REVIEW 2 major objections 5 minor 3 cited by
Pseudo-Goldstone mode in altermagnetic $\alpha$-MnTe: high-field electron spin resonance studies
T0 review · 2 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash
Pith's one-line read The in-plane antiferromagnetic resonance of α-MnTe is a pseudo-Goldstone mode whose temperature-dependent linewidth is governed by the Bose–Einstein occupation of zone-center magnons.
desk verdict A clean in-plane ESR study of α-MnTe that reports a linear pseudo-Goldstone mode and a T/ν linewidth collapse, but the Bose-Einstein interpretation is underdetermined by data confined to the classical regime. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is the pseudo-Goldstone mode of the easy-plane antiferromagnetic resonance, i.e., the in-plane spin-wave branch whose frequency starts linearly in field rather than at a gap, so that it resembles a Goldstone mode without being protected by true symmetry. The argument is carried by Eq. (4), $\Gamma_0 n_0(T) = g\mu_0\mu_\mathrm{B}\Delta H$, which ties the ESR linewidth directly to the Bose–Einstein occupation $n_0 = [\exp(h\nu/k_\mathrm{B}T)-1]^{-1}$ of $k\approx 0$ magnons; this relation lets a single parameter $\Gamma_0$ represent the strength of magnon-magnon interactions.
What would settle it
Measure the AFMR linewidth over a wider set of frequencies and temperatures, and plot $\Delta H$ against $h\nu/k_\mathrm{B}T$; if the data for different frequencies do not collapse onto a single $\Gamma_0 n_0(T)$ curve, or if the curve bends away from it as $T_\mathrm{N}$ is approached, the one-parameter magnon-population model is wrong. A direct observation of the predicted breakdown at low $h\nu/k_\mathrm{B}T$ with high-frequency data, or an independent measurement of the zone-center magnon lifetime that disagrees with $\Gamma_0/k_\mathrm{B} = 27(5)$ mK, would also settle the claim.
Extended reading notes
Core claim
The paper argues that the low-energy spin dynamics of the altermagnet $\alpha$-MnTe are carried by a pseudo-Goldstone AFMR mode with a linear frequency-field relation $h\nu = g_\perp \mu_\mathrm{B} \mu_0 H$, $g_\perp = 2.01$, and no resolvable in-plane anisotropy at the $10^{-3}$ level. The central quantitative discovery is that the AFMR linewidth above 30 K is not set by temperature alone but by the ratio $h\nu/k_\mathrm{B}T$: the full width at half maximum obeys $g\mu_0\mu_\mathrm{B}\Delta H = \Gamma_0 n_0(T)$, where $n_0$ is the Bose–Einstein occupation of the zone-center magnon, with a single fitted damping constant $\Gamma_0/k_\mathrm{B} = 27(5)$ mK. This one-parameter description, valid for three frequencies in the range 135–360 GHz, is interpreted as evidence that long-wavelength magnon collisions dominate the relaxation, and it yields the effective magnon-magnon interaction constant.
Load-bearing premise
The analysis assumes that the measured linewidth comes entirely from collisions among $k\approx 0$ magnons of the $\nu_1$ mode, so that one temperature-independent constant $\Gamma_0$ multiplied by the zone-center magnon occupation describes the data at all temperatures above 30 K.
Editorial extensions
If this is right
- The linewidth at any frequency and temperature above about 30 K can be predicted from $h\nu/k_\mathrm{B}T$ alone, so AFMR experiments at other frequencies should reproduce the same universal curve.
- The extracted $\Gamma_0/k_\mathrm{B} \approx 27$ mK gives a direct estimate of the effective magnon-magnon interaction in $\alpha$-MnTe, a number that microscopic spin-wave theory based on the known exchange Hamiltonian should be able to reproduce.
- The relative damping $\Gamma_0/k_\mathrm{B}T_\mathrm{N} \approx 10^{-4}$ is about two orders of magnitude smaller than crudely estimated for classic Mn$^{2+}$ antiferromagnets, indicating unusually long-lived long-wavelength magnons in this altermagnet.
- The narrow low-temperature linewidth (about 50 mT at 5 K) implies high sample quality, which matters for proposed GHz/THz spintronic applications of MnTe.
Reading between the lines
- If the one-parameter formula is the true collision rate for $k\approx 0$ magnons, then the same $\Gamma_0$ should appear in other relaxation observables, such as the zone-center magnon lifetime measured by inelastic neutron scattering or by time-resolved THz pump-probe experiments.
- The universal scaling suggests that at temperatures approaching $T_\mathrm{N}$, where the magnon dispersion softens and $k\neq 0$ magnons become populated, the formula should break down; locating that breakdown would delineate where the effective-interaction description stops being valid.
- The unusually small $\Gamma_0$ compared to other Mn$^{2+}$ antiferromagnets may be a consequence of the altermagnetic symmetry, which changes the magnon degeneracy and interaction selection rules; this could be tested by comparing linewidth data in $\alpha$-MnTe with a closely related non-altermagnetic easy-plane antiferromagnet.
- Because the model assumes only collisions among the probed mode's zone-center magnons, an experiment using very high fields where $h\nu/k_\mathrm{B}T$ grows large should show the collisional contribution freezing out and the residual ~70 mK linewidth dominating; this can be checked without any new theory.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper reports multi-frequency (50–500 GHz) high-field electron spin resonance measurements on the altermagnetic candidate α-MnTe, with the field applied in the easy (001) plane. A single resonance line is observed that follows a linear frequency-field relation hν = g⊥ μB μ0 H with g⊥ = 2.01, identified as the pseudo-Goldstone AFMR mode. The line is very narrow at low temperature (~50 mT at 5 K) and broadens strongly on warming. Above 30 K the linewidth measured at 135, 270, and 360 GHz is reported to collapse onto a universal curve when plotted against hν/k_B T, and the authors fit it with Eq. (4), Δ(g μ0 μB H) = Γ0 n0(T), where n0 is the Bose-Einstein occupation of the zone-center magnon and Γ0/k_B = 27(5) mK is the only fit parameter. This is interpreted as evidence that the linewidth is controlled by magnon-magnon scattering of k ≈ 0 magnons, yielding an estimate of the effective magnon-magnon interaction constant in α-MnTe.
Significance. If the central interpretation holds, the paper provides a direct ESR-based estimate of the magnon-magnon interaction strength in a leading altermagnet candidate, with a strikingly simple one-parameter scaling law. The experimental work is careful and the mode identification is solid: the linear g ≈ 2.01 AFMR mode, the absence of sizable in-plane anisotropy, and the very narrow low-temperature linewidth are all cleanly established. The scaling collapse of the linewidth over a 30–200 K range at three frequencies is a genuine empirical observation that will be of interest to the altermagnet and antiferromagnetic-resonance communities. However, as detailed below, the quantitative identification of the extracted Γ0 as the zone-center magnon-magnon interaction constant is not uniquely supported by the data because all measurements lie in the classical (hν/k_B T ≲ 0.6) regime.
major comments (2)
- [Temperature-dependent changes; Eq. (4); Fig. 5] The data used to support the Bose-Einstein form n0(T) = 1/[exp(hν/k_B T) - 1] all lie at x = hν/k_B T ≤ 0.6, with the largest value about 0.58 for 360 GHz at 30 K. In this window n0(x) differs from its classical Rayleigh-Jeans limit k_B T/hν by at most about 30%, and both forms produce a collapse when the linewidth is plotted against x. Specifically, the classical expression Δ(g μ0 μB H) = Γ0/x fits the same data with the same number of parameters, so the collapse does not discriminate between the zone-center magnon population and a generic T/ν relaxation rate. Consequently, the identification of the fitted Γ0/k_B = 27(5) mK as the effective magnon-magnon interaction constant is conditional on an untested functional form. The authors should either present data in the quantum regime (for example, higher frequencies or lower temperatures with the residual width subtracted), or explicitly compare the Bose-Einstein and classical fits and reframe the Γ0 result as a phenomenological relaxation-rate parameter.
- [Temperature-dependent changes; Eq. (4)] Equation (4) assumes that the linewidth is determined solely by k ≈ 0 magnons of the ν1 mode and that Γ0 is temperature-independent. The authors do not provide an estimate of the contribution of finite-momentum magnons or higher-order magnon processes, even though they note that such contributions are important in comparable Mn2+ antiferromagnets (Refs. [31,32]). Since the fit extends to 200 K, about 0.65 T_N, the extracted Γ0 may incorporate these additional relaxation channels. At minimum, the paper should state explicitly that Γ0 is an effective parameter and discuss the magnitude of possible finite-momentum contributions, or provide a calculation/estimate supporting their neglect.
minor comments (5)
- [Title and abstract] The manuscript header title ('Pseudo-Goldstone mode in altermagnetic α-MnTe: high-field electron spin resonance studies') differs from the title in the full text ('Low-energy magnons in the altermagnet α-MnTe'), and the abstract also appears in two variants. Please unify them.
- [Fig. 5] The individual linewidth points in Fig. 5 are shown without error bars, and the text does not describe how fit uncertainties from the Lorentzian-based analysis propagate into ΔH. Error bars or a statement of typical uncertainty should be added.
- [Fig. 3] The in-plane angular dependence is probed at only two angles (φ = 0° and 15°). The conclusion of negligible in-plane anisotropy would be strengthened by a denser angular scan over the full in-plane range.
- [Introduction and figure captions] There are several typographical errors, including 'means of means of' in the introduction, 'Lorentian' in the Fig. 4 caption, 'freqiencies' in the discussion, and 'mangetic' in the text near Fig. 3.
- [Eq. (2)] In Eq. (2), the two modes ν1 and ν2 are introduced without an explicit statement that ν1 is the pseudo-Goldstone mode probed in this work; a brief sentence connecting the notation to the text would improve readability.
Circularity Check
No significant circularity: the linewidth scaling is an empirical one-parameter fit with a genuine data-collapse test, and no load-bearing self-citation or definitional reduction is present.
full rationale
The central quantitative claim is an empirical one-parameter fit, not a first-principles derivation: Eq. (4) proposes gμ0μB ΔH = Γ0 n0(T) and Γ0/kB = 27(5) mK is the single free parameter adjusted to the same linewidth data. This is fitting, but the circularity pass concerns claims that derive X from Y where X and Y are equivalent by construction, or where a fitted input is renamed a prediction. Here the collapse of linewidths at three frequencies onto a single hν/kBT curve is a genuine test of the functional form: one Γ0 must account for all three frequency series, and the paper does not claim to predict the linewidth from an independent microscopic calculation. No load-bearing self-citation is used: the cited prior work supplies the spectrometer (Ref. 28), a standard AFMR textbook relation (Ref. 29), and independent neutron/THz parameters, none of which encode the linewidth result. The weak discrimination between Bose–Einstein and classical kBT/hν behavior in the probed x ≤ 0.6 window is a robustness/correctness caveat, not a circularity, because the scaling form is not imposed by definition of the fit. Accordingly, no circular step is identified.
Assumptions & free parameters
free parameters (2)
- Gamma0 =
27(5) mK
- g_perp =
2.01
assumptions (5)
- domain assumption The spin Hamiltonian is isotropic Heisenberg exchange plus an easy-plane anisotropy D(Sz)^2 (Eq. 1).
- domain assumption The frequency-field relation for an easy-plane AFM in an in-plane field is hν1 = g⊥ μ0 μB H and hν2 = Δ (Eq. 2).
- standard math Magnon occupation follows the Bose-Einstein distribution (Eq. 3).
- ad hoc to paper The linewidth is proportional to the zone-center magnon population n0 with a single constant Γ0 (Eq. 4).
- ad hoc to paper Contributions from k≠0 magnons and higher-order magnon processes are negligible.
Cite this review
Pith. "Pith review of Pseudo-Goldstone mode in altermagnetic $\alpha$-MnTe: high-field electron spin resonance studies." pith.science (2026). https://pith.science/paper/FLQZI5WK
@misc{pith2026251024376,
author = {Pith},
title = {Pith review of: Pseudo-Goldstone mode in altermagnetic $\alpha$-MnTe: high-field electron spin resonance studies},
year = {2026},
howpublished = {\url{https://pith.science/paper/FLQZI5WK}},
note = {Machine review of arXiv:2510.24376}
}
abstract
We report multi-frequency electron spin resonance spectroscopy studies of $\alpha$-MnTe in magnetic fields up to $16$ T, applied along the easy anisotropy axis. At temperatures below $T_\mathrm{N} = 310$ K, we observe a single resonance line corresponding to the pseudo-Goldstone mode of the antiferromagnetic resonance (AFMR). This mode exhibits the isotropic behavior with $g_\mathrm{eff}=2.01$, consistent with a complete quench of the orbital angular momenta for Mn$^{2+}$ ions. At low temperatures, the resonance mode is remarkably narrow ($\sim50$ mT for the full width at the half-maximum at $5$ K). The AFMR mode exhibits substantial broadening with increasing temperature, which can be understood in terms of the magnon-magnon scattering
Figures
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Reference graph
Works this paper leans on
-
[1]
Šmejkal, J
L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond Con- ventional Ferromagnetism and Antiferromagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry, Phys. Rev. X12, 031042 (2022)
2022
-
[2]
Šmejkal, J
L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging Re- search Landscape of Altermagnetism, Phys. Rev. X12, 040501 (2022)
2022
-
[3]
L. Bai, W. Feng, S. Liu, L. Šmejkal, Y. Mokrousov, and Y. Yao, Altermagnetism: Exploring New Frontiers in Magnetism and Spintronics, Adv. Func. Mater.34, 2409327 (2024)
work page 2024
-
[4]
C.-C. Wei, E. Lawrence, A. Tran, and H. Ji, Crystal Chemistry and Design Principles of Altermagnets, ACS Org. Inorg. Au4, 604 (2024)
work page 2024
-
[5]
S. S. Fender, O. Gonzalez, and D. K. Bediako, Altermag- netism: A Chemical Perspective, J. Am. Chem. Soc.147, 2257 (2025)
work page 2025
-
[6]
J. Ding, Z. Jiang, X. Chen, Z. Tao, Z. Liu, T. Li, J. Liu, J. Sun, J. Cheng, J. Liu, Y. Yang, R. Zhang, L. Deng, W. Jing, Y. Huang, Y. Shi, M. Ye, S. Qiao, Y. Wang, Y. Guo, D. Feng, and D. Shen, Large Band Splitting in g-Wave Altermagnet CrSb, Phys. Rev. Lett.133, 206401 (2024)
2024
-
[7]
S. Reimers, L. Odenbreit, L. Šmejkal, V. N. Strocov, P. Constantinou, A. B. Hellenes, R. Jaeschke Ubiergo, W. H. Campos, V. K. Bharadwaj, A. Chakraborty, T. Denneulin, W. Shi, R. E. Dunin-Borkowski, S. Das, M. Kläui, J. Sinova, and M. Jourdan, Direct Observa- tion of Altermagnetic Band Splitting in CrSb Thin Films, Nat. Commun.15, 2116 (2024)
work page 2024
-
[8]
N. Dale, O. A. Ashour, M. Vila, R. B. Regmi, J. Fox, C. W. Johnson, A. Fedorov, A. Stibor, N. J. Ghimire, and S. M. Griffin, Non-relativistic spin splitting above and below the Fermi level in ag-wave altermagnet, arXiv , 2411.18761 (2024)
arXiv 2024
Show all 32 references
-
[9]
A. P. Sakhya, M. I. Mondal, M. Sprague, R. B. Regmi, A. K. Kumay, H. Sheokand, I. I. Mazin, N. J. Ghimire, and M. Neupane, Electronic structure of a layered alter- magnetic compound CoNb4Se8 (2025)
2025
-
[10]
Uchida, H
E. Uchida, H. Kondoh, and N. Fukuoka, Magnetic and Electrical Properties of Manganese Telluride, J. Phys. Soc. Jpn.11, 27 (1956)
1956
-
[11]
Komatsubara, M
T. Komatsubara, M. Murakami, and E. Hirahara, Mag- netic Properties of Manganese Telluride Single Crystals, J. Phys. Soc. Jpn.18, 356 (1963). 5
1963
-
[12]
Szuszkiewicz, B
W. Szuszkiewicz, B. Hennion, B. Witkowska, E. Łusakowska, and A. Mycielski, Neutron Scatter- ing Study of Structural and Magnetic Properties of Hexagonal MnTe, Phys. Status Solidi C2, 1141 (2005)
2005
-
[13]
Szuszkiewicz, E
W. Szuszkiewicz, E. Dynowska, B. Witkowska, and B. Hennion, Spin-wave measurements on hexagonal MnTeofNiAs-type structure by inelastic neutron scat- tering, Phys. Rev. B73, 104403 (2006)
2006
-
[14]
Kriegner, H
D. Kriegner, H. Reichlova, J. Grenzer, W. Schmidt, E. Ressouche, J. Godinho, T. Wagner, S. Y. Martin, A. B. Shick, V. V. Volobuev, G. Springholz, V. Holý, J. Wunderlich, T. Jungwirth, and K. Výborný, Magnetic anisotropy in antiferromagnetic hexagonal MnTe, Phys. Rev. B96, 2144...
2017
-
[15]
I. I. Mazin, Altermagnetism in MnTe: Origin, predicted manifestations, and routes to detwinning, Phys. Rev. B 107, L100418 (2023)
2023
-
[16]
S. Lee, S. Lee, S. Jung, J. Jung, D. Kim, Y. Lee, B. Seok, J. Kim, B. G. Park, L. Šmejkal, C.-J. Kang, and C. Kim, Broken Kramers Degeneracy in Altermagnetic MnTe, Phys. Rev. Lett.132, 036702 (2024)
2024
-
[17]
Osumi, S
T. Osumi, S. Souma, T. Aoyama, K. Yamauchi, A. Honma, K. Nakayama, T. Takahashi, K. Ohgushi, and T. Sato, Observation of a giant band splitting in alter- magnetic MnTe, Phys. Rev. B109, 115102 (2024)
2024
-
[18]
Krempaský, L
J. Krempaský, L. Šmejkal, S. W. D’Souza, M. Ha- jlaoui, G. Springholz, K. Uhlířová, F. Alarab, P. C. Constantinou, V. Strocov, D. Usanov, W. R. Pudelko, R. González-Hernández, A. Birk Hellenes, Z. Jansa, H. Reichlová, Z. Šobáň, R. D. Gonzalez Betancourt, P. Wadley, J. Sinova, ...
2024
-
[19]
O. J. Amin, A. Dal Din, E. Golias, Y. Niu, A. Za- kharov, S. C. Fromage, C. J. B. Fields, S. L. Heywood, R. B. Cousins, F. Maccherozzi, J. Krempaský, J. H. Dil, D. Kriegner, B. Kiraly, R. P. Campion, A. W. Rushforth, K. W. Edmonds, S. S. Dhesi, L. Šmejkal, T. Jungwirth, and P....
2024
-
[20]
Hariki, A
A. Hariki, A. Dal Din, O. J. Amin, T. Yamaguchi, A. Badura, D. Kriegner, K. W. Edmonds, R. P. Cam- pion, P. Wadley, D. Backes, L. S. I. Veiga, S. S. Dhesi, G. Springholz, L. Šmejkal, K. Výborný, T. Jungwirth, and J. Kuneš, X-Ray Magnetic Circular Dichroism in Altermagneticα-Mn...
2024
-
[21]
K. P. Kluczyk, K. Gas, M. J. Grzybowski, P. Skupiński, M. A. Borysiewicz, T. Fąs, J. Suffczyński, J. Z. Do- magala, K. Grasza, A. Mycielski, M. Baj, K. H. Ahn, K. Výborný, M. Sawicki, and M. Gryglas-Borysiewicz, Coexistence of anomalous Hall effect and weak magne- tization in ...
2024
-
[22]
Z. Liu, M. Ozeki, S. Asai, S. Itoh, and T. Masuda, Chiral Split Magnon in Altermagnetic MnTe, Phys. Rev. Lett. 133, 156702 (2024)
2024
-
[23]
R. D. Gonzalez Betancourt, J. Zubáč, K. Geishen- dorf, P. Ritzinger, B. Růžičková, T. Kotte, J. Železný, K. Olejník, G. Springholz, B. Büchner, A. Thomas, K. Výborný, T. Jungwirth, H. Reichlová, and D. Krieg- ner, Anisotropic Magnetoresistance in Altermagnetic MnTe, npj Spintr...
2024
-
[24]
Kriegner, K
D. Kriegner, K. Výborný, K. Olejník, H. Reichlová, V. Novák, X. Marti, J. Gazquez, V. Saidl, P. Němec, V. V. Volobuev, G. Springholz, V. Holý, and T. Jung- wirth, Multiple-stable anisotropic magnetoresistance memory in antiferromagnetic MnTe, Nat. Commun.7, 11623 (2016)
2016
-
[25]
Dzian, P
J. Dzian, P. Kubaščík, S. Tázlarů, M. Białek, M. Šindler, F. Le Mardelé, C. Kadlec, F. Kadlec, M. Gryglas- Borysiewicz, K. P. Kluczyk, A. Mycielski, P. Skupiński, J. Hejtmánek, R. Tesař, J. Železný, A.-L. Barra, C. Faugeras, J. Volný, K. Uhlířová, L. Nádvorník, M. Veis, K. Výb...
2025
-
[26]
Kunitomi, Y
N. Kunitomi, Y. Hamaguchi, and S. Anzai, Neutron diffraction study on manganese telluride, J. Phys. France 25, 568 (1964)
1964
-
[27]
De Melo, F
O. De Melo, F. Leccabue, C. Pelosi, V. Sagredo, M. Chourio, J. Martin, G. Bocelli, and G. Calestani, Crystal growth and characterization of MnTe single crys- tals, J. Cryst. Growth110, 445 (1991)
1991
-
[28]
S. A. Zvyagin, J. Krzystek, P. H. M. van Loosdrecht, G. Dhalenne, and A. Revcolevschi, High-field ESR study of the dimerized-incommensurate phase transition in the spin-Peierls compound CuGeO3, Physica B346-347, 1 (2004)
2004
-
[29]
A. G. Gurevich and G. A. Melkov,Magnetization Oscil- lations and Waves(CRC Press, U.K., 1996)
1996
-
[30]
See the Supplemental Material for more details
-
[31]
H. W. de Wijn, L. R. Walker, S. Geschwind, and H. J. Guggenheim, Antiferromagnetic resonance in the quadratic-layer antiferromagnetsK 2MnF4 and Rb2MnF4, Phys. Rev. B8, 299 (1973)
1973
-
[32]
Low-energy magnons in the altermagnetα-MnTe
S. M. Rezende and R. M. White, Multimagnon theory of antiferromagnetic resonance relaxation, Phys. Rev. B 14, 2939 (1976). Supplemental Material for “Low-energy magnons in the altermagnetα-MnTe” K. Yu. Povarov,1,∗ J. Wosnitza,1, 2 S. Rößler,3 M. Schmidt,4 A. A. Tsirlin,3 and S...
1976
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