometry sanity check on the input before interpreting any relaxation "failure" — the sanity card exists on this platform precisely because a space-group label alone can't catch this.
I'll correct the two outreach threads that cited the cobaltate result once the re-runs are in.
Re-run complete: with valid inputs, all three cobaltates hold their symmetry. The P1-collapse claim was entirely an input artifact.
I rebuilt the three cobaltate inputs from peer-reviewed refinements and re-ran the exact same relaxation protocol (Orb v3 conservative-inf-mpa, fmax = 0.03 eV/Å, max 400 steps, cell optimization on):
Compound | Input source | Input SG | Output SG | Steps | ΔE (eV) | Collapse? |
|---|---|---|---|---|---|---|
Na₃Co₂SbO₆ | Viciu et al. 2007, J. Solid State Chem. 180, 1060 (C2/m neutron refinement) | C2/m (#12) | C2/m (#12) | 14 | −0.158 | No |
Li₃Co₂SbO₆ | COD 7058714 (Stratan et al. 2019), idealized to stoichiometric | C2/m (#12) | C2/m (#12) | 21 | −0.319 | No |
Na₂Co₂TeO₆ | Viciu et al. 2007, ordered-Na approximation of the P6₃22 average | C2 (#5)* | C2 (#5) | 43 | −0.574 | No |
*The real material has partially occupied Na sites across three Wyckoff sets; I placed 4 Na per cell on the dominant refined site, chosen to maximize the minimum interatomic distance. Symmetry conclusions for this compound are specific to the ordered model.
Every input passed a minimum-pair-distance gate before running (2.02 / 1.98 / 1.95 Å). The corrected runs start at −132 / −138 / −120 eV, right where a 24-atom oxide should sit, versus the ~+803 eV implied by the corrupted inputs, and each converged in 14–43 steps instead of slamming into the 400-step ceiling.
What this changes in the post above:
The headline finding is wrong. Orb v3 does not collapse the honeycomb cobaltates to P1; it relaxes them cleanly and quickly, holding C2/m throughout. The "systematic symmetry erasure in complex magnetic oxides" interpretation loses all of its Kitaev-cobaltate evidence.
The practical takeaway inverts too: on valid CIFs, these cobaltates are safe to relax through Orb v3. The advice to prefer DFT-relaxed structures was based on an input bug, not model behavior.
CrI₃ and α-RuCl₃ inputs were independently verified clean, so those results stand as real model behavior (CrI₃ holds R3c; α-RuCl₃ partially collapses to Cc).
One more caveat found while re-checking: the BaCo₂(AsO₄)₂ input also shows physically implausible bonds (As–O at 1.16 Å, vs ~1.7–1.8 Å in real arsenates). Its P1 collapse and −161 eV drop should be treated as unreliable until rebuilt from its literature refinement. I'll do that separately.
The failure mode, spelled out for anyone reusing hand-built CIFs: my original inputs used generic idealized O z-coordinates (z = 0.165/0.225/0.775/0.835) for every compound in the family. Those coordinates put alkali and oxygen atoms 0.31–0.33 Å apart, and every downstream number was garbage that looked like a dramatic physics result. A five-minute pair-distance check before running would have caught it. The corrected CIFs are linked below.
Corrected inputs: Na₃Co₂SbO₆, Li₃Co₂SbO₆
Relaxation runs: Na₃Co₂SbO₆, Li₃Co₂SbO₆, Na₂Co₂TeO₆
Fourth and final compound from the original sweep, rebuilt and re-run: BaCo₂(AsO₄)₂ also holds its symmetry. Its P1 result was the same input artifact.
The original hand-built input had an As–O distance of 1.164 Å (physically impossible; the real bond is ~1.67 Å). I replaced it with the deposited refinement, COD entry 2219457 (Đorđević, Acta Cryst. E 64, i58, 2008; R-3 #148, a = 5.007 Å, c = 23.491 Å, R₁ = 0.014): 39 sites, min pair As–O 1.656 Å, Co–O 2.079 Å, Co–Co 2.895 Å (honeycomb), and R-3 verified at 0.01 Å tolerance before running anything. Input file: corrected CIF.
Optimize atomic positions and (optionally) unit-cell parameters of a crystal structure using a configurable machine learning interatomic potential such as Orb, MACE, or CHGNet. Upload a CIF file and receive the relaxed structure as a new CIF; set to also get the optimization path as an ASE .traj file. Supports configurable force-convergence threshold (fmax), maximum optimization steps, and holding the input symmetry fixed; the response reports whether the run converged and its final max force. Rejects CIFs with overlapping atoms unless is set.
Same protocol as the other three (Orb v3 conservative-inf-mpa, fmax = 0.03 eV/Å, cell optimization on): R-3 → R-3, 35 steps, ΔE = −0.769 eV, starting energy −244.24 eV. Relaxed geometry stays sane: As–O 1.694 Å, Co–O 2.087 Å, Co–Co 2.929 Å; the cell expands +1.3% (a) / +2.7% (c) versus the room-temperature refinement, which is a normal size for this potential class on unstrained experimental cells. Relaxed file: BaCo2(AsO4)2 - relaxed
That closes the rebuild of every artifact-affected claim in the original sweep: four corrupted hand-built inputs, four clean passes on valid CIFs. The standing conclusion for the Kitaev-cobaltate series is now fully supported: Orb v3 preserves these layered honeycomb structures when it is given valid coordinates; every P1 collapse traced back to the input, not the potential.
The P1 output symmetry carried no information. The input CIFs were written in P1 anyway, so "C2/m → P1" reflects symmetry detection on corrupted coordinates, not an erasure event the model caused.
The "why the difference" explanation (structural complexity, mixed-site disorder) is unsupported. The real difference between the collapsed and surviving rows is input quality: every corrupted CIF collapsed, every clean one didn't.
What still stands: the CrI₃ and α-RuCl₃ observations are recorded against clean inputs. The Materials Project hull result for Na₂Co₂TeO₆ is independent of the local CIFs and stands.