Pith. sign in

REVIEW 3 major objections 5 minor 55 references

Magnetotransport evolution and nonlinear Hall effect in altermagnetic MnTe

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Zero-field second-order nonlinear Hall transport in bulk MnTe single crystals provides evidence that this altermagnetic semiconductor hosts an effective inversion-asymmetric macroscopic response.

desk verdict Bulk MnTe transport evolution is a solid, citable dataset; the zero-field V2ω claim is plausible but needs a contact-swap/current-reversal control before it carries the inversion-symmetry conclusion. read the letter →

arxiv 2608.09371 v1 pith:PEEHQPMN submitted 2026-08-10 cond-mat.mtrl-sci cond-mat.dis-nncond-mat.str-elphysics.app-ph

Wei Zhou , Zhifeng Xue , Yunxing Li , Nannan Tang , Ye Tao , Dingyong Zhong , Jiawei Luo , Donghui Guo
show 1 more author
Huichao Wang
This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.dis-nncond-mat.str-elphysics.app-ph PACS 72.20.My75.50.Ee
keywords altermagnetMnTenonlinearHalleffectanisotropicmagnetoresistanceplanarvariable-rangehoppingspin-orbitcouplinginversionsymmetrybreaking
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 studies bulk single crystals of the semiconducting altermagnet α-MnTe across its metallic and localized transport regimes. The authors find that the anisotropic magnetoresistance and planar Hall effect develop six-fold and four-fold angular harmonics only in the high-temperature metallic regime, and that these features disappear as conduction crosses into nearest-neighbor and variable-range hopping at lower temperatures. The central discovery is a distinct zero-field second-order nonlinear Hall signal: a transverse voltage at twice the drive frequency that scales quadratically with current and is anisotropic with respect to the current direction. The paper takes this signal as evidence for an effective macroscopic inversion-asymmetric response, indicating that the combined lattice-plus-magnetic structure of MnTe is not centrosymmetric. If correct, this would establish bulk MnTe as a platform for nonlinear responses in a semiconducting antiferromagnet.

What carries the argument

The central object is the second-order nonlinear Hall coefficient extracted from the transverse voltage at twice the drive frequency, $V_{2\omega}/I_\omega^2$, whose presence at zero field is a symmetry-sensitive probe of spatial inversion breaking. The argument also rests on the harmonic decomposition of the angular magnetotransport data into $A_n \cos(n\theta + \alpha_n)$ components, and on the identification of three distinct charge-transport regimes (metallic, nearest-neighbor hopping, and Mott variable-range hopping) via fits of $\rho(T)$. The quadratic scaling of $V_{2\omega}$ with $I_\omega$, together with frequency independence and current-axis anisotropy, is the fingerprint that isolates the intrinsic nonlinear Hall response from heating and capacitive artifacts.

What would settle it

Measure the $2\omega$ transverse voltage after reversing the current direction and swapping the transverse voltage contacts: an intrinsic nonlinear Hall signal must change sign or follow the predicted angular form under such reversals, while a contact- or rectification-induced signal would not. As a complementary check, if the signal is tied to the altermagnetic order it should vanish above the Néel temperature (about 304 K); a persistent signal at 350 K would indicate a different origin.

Watch

Extended reading notes

Core claim

We report a systematic magnetotransport study of bulk α-MnTe single crystals. In the metallic regime (approximately 100–300 K), the AMR contains a six-fold harmonic and the PHE a four-fold harmonic beyond the conventional two-fold term; these higher-order components are symmetry-allowed and reflect the interplay of the altermagnetic order, crystal symmetry, and spin-orbit coupling. Upon cooling into the nearest-neighbor hopping regime (20–100 K) and the Mott variable-range hopping regime (below 20 K), the higher-order harmonics vanish while the two-fold term persists, showing that carrier localization suppresses the transport sensitivity to Fermi-surface anisotropy. At zero magnetic field we observe a robust second-order nonlinear Hall voltage for current along both crystallographic axes: the transverse $2\omega$ signal scales quadratically with the applied current, is frequency independent, and is anisotropic between the $x$ and $y$ axes, ruling out Joule heating and capacitive coupling and indicating an electronic origin. We interpret the nonlinear Hall response as evidence for a macroscopic inversion-asymmetric response in this altermagnetic semiconductor.

Load-bearing premise

The measured second-harmonic transverse voltage is an intrinsic nonlinear Hall effect rather than an artifact of contact misalignment, local rectification, or sample inhomogeneity.

Editorial extensions

If this is right

  • The zero-field nonlinear Hall signal marks MnTe as a candidate for nonlinear spin-charge interconversion and rectification effects in a semiconducting antiferromagnet.
  • Magnetotransport harmonics track the conduction mechanism: higher-order AMR/PHE components can serve as a fingerprint of coherent band transport and are suppressed when hopping dominates.
  • The robust two-fold AMR/PHE in the hopping regime implies that spin-orbit-coupled magnetic background effects persist even without coherent Fermi-surface transport.
  • The observation of a nonlinear Hall effect outside the regime where Boltzmann transport theory applies calls for a theoretical description of nonlinear responses in disordered, localized conductors.

Reading between the lines

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

  • A direct experimental check that would further harden the central claim is the antisymmetry test: an intrinsic nonlinear Hall voltage should transform predictably when current and voltage contacts are swapped or the current direction is reversed; the paper does not report such a test for the $2\omega$ signal.
  • If the nonlinear Hall effect is tied to the altermagnetic order and its accompanying structural distortion, it should disappear above the Néel temperature; measuring $2\omega$ transport at 320 K or higher would test this connection.
  • The qualitative picture proposed for the localized regime—spin-dependent, anisotropic hopping rates mediated by spin-orbit coupling—could be tested in samples with controlled defect concentrations, where the hopping energy $\Delta$ and the magnitude of the nonlinear Hall coefficient should track each other.
  • The apparent inversion asymmetry bears on the debated presence of a non-centrosymmetric structural distortion in MnTe: the transport data support the optical and atomic-scale studies, and suggest that nonlinear transport may be a general probe of altermagnetic symmetry lowering.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript reports temperature-dependent anisotropic magnetoresistance (AMR), planar Hall effect (PHE), and nonlinear transport in bulk single crystals of the altermagnetic semiconductor MnTe. The authors identify a high-temperature metallic-like regime with AMR/PHE harmonics consistent with a symmetry analysis from the literature, a crossover to nearest-neighbor hopping and then to Mott variable-range hopping at lower temperatures, and a zero-field transverse second-harmonic signal that they interpret as evidence for a macroscopic inversion-asymmetric response. The paper also connects the suppression of higher-order AMR/PHE harmonics to carrier localization, and discusses the role of spin-orbit coupling and disorder.

Significance. If the zero-field second-harmonic transverse signal is intrinsic, the observation would constitute transport evidence for effective inversion-symmetry breaking in a nominally centrosymmetric altermagnetic material and would extend nonlinear Hall studies into the localized hopping regime, which is largely unexplored. The paper also provides a useful temperature-evolution map of AMR/PHE harmonics across distinct conduction regimes in bulk MnTe, a material of current interest. These strengths are, however, tempered by two load-bearing issues: the nonlinear Hall signal lacks the contact-geometry controls needed to exclude spurious contributions, and the harmonic fits exclude symmetry-allowed terms without quantifying them. Both issues appear addressable with additional measurements and analysis, but they currently prevent the central claims from being fully verified.

major comments (3)
  1. [Section 3, nonlinear transport (Figs. 3 and 4)] The zero-field second-harmonic transverse voltage is the central evidence for macroscopic inversion asymmetry, but the paper reports no contact-swapping, current-reversal, or antisymmetrization test for the V2ω signal. Contact misalignment can mix a portion of the longitudinal second-harmonic voltage into the transverse channel, and local electrode nonlinearities can produce a frequency-independent V2ω that scales as Iω^2, precisely matching the reported data. The controls listed in the text (frequency independence, x/y anisotropy, and linear Iω–Vω) do not exclude these spurious sources. Please provide measurements with swapped voltage and current contacts, and with reversed current polarity, or otherwise demonstrate that the transverse second-harmonic signal has the antisymmetry expected of a nonlinear Hall response.
  2. [Section 3, harmonic fits (Figs. 2(a)–(f))] The fitting model is restricted to the 2nd and 6th harmonics for AMR and the 2nd and 4th harmonics for PHE, with symmetry-allowed terms such as the 4th harmonic in AMR and the 3rd/6th harmonics in PHE excluded based on the absence of AHE signatures related to A3 and on overfitting concerns. Because the temperature evolution of the amplitudes A_n is a primary result, please quantify the amplitudes of all symmetry-allowed harmonics (or show residuals from full fits) and report error bars or confidence intervals for A_n and for the activation energy Δ. Without this information, the claim that higher-order components disappear in the hopping regime cannot be properly assessed.
  3. [Section 4, Discussion] The paper states that no quantitative theoretical framework exists for the nonlinear Hall effect in the localized hopping regime and that 'transport measurements alone are insufficient to establish its microscopic origin.' Given that the abstract and summary present the nonlinear Hall signal as 'evidence for a macroscopic inversion-asymmetric response,' the authors should either strengthen the phenomenological case by showing how the V2ω signal transforms under current reversal and magnetic-field reversal, or temper the claim to state explicitly that this is a transport signature consistent with, but not yet conclusive proof of, inversion-symmetry breaking. The structural evidence in refs 25–27 is supportive but does not by itself validate the electrical measurement.
minor comments (5)
  1. [Section numbering] The manuscript contains two sections numbered '3', both titled 'Introduction'; the second should be relabeled as 'Results' or 'Experimental Results'.
  2. [Affiliations] The affiliation 'Sun Yet-sen University' should read 'Sun Yat-sen University.'
  3. [Figure 2 and Figure 1(e)] No error bars are shown for the AMR/PHE amplitudes A_n in Figs. 2(g)–(h) or for the activation energy Δ extracted in Fig. 1(e). Please include uncertainties and specify the number of samples and measurement repetitions used for each reported quantity.
  4. [Section 3, harmonic model] The defining equation for the harmonic model is garbled in the main text (the expression 'A_n cos(nθ + α_n) [21,24]' appears with corrupted symbols). Please state the model explicitly, including the constant offset used in the AMR fits and the definition of the angle θ.
  5. [Section 3, nonlinear transport controls] The statement that frequency independence rules out Joule heating is too strong: frequency independence alone does not eliminate a thermal contribution if the thermal response time is fast. A comparison of the 2ω and 4ω responses, or a check of the power dependence at several frequencies, would provide stronger evidence against a thermal origin.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central claims are direct measurements interpreted via external symmetry analyses; the only self-citation (ref. 47) is minor and not load-bearing.

full rationale

The paper's central claims are experimental characterizations, not derivations. In the AMR/PHE section, the harmonic amplitudes A_n are obtained by fitting a symmetry-motivated Fourier model (Sec. 3, Fig. 2); the fitted coefficients are then plotted versus temperature. No quantity is predicted from the fit, and the good quality of the restricted 2nd/6th (AMR) and 2nd/4th (PHE) fits is an empirical outcome, not an identity. The symmetry-allowed harmonic list is imported from ref. 21, an independent group, so no uniqueness or ansatz is smuggled in via self-citation. The nonlinear Hall claim rests on direct measurement of V_{2ω} proportional to I_ω^2 under zero field, with frequency-independence and x/y anisotropy controls. The interpretation that a second-order transverse response indicates inversion-symmetry breaking is a standard external symmetry condition, and the paper cites independent structural and optical evidence (refs. 25-27) for a noncentrosymmetric distortion; those references are not used to define the measured quantity. The sole self-citation (ref. 47, Q. Li et al., which includes several of the present authors) supports the routine geometric-asymmetry removal in the linear AMR/PHE processing; it is not load-bearing for the main claims. The paper explicitly concedes that no quantitative theory exists for the nonlinear Hall effect in the hopping regime and that transport measurements alone cannot establish the microscopic origin, an honest limitation rather than a circular step. Concerns about contact misalignment or local rectification in the V_{2ω} channel are validity/correctness risks, not circularity, because no argument in the paper forces the V_{2ω} signal to equal the fitted parameters or the cited references by construction. Therefore no circular step is identified; the score of 2 reflects only the presence of a minor, non-load-bearing self-citation.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper contributes measurements, not a derivation; it borrows the symmetry analysis, the structural inversion-breaking evidence, and the hopping-transport models from cited works, and fits several empirical parameters (resistivity coefficients, harmonic amplitudes, activation energy) that the interpretations depend on.

free parameters (3)
  • Resistivity fit coefficients rho0, a, b = not reported
    Fitted to the 100-300 K metallic conduction data in Fig. 1(d) to support the high-temperature metallic regime classification.
  • Harmonic amplitudes A_n and phases alpha_n = temperature-dependent, not tabulated
    Extracted from AMR and PHE angular sweeps in Fig. 2; the claim about emergence and suppression of high-order harmonics depends on these fitted values.
  • Nearest-neighbor hopping activation energy Delta = ~1.4 meV
    Obtained from the Arrhenius fit in the 20-100 K range and used to identify impurity-band NNH conduction.
assumptions (5)
  • domain assumption The angular magnetotransport is representable by a harmonic sum of cos(nθ+α_n) with the chosen subset of harmonics.
    The symmetry analysis in ref 21 allows several harmonics, and the paper assumes the omitted terms are negligible without quantitative comparison.
  • domain assumption The noncentrosymmetric lattice distortion in MnTe is established by refs 25-27.
    The nonlinear Hall interpretation rests on this external structural evidence rather than on a measurement performed in this paper.
  • domain assumption Spin-orbit coupling is required to convert magnetic order into anisotropic magnetotransport in MnTe.
    The paper takes this from refs 50-52 and uses it to explain the persistent two-fold term in the hopping regime.
  • domain assumption The resistivity fits correctly identify three transport regimes: metallic above 100 K, NNH 20-100 K, and VRH below 20 K.
    The correlation between harmonic suppression and carrier localization depends on this regime classification.
  • ad hoc to paper Hopping-transport models from refs 53 and 57 can be qualitatively extended to the nonlinear Hall response in the localized regime.
    The authors state that no dedicated theory exists and offer this as a tentative physical picture.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Magnetotransport evolution and nonlinear Hall effect in altermagnetic MnTe." pith.science (2026). https://pith.science/paper/PEEHQPMN

@misc{pith2026260809371,
  author       = {Pith},
  title        = {Pith review of: Magnetotransport evolution and nonlinear Hall effect in altermagnetic MnTe},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PEEHQPMN}},
  note         = {Machine review of arXiv:2608.09371}
}
read the original abstract

Hexagonal MnTe is a prototypical semiconducting altermagnet whose properties are heavily influenced by intrinsic disorder, yet how the resulting diverse transport regimes shape its magnetotransport behavior remains to be clarified alongside the role of relativistic spin-orbit coupling (SOC). Here, we present a systematic study of the anisotropic magnetoresistance (AMR), planar Hall effect (PHE), and nonlinear transport in MnTe bulk single crystals. Below the N\'eel temperature (TN ~ 304 K), the emergence of high-order harmonics in AMR and PHE within the high-temperature metallic regime reveals the interplay of magnetic order, crystalline symmetry, and SOC. At relatively lower temperatures, the disappearance of higher-order symmetries coincides with a transport crossover into the hopping conduction regime, suggesting that carrier localization diminishes the transport sensitivity to the Fermi-surface topology. In addition, we detect distinct second-order nonlinear Hall signals, providing evidence for a macroscopic inversion-asymmetric response in altermagnetic MnTe. Extending the investigations into the localized regime provides key insights into the subtle role of disorder and SOC in macroscopic charge transport. Our work thus underscores the necessity of exploring magnetotransport across diverse conducting regimes to comprehensively understand altermagnetic properties.

Figures

Figures reproduced from arXiv: 2608.09371 by the authors.

Figure 1
Figure 1. (a) Temperature dependence of magnetization measured under field-cooling at 4000 Oe. The inset shows a schematic of crystal structure. (b) Isothermal magnetization M(H) curves at various temperatures from 2 to 350 K. The inset shows the differential susceptibility dM/dH, identifying the spin-flop process in 0.2-2 T. (c) Low-temperature M(H) hysteresis loop. (d) Temperature dependence of the resistivity (sample 1). T… view at source ↗
Figure 2
Figure 2. (a) Experimental schematic, (b) AMR and (c) PHE measured at various temperatures under a fixed 9 T with the current j applied along the [21￾1￾0] direction (x￾axis). (d) Experimental schematic, (e) AMR and (f) PHE measured at 9 T with the current j applied along the [011￾0] direction (y-axis). Here the AMR ratio is defined as (()-())/() × 100%. Solid lines in (b,c,e,f) represent fits based on the phenomenol… view at source ↗
Figure 3
Figure 3. (a, c) Longitudinal voltages (￾￾￾ ￾ and ￾￾￾ ￾ ) versus the AC current (￾￾ ) measured under zero magnetic field along the x- and y-axes (sample 6), demonstrating linear Ohmic behavior. (b, d) Transverse second-harmonic voltages (￾￾￾ ￾￾ and ￾￾￾ ￾￾) versus the square of the applied current. The linear scaling confirms an intrinsic quadratic transport response [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

55 extracted references · 47 canonical work pages

  1. [1]

    Šmejkal, J

    L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond conventional ferromagnetism and antiferromagnetis m: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X 12, 031042 (2022)

    work page 2022

  2. [2]

    J. - K. Yuan, Z. Pan, and C. Wu, Unconventional magnetism in spin - orbit coupled systems, Phys. Rev. B 113, 014426 (2026)

    work page 2026

  3. [3]

    Q. Liu, X. Dai, and S. Blügel, Diffe rent facets of unconventional magnetism, Nat. Phys. 21, 329 (2025)

    work page 2025

  4. [5]

    Krempasky, L

    J. Krempasky, L. Smejkal, S. W. D'Souza, M. Hajlaoui, G. Springholz, K. Uhlirova et al., Altermagnetic lifting of Kramers spin degeneracy, Nature 626, 517 (2024)

    work page 2024

  5. [6]

    S. Lee, S. Lee, S. Jung, J. Jung, D. Kim, Y. Lee et al., Broken Kramers Degeneracy in A ltermagnetic MnTe , Phys. Rev. Lett. 132, 036702 (2024)

    work page 2024

  6. [7]

    Hajlaoui, S

    M . Hajlaoui, S. W. D'Souza, L. Smejkal, D. Kriegner, G. Krizman, T. Zakusylo et al., Temperature dependence of relativistic valence band splitting induced by an altermagnetic phase transition, Adv. Mater. 36, e2314076 (2024)

    work page 2024

  7. [8]

    R. D. Gonzalez Betancourt, J. Zubac, R. Gonzalez - Hernandez, K. Geishendorf, Z. Soban, G. Springholz et al., Sponta neous anomalous Hall effect arising from an unconventional compensated magnetic phase in a semiconductor, Phys. Rev. Lett. 130, 036702 (2023)

    work page 2023

  8. [9]

    C. C. Ye, K. Tenzin, J. Sławińska, C. Autieri, Dominant orbital magnetization in the prototypical altermagnet MnTe, Phys. Rev. B 113, 014413 (2026). 13

    work page 2026

Show all 55 references
  1. [10]

    S. Li, J. Wu, B. Liang, L. Liu, W. Zhang, N. Wazir et al., Antiferromagnetic α - MnTe: Molten - salt - assisted chemical vapor deposition growth and magneto - transport properties, Chem. Mater. 34, 873 (2022)

    2022

  2. [11]

    N. N. Orlova, V . D. Esin, A. V. Timonina, N. N. Kolesnikov, and E. V. Deviatov, Magnetization symmetry for the altermagnetic candidate MnTe, Phys. Rev. B 111, 224414 (2025)

    2025

  3. [12]

    K. P. Kluczyk, K. Gas, M. J. Grzybowski, P. Skupiński, M. A. Borysiewicz, T. Fąs et al., Coexist ence of anomalous Hall effect and weak magnetization in a nominally collinear antiferromagnet MnTe, Phys. Rev. B 110, 155201 (2024)

    2024

  4. [13]

    M. Zeng, P. Liu, M. - Y. Zhu, N. Zheng, X. - R. Liu, Y. - P. Zhu et al., Non - altermagnetic spin texture in MnTe, arXiv:2511.02447

  5. [14]

    Dal Din, D

    A. Dal Din, D. A. Usanov, L. Šmejkal, S. W. D'Souza, F. Guo, O. J. Amin et al., Unconventional relativistic spin polarization of electronic bands in an altermagnet, arXiv:2511.01690

  6. [15]

    Autieri and A

    C. Autieri and A. Fakhredine, Relativistic spin - momentum locking in alt ermagnets, J . Phys . Chem . Lett . 17, 449 (2026)

    2026

  7. [16]

    I. I. Mazin and K. D. Belashchenko, Origin of the gossamer ferromagnetism in MnTe, Phys. Rev. B 110, 214436 (2024)

    2024

  8. [17]

    Autieri, R

    C. Autieri, R. M. Sattigeri, G. Cuono, and A. Fakhredine, Staggered Dzyaloshinskii - Moriya interaction inducing weak ferromagnetism in centrosymmetric altermagnets and weak ferrimagnetism in noncentrosymmetric altermagnets, Phys. Rev. B 111, 054442 (2025)

    2025

  9. [18]

    Kriegner, K

    D. Kriegner, K. Vyborny, K. Olejnik, H. Reichlova, V. Novak, X. Marti et al., Multiple - sta ble anisotropic magnetoresistance memory in antiferromagnetic MnTe, Nat. Commun. 7, 11623 (2016)

    2016

  10. [19]

    Chilcote, A

    M. Chilcote, A. R. Mazza, Q. Lu, I. Gray, Q. Tian, Q. Deng et al., Stoichiometry - induced ferromagnetism in altermagnetic candidate MnTe, Adv. Funct. Mater. 34 , 2405829 (2024). 14

    2024

  11. [20]

    Z. Liu, S . Xu, J. M. DeStefano, E. Rosenberg, T.. Zhang, J. Li et al., Strain - tunable anomalous Hall effect in hexagonal MnTe, arXiv:2509.19582

  12. [21]

    R. D. Gonzalez Betancourt, J. Zubac, K. Geishendorf, P. Ritzinger, B. Ruzickova, T. Kotte et al., Anisotropic magnetoresistance in altermagnetic MnTe, npj Spintron . 2, 45 (2024)

    2024

  13. [22]

    G. Yin, J. X. Yu, Y. Liu, R. K. Lake, J. Zang, and K. L. Wang, Planar Hall effect in antiferromagnetic MnTe thin films, Phys. Rev. Lett. 122, 106602 (2019)

    2019

  14. [23]

    Bangar, P

    H. Bangar, P. Tsipas, P. Rout, L. Pandey, A. Kalaboukhov, A. Lintzeris et al., Interplay between altermagnetic order and crystal symmetry probed using magnetotransport in epitaxial altermagnet MnTe, arXiv:2505.14589

    arXiv

  15. [24]

    Y . Dai, C . Zhang, Y . Zhang, Z .. Zhang, H . Chen, L . L iu at al., Observation of Unidirectional Anisotropic Magnetoresistance in Altermagnetic MnTe (0001) Films, Adv. Funct. Mater.36, e26026 (2026)

    2026

  16. [25]

    A. Wu, D. Cheng, X. Wang, M. Zeng, C. Liu, and X. Li, Optical signatures of noncentrosymmetric structural distor tion in altermagnetic MnTe, arXiv:2503.17742

    arXiv

  17. [26]

    G . Ren, J . M. DeStefano, X . - W .. Zhang, A . S. Thind, R . Giridharagopal, J . A . Castellanos - Reyes at al., Atomic - Scale Observation of Symmetry Breaking in Altermagnetic MnTe, arXiv:2605.27543

    arXiv

  18. [27]

    Benny, S

    M . Benny, S . I . Vishkayi, A . Fakhredine, C . K. Barman, C . Autieri, Effect of polar distortions on the anomalous Hall conductivity of altermagnetic α - MnTe, arXiv:2606.12311

    arXiv

  19. [28]

    Sodemann and L

    I. Sodemann and L. Fu, Quantum nonlinear Hall effect induced by Berry curvature dipole in time - reve rsal invariant materials, Phys. Rev. Lett. 115, 216806 (2015)

    2015

  20. [29]

    Tokura, N

    Y. Tokura, N. Nagaosa, Nonreciprocal responses from non - centrosymmetric quantum materials, Nat. Commun. 9, 3740 (2018)

    2018

  21. [30]

    C. Xiao, H. Zhou, and Q. Niu, Scaling parameters in anomalous and nonlinear Hall effects depend on temperature, Phys. Rev. B 100, 161403(R) (2019). 15

    2019

  22. [31]

    Z. Z. Du, H. - Z. Lu, and X. C. Xie, Nonlinear Hall effects, Nat. Rev. Phys. 3, 744 (2021)

    2021

  23. [32]

    Z. - H. Gong, Z. Z. Du, H. - P. Sun, H. - Z. Lu, and X. C. Xie, Nonlinear transport theory at the order of quantum metric, arXiv:2410.04995

    arXiv

  24. [33]

    Y. - X. Huang, C. Xiao, S. A. Yang, and X. Li, Scaling law and extrinsic mechanisms for time - reversal - odd second - order nonlinear transport, Phys. Rev. B 111, 155127 (2025)

    2025

  25. [34]

    L. Li, H. Li, J. Li, H. Wu, L. Yan g, W. Zhang, and H. Chang, Chemical vapor deposition - grown nonlayered α - MnTe nanosheet for photodetectors with ultrahigh responsivity and external quantum efficiency, Chem. Mater. 33, 338 (2020)

    2020

  26. [35]

    Zanmarchi, Optical measurements on the antiferromagnetic semiconductor MnTe, J

    G. Zanmarchi, Optical measurements on the antiferromagnetic semiconductor MnTe, J. Phys. Chem. Solids 28, 2123 (1967)

    1967

  27. [36]

    Szuszkiewicz, E

    W. Szuszkiewicz, E. Dynowska, B. Witkowska, and B. Hennion, Spin - wave measurements on hexagonal MnTe of NiAs - type structure by inelastic neutron scattering, Phys. Rev. B 73, 104403 (2006)

    2006

  28. [37]

    Mor i, Y

    S. Mor i, Y. Sutou, D. Ando, and J. Koike, Optical and electrical properties of α - MnTe thin films deposited using rf magnetron sputtering, Mater. Trans. 59, 1506 (2018)

    2018

  29. [38]

    S. Wu, Y. Huang, H. Song, and B. Wang, Bulk single crystal growth and magneto - transport prope rties of α - MnTe, J. Magn. Magn. Mater. 627, 173106 (2025)

    2025

  30. [39]

    Kriegner, H

    D. Kriegner, H. Reichlova, J. Grenzer, W. Schmidt, E. Ressouche, J. Godinho et al., Magnetic anisotropy in antiferromagnetic hexagonal MnTe, Phys. Rev. B 96, 214418 (2017)

    2017

  31. [41]

    Yamada, S

    H. Yamada, S. Takada, On the Electrical Resistivity of Antiferromagnetic Metals at Low Temperatures, Prog. Theor. Phys. 52, 1077 (1974). 16

    1974

  32. [42]

    Rößler, V

    S. Rößler, V. Ginga, M. Schmidt, Y. Prots, H. Rosner, U. Burkhardt, et al., Low - field magnetization processes of hexagonal easy - plane altermagnet α - MnTe, arXiv:2511.01388

  33. [44]

    C. C. Lien, C. Y. Wu, Z. Q. Li, and J. J. Lin, Electrical conduction processes in ZnO in a wide temperature range 20 – 500 K, J. Appl. Phys. 110, 063706 (2011)

    2011

  34. [45]

    N. F. Mott, Conduction in non - crystalline materials: III. Localized states in a pseudogap and near extremities of conduction and valence bands, Philos. Mag. 19, 835 (1969)

    1969

  35. [46]

    R. C. Budhani, J. S. Higgins, D. McAlmont, and J. Paglione, Planar Hall effect in c - axis textured films of Bi 85 Sb 15 topological insulator, AIP Adv. 11, 055020 (2021)

    2021

  36. [47]

    Q. Li, G. Jin, N. Tang, B. Wang, B. Shen, D. Guo, D. Zhong, H. Zuo, and H. Wang, Shubnikov – de Haas oscillations and planar Hall effect in HfTe 2 , Phys. Rev. B 108, 235155 (2023)

    2023

  37. [49]

    T. R. McGuire and R. I. Potter, Anisotropic Magnetoresistance in Ferromagnetic 3d Alloys, IEEE Trans. Magn. 11, 1018 (1975)

    1975

  38. [50]

    Ritzinger, O

    P. Ritzinger, O. Sedláček, J. Železný, and K. Výborný, Non - Relativist ic Anisotropic Magnetoresistance with Collinear and Non - Collinear Magnetic Order, arXiv:2506.22115

    arXiv

  39. [51]

    X. P. Zhang, W. X. Feng, R. W. Zhang, X. L. Fan, X. R. Wang, and Y. G. Yao, Theory of Anisotropic Magnetoresistance in Altermagnets and Its Applications, Phys. Rev. Lett. 135, 266706 (2025)

    2025

  40. [52]

    B. F. Chen, J. X. Yu, and G. Yin, Large anisotropic magnetoresistance in α - MnTe induced by strain, Phys. Rev. B 113, 054412 (2026). 17

    2026

  41. [53]

    Lyanda - Geller, S

    Y. Lyanda - Geller, S. H. Chun, M. B. Salamon, P. M. Goldbart, P. D. Han, Y. Tomioka, et al., Charge transport in manganites: Hopping conduction, the anomalous Hall effect, and universal scaling, Phys. Rev. B 63, 184426 (2001)

    2001

  42. [54]

    Y. D. Park, A. Wilson, A. T. Hanbicki, J. E. Mattson, T. Ambrose, G. Spanos, et al., Magnetoresistance of Mn: Ge ferr omagnetic nanoclusters in a diluted magnetic semiconductor matrix, Appl. Phys. Lett. 78, 2739 (2001)

    2001

  43. [55]

    Galindez - Ruales, R

    E. Galindez - Ruales, R. Gonzalez - Hernandez, C. Schmitt, S. Das, F. Fuhrmann, A. Ross, et al., Revealing the Altermagnetism in Hematite via XMCD Imaging and Anomalous Hall Electrical Transport, Adv. Mater. 37, e05019 (2025)

    2025

  44. [56]

    J. A. Horn, Y. S. Eo, K. Avers, H. Yoon, R. G. Dorman, S. R. Saha, et al., Magnetocrystalline anisotropy and three - dimensional hopping conduction at the surface of FeSb 2 , Phys. Rev. B 113 , 125142 (2026)

    2026

  45. [57]

    A. A. Burkov and L. Balents, Anomalous Hall Effect in Ferromagnetic Semiconductors in the Hopping Transport Regime, Phys. Rev. Lett. 91, 057202 (2003)

    2003

  46. [58]

    S. Qu, Z. - F. Ouyang, Z. - F. Gao, H. Sun, K. Liu, P. - J. Guo at al . , Extremely strong spin−orbit coupling effect in light - element altermagnetic materials, Front. Phys., 21, 045203 (2026)

    2026

  47. [59]

    H. - Y. Ma, J. - F. Jia, Altermagnetic topological insulator with C - paired spin - valley locking, Quantum Front., 3, 22 (2024) . 18 Figure

    2024

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.