Origin of $A$-type antiferromagnetism and chiral split magnons in altermagnetic $\alpha$-MnTe

Alireza Qaiumzadeh; Andrzej Ptok; Artem R. Oganov; Mojtaba Alaei; Nafise Rezaei; Pawel Sobieszczyk

REVIEW 3 major objections 5 minor 1 cited by

Origin of $A$-type antiferromagnetism and chiral split magnons in altermagnetic $\alpha$-MnTe

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read With ~60 magnetic configurations instead of 18, density-functional theory gives α-MnTe a ferromagnetic in-plane exchange, resolving a dispute with experiment.

desk verdict The J2 sign flip is plausible but not yet bulletproof, while the chiral magnon mechanism via J10 is solid and worth citing. read the letter →

arxiv 2411.11985 v3 pith:ZO2Z2EGN submitted 2024-11-18 cond-mat.mtrl-sci cond-mat.mes-hall

Mojtaba Alaei , Pawel Sobieszczyk , Andrzej Ptok , Nafise Rezaei , Artem R. Oganov , Alireza Qaiumzadeh This is my paper · ORCID

classification cond-mat.mtrl-scicond-mat.mes-hall

keywords altermagnetismα-MnTeA-typeantiferromagnetismHeisenbergexchangeinteractionchiralmagnonsplittingDFT+Utotal-energymappingpressuretuningmagneticconfigurationconvergence

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper targets a specific contradiction in the altermagnetic semiconductor $\alpha$-MnTe: experiments say the in-plane magnetic exchange $J_2$ is ferromagnetic, while earlier density-functional calculations found it antiferromagnetic. The authors argue that the old calculations simply used too few magnetic configurations, and show that fitting about 60 spin arrangements to a classical Heisenberg model makes $J_2$ positive and small, matching measurement. That single sign change removes the need for a strong third-neighbor exchange to stabilize the A-type antiferromagnetic order. The same fitted model attributes the experimentally observed chiral splitting of magnon bands to a direction-dependent tenth-neighbor exchange, and predicts that compressive pressure substantially enhances both spin and chiral magnon splittings and raises the Néel temperature.

What carries the argument

The load-bearing object is the total-energy mapping from ~60 (ambient pressure) or ~120 (15 GPa) self-consistent DFT+U spin configurations onto the classical Heisenberg Hamiltonian $H = -\sum_{i<j} J_{ij}\,\hat{\mathbf{S}}_i\cdot\hat{\mathbf{S}}_j$ with exchange interactions out to the 16th nearest neighbor. The sign of $J_2$ is shown to depend on the number of configurations included: with 18 configurations it is antiferromagnetic, and it crosses to ferromagnetic and stabilizes only as the count grows. A minimal supercell construction, the 34-Mn-atom SUPERHEX cell, makes the large configuration set computationally tractable. The direction-dependent tenth-neighbor pair $J_{10,a}$ and $J_{10,b}$ is the specific mechanism that carries the chiral magnon splitting.

What would settle it

If a different selection of ~60 magnetic configurations at the same DFT+U level yields $J_2 < 0$, or if re-fitting the experimental magnon data with all 16 exchange parameters still gives an antiferromagnetic in-plane coupling, the central claim collapses; a direct check is to plot $J_2$ versus the number of configurations for several independent random subsets and look for sign stability.

Watch

Extended reading notes

Core claim

The paper's central claim is that with a sufficient number of magnetic configurations (~60), the least-squares map of DFT+U total energies onto a 16-parameter classical Heisenberg Hamiltonian yields a ferromagnetic in-plane second-nearest-neighbor exchange $J_2 = +0.17$ meV at ambient pressure, in agreement with experiments and in contrast to earlier DFT results. The correct sign of $J_2$, together with a large antiferromagnetic $J_3$, stabilizes the collinear A-type antiferromagnetic ground state. The paper also identifies the tenth-neighbor exchange as two distinct values $J_{10,a} = -0.28$ meV and $J_{10,b} = +0.09$ meV whose directional anisotropy produces the observed nonrelativistic chiral splitting of magnon bands. Under a compressive pressure of 15 GPa, $J_2$ reverses sign but the A-type order persists, while the spin subband splittings grow roughly 35–70% and the Néel temperature roughly doubles.

Load-bearing premise

The result rests on the assumption that least-squares fitting roughly 60 DFT+U total energies to a 16-parameter Heisenberg Hamiltonian gives a converged and unique set of exchange couplings, so the sign flip in $J_2$ reflects physics rather than an accident of configuration selection; the Hubbard $U = 4$ eV value is a secondary load-bearing input.

Editorial extensions

If this is right

The A-type antiferromagnetic ground state of $\alpha$-MnTe is controlled by a small positive in-plane $J_2$ plus a large negative interlayer $J_3$, not by a frustrated antiferromagnetic $J_2$ as previously inferred.
Chiral magnon splitting in $\alpha$-MnTe is a nonrelativistic effect arising from the spatial anisotropy of the tenth-neighbor exchange, not from spin-orbit coupling.
A compressive pressure of 15 GPa reverses the sign of $J_2$ while preserving the A-type order, and it increases the electronic spin splittings by 35–70% and roughly doubles the Néel temperature.
Reliable exchange parameters in complex antiferromagnets require convergence checks against the number of magnetic configurations; small sets can flip signs.
The computed chiral magnon splitting is 1.5 times larger than the five-parameter experimental fit, indicating that model fits to neutron data need more exchange terms than previously used.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same configuration-convergence check should be applied to other altermagnetic candidates, where published exchange couplings may come from under-sampled fits.
Because the ambient-pressure $J_2$ is small (+0.17 meV), modest strain, doping, or pressure gradients may drive $\alpha$-MnTe toward a frustrated or different ordered state, offering a route to magnetic phase engineering.
Reporting exchange couplings only after demonstrating stability against both the number and the choice of magnetic configurations would make future total-energy-mapping studies more reproducible.
If direction-dependent exchange anisotropy of this kind is the generic source of chiral magnons in altermagnets, then magnonic altermagnetism should be expected in any centrosymmetric antiferromagnet whose exchange network contains inequivalent tenth-neighbor bonds, not just MnTe.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Bottom line: this paper gives a plausible resolution of the J2 sign controversy in α-MnTe and provides the first ab initio identification of the direction-dependent J10 exchange as the source of the measured chiral magnon splitting. The J2 story is not yet airtight, but the chiral magnon part is solid and the paper is honest about its quantitative mismatches.

What's genuinely new: the demonstration that the fitted J2 flips from AFM to FM when the number of magnetic configurations grows from 18 to ~60. That is a concrete methodological insight, not just a rehash. The use of SUPERHEX to build a 34-atom cell is clever and makes the 60-configuration fit feasible. The J10,a/J10,b asymmetry, with opposite signs, matches the experiment and appears robust. The pressure calculations are a natural extension: a 70% increase in spin splitting, larger chiral splitting, and a TN that roughly doubles are testable predictions.

Where I'd push back: the paper never shows the configuration list, the fit residuals, or any resampling check. J2 is +0.17 meV, about two orders of magnitude smaller than J1 and twenty times smaller than J3. Someone could select a different set of 60 configurations and plausibly get the opposite sign. The U=4 eV choice comes from a benchmarking paper by one of the authors; a short U-sweep would settle whether the small positive J2 survives. The pressure result that the ground state stays A-type even after J2 turns negative is counter-intuitive; the authors say it's due to large J3, but the main text doesn't show the evidence — that lives in the SM. These are fixable reporting gaps, not signs of a broken calculation.

The stress-test note worries that the sign flip's sensitivity is demonstrated, not refuted, by Fig. 1(b). I think that's fair, but it's a reason to demand more detail, not to reject the paper. The comparison with experiment for J1, J3, and J10 is decent, and the authors explicitly flag that TN is 20–50 K low and chiral splitting is 1.5× too large. They aren't overselling.

Who should read this: anyone working on altermagnets or on exchange-parameter extraction from DFT. The methodological warning about configuration convergence is the kind of thing that should be disseminated widely. I'd bring it to a reading group and cite it if I worked on MnTe.

Recommendation: send to peer review. No desk reject. The referees should ask for the configuration set, residuals, a U-dependence check, and the SM evidence for the pressure ground state.

Referee Report

3 major / 5 minor

Summary. The paper addresses two open questions for the altermagnetic semiconductor α-MnTe: the origin of its A-type antiferromagnetic order and the microscopic mechanism of chiral splitting in its magnon spectrum. Using DFT+U total energies from roughly 60 magnetic configurations in a 34-atom SUPERHEX supercell, the authors fit a classical Heisenberg Hamiltonian with exchange interactions up to the 16th nearest neighbor. They obtain a positive (ferromagnetic) in-plane second-nearest-neighbor exchange J2 at ambient pressure, in contrast to earlier DFT studies and in agreement with experiment, and they attribute the previous discrepancy to an insufficient number of magnetic configurations. They further find that the 10th nearest-neighbor exchange splits into two inequivalent couplings J10,a and J10,b, which they identify as the source of the nonrelativistic chiral magnon splitting measured recently. They also predict that 15 GPa compressive strain enhances the spin splitting, chiral magnon splitting, and Néel temperature, while reversing the sign of J2 without changing the A-type ground state.

Significance. If the central fitting result is robust, the paper resolves a long-standing sign discrepancy in α-MnTe and makes a methodological point that should influence future exchange-mapping studies in complex antiferromagnets: convergence with respect to the number of magnetic configurations must be demonstrated. The identification of J10,a and J10,b as the source of chiral magnon splitting is a concrete and useful result, and the strain predictions provide falsifiable targets for experiment. The paper also showcases the computational efficiency of the SUPERHEX approach and provides a complete table of computed exchange parameters (Table I) with explicit comparisons to experiment. However, the main quantitative claim currently lacks the diagnostics needed to establish robustness, and the paper's own acknowledgments of quantitative discrepancies (TN about 20-50 K below experiment, chiral splitting 1.5 times larger than experiment) underline the need for a more careful uncertainty analysis.

major comments (3)

[Normalized Heisenberg exchange interactions; Fig. 1(b)] The central claim that the in-plane exchange J2 is ferromagnetic at ambient pressure rests on a least-squares fit of approximately 60 DFT total energies to a 16-parameter classical Heisenberg Hamiltonian, but the manuscript reports no residuals, no list or selection criterion for the magnetic configurations, and no resampling or conditioning analysis. Because Fig. 1(b) itself shows that the sign of J2 changes when the number of configurations is increased from 18, the possibility that the sign is sensitive to the specific subset of configurations, or to correlations imposed by the 34-atom SUPERHEX cell, rather than to the count is not excluded. Please provide the full configuration set, fit residuals, a leave-one-out or bootstrap stability test, and a check with an independently generated set of configurations. Without these diagnostics, the positive J2 = 0.17 meV, which is two orders of magnitude smaller than J1, is not established as a converged result.
[Computational methods; Hubbard U] The Hubbard U = 4 eV is adopted from Ref. [55] without any sensitivity check. Since J2 = +0.17 meV at ambient pressure is very small compared with J1 and J3, and since DFT+U double-counting corrections can shift small exchange couplings by several tenths of an meV, the sign of J2 could depend on the chosen U. Please report J2, and at least J1, J3, J10a, and J10b, for a range of U values (for example 3, 4, and 5 eV) at ambient pressure, or otherwise justify that the sign of J2 is stable with respect to this choice.
[Normalized Heisenberg exchange interactions; SUPERHEX] The exchange interactions are truncated at the 16th nearest neighbor and fitted with a 34-atom SUPERHEX supercell, but the paper does not demonstrate convergence with respect to the interaction range or the supercell size. Given the small magnitude of J2, truncation bias could also affect its sign. Please show how J2 changes when the number of exchange shells is increased beyond 16, or compare with a larger supercell for a representative subset of configurations, to rule out an artifact of the truncation or of the supercell geometry.

minor comments (5)

[Table I] Table I compares the present normalized exchange parameters Jn = S^2 Jtilde_n with experimental values from Ref. [49], but it is not stated whether the experimental values were also normalized by S^2 or are raw exchange constants from the five-parameter spin Hamiltonian; please clarify the normalization convention in the table caption.
[Computational methods] The number of magnetic configurations is given only as 'approximately 60' at ambient pressure and 'about 120' at 15 GPa; please give exact counts and describe how the configurations were generated, including any symmetry constraints or random sampling strategy.
[Normalized Heisenberg exchange interactions] The statement that the 3d-orbital occupancy of Mn2+ is 'approximately 5.3' is used to motivate the ferromagnetic in-plane exchange, but no source or computational method for this occupancy is given; please provide a reference or an explicit DFT population analysis.
[Magnon dispersion and magnetic susceptibility] The paper compares its calculated chiral magnon splitting and Néel temperature with experiment and finds discrepancies (splitting 1.5 times larger; TN about 20-50 K lower), but the discussion is qualitative; a brief sensitivity analysis using the experimental exchange parameters from Ref. [49] would clarify whether the discrepancies originate mainly from J1, from J10a/J10b, or from the simplified experimental model.
[Fig. 1(b)] The main panel of Fig. 1(b) lacks axis labels with units for the normalized exchange interaction, and the inset does not clearly distinguish the P = 0 and P = 15 GPa curves; please add labels and a legend.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the DFT total-energy mapping and the comparisons with experimental magnon data are independent; the only author-overlap citation is a Hubbard-U input parameter, not a fitted target.

full rationale

The derivation chain is self-contained: DFT+U total energies for approximately 60 magnetic configurations (120 at 15 GPa) are fitted by least squares to the classical Heisenberg Hamiltonian H = -Σ Jij Ŝi·Ŝj, yielding J1 through J16 (Computational methods section and Table I). The central claimed prediction, J2 > 0 at ambient pressure, is obtained from total-energy mapping rather than from the experimental magnon data of Ref. [49]; the comparison with experiment is therefore an external benchmark, not a fitted input. Similarly, the chiral-splitting result follows from the fitted directional values J10,a and J10,b used in the spin Hamiltonian, and the computed magnon splitting is subsequently compared with, not fitted to, the measured chiral splitting. The Néel temperature is obtained by Monte Carlo from the same fitted exchanges together with an experimentally adopted anisotropy K = 6.25 meV, so it is also an independent prediction rather than a restatement of an input. The only author-overlap citation is U = 4 eV from Ref. [55] (same first author), used as a Hubbard parameter; the present paper does not tune U to the experimental quantities it later compares against, so this is a parameter provenance choice rather than a circular reduction. The reviewer concern that the small fitted value J2 = +0.17 meV might depend on the particular set of magnetic configurations is a robustness and correctness question, not a circularity: no equation in the paper defines J2 in terms of the experimental exchange value or of the measured chiral splitting.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The paper's conclusions rest on the validity of the Heisenberg mapping, the DFT+U approximation with a fixed U, and the convergence of the fit. These are domain assumptions, not established standards for MnTe. There are two fitted constants (U and K) imported from prior work.

free parameters (3)

U = 4 eV
Hubbard correction adopted from Ref. [55], a prior benchmarking paper by the same first author; not fitted in this work, but its value strongly affects exchange parameters.
K = 6.25 meV
Single-ion uniaxial magnetic anisotropy constant taken from Refs. [47,50]; entered into the spin Hamiltonian Eq. (1).
Range of exchange interactions = up to 16th nn
Choice of how many exchange parameters to include in the fit; affects the extracted J values.

assumptions (6)

domain assumption Classical Heisenberg Hamiltonian with bilinear exchanges up to 16th nn describes the magnetism of α-MnTe.
Total energy mapping assumes this model; the paper does not justify including further neighbor interactions or higher-order terms.
domain assumption DFT+U with U=4 eV gives accurate relative total energies for different spin configurations.
All exchange parameters derive from these energies; no validation against higher-level methods is shown.
domain assumption The least-squares fit with ~60 configurations yields a unique, converged set of exchange parameters.
Central methodological premise; the paper shows a sign flip with configuration count but no error analysis.
domain assumption Linear spin wave theory is sufficient for magnon dispersions.
Magnon spectra in Fig. 3 are computed from a spin wave Hamiltonian of Eq. (1); validity for this system is assumed.
domain assumption Atomistic spin dynamics Monte Carlo results determine the magnetic ground state and TN.
Used to claim the ground state remains A-type under pressure and to compute susceptibility.
domain assumption The experimental exchange parameters from Ref. [49] are reliable benchmarks, though they came from a 5-parameter fit.
The comparison in Table I treats them as ground truth, while the paper also criticizes their limited number of exchange terms.

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Cite this review

Pith. "Pith review of Origin of $A$-type antiferromagnetism and chiral split magnons in altermagnetic $\alpha$-MnTe." pith.science (2026). https://pith.science/paper/ZO2Z2EGN

@misc{pith2026241111985,
  author       = {Pith},
  title        = {Pith review of: Origin of $A$-type antiferromagnetism and chiral split magnons in altermagnetic $\alpha$-MnTe},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZO2Z2EGN}},
  note         = {Machine review of arXiv:2411.11985}
}

abstract

The origin of the $A$-type antiferromagnetic ordering, characterized by ferromagnetic layers coupling antiferromagnetically, in the prototype semiconductor altermagnet $\alpha$-MnTe has been a topic of ongoing debate. Experimentally, $\alpha$-MnTe exhibits an in-plane ferromagnetic exchange interaction, whereas previous \emph{ab initio} calculations predicted an antiferromagnetic interaction. In this paper, we resolve this discrepancy by considering an expanded set of magnetic configurations, which reveals a ferromagnetic in-plane exchange interaction in agreement with experimental findings. Additionally, we demonstrate that the 10th nearest-neighbor exchange interaction is directionally dependent, inducing a nonrelativistic chiral splitting in the magnon bands, as recently observed experimentally. We further show that applying a compressive strain may significantly enhance both nonrelativistic spin and chiral magnon splittings. The strain can also change the sign of the in-plane exchange interaction. Computing magnetic susceptibility, we show that strain enhances the N{\'e}el temperature, significantly. Our results highlight the critical importance of convergence in the number of magnetic configurations for spin interactions in antiferromagnetic materials.

Figures

Figures reproduced from arXiv: 2411.11985 by the authors.

**Figure 2.** FIG. 2. Electronic band structure of altermagnetic semicon [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** shows the magnon dispersion of α-MnTe in the absence and presence of pressure. Low energy magnons around the Γ symmetry point are degenerate, while along the L-Γ-L symmetry path this degeneracy is broken. The pressure enhances the band splitting and also the magnon bandwidth. The spin-flop magnetic field in AFM systems is proportional to √ J1K. Using dispersion relation calculations, we find a spin-flop magnetic fi… view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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Altermagnetic spin splitting and symmetry-enforced partial spin degeneracy in hexagonal MnTe
cond-mat.mtrl-sci 2025-02 conditional novelty 6.0 of 10

Spin degeneracy is symmetry-protected in the kz=0 and ky=0 planes of hexagonal MnTe, while spin splitting appears elsewhere except on nodal lines.

Reference graph

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