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Altermagnetic spin-split Fermi surfaces in CrSb revealed by quantum oscillation measurements

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read All measured quantum-oscillation frequencies in CrSb match the spin-split Fermi surface of an altermagnetic band calculation, providing bulk-sensitive evidence for altermagnetic spin splitting.

desk verdict The most complete quantum-oscillation study of CrSb so far, with a solid band-1/2 Fermi surface picture but band-3 assignments that ride on a U-sensitive reconstruction. read the letter →

arxiv 2601.19105 v2 pith:DVLWZDCA submitted 2026-01-27 cond-mat.mtrl-sci

Taichi Terashima , Yuya Hattori , David Graf , Takahiro Urata , Tomoki Yoshioka , Wataru Hattori , Hiroshi Ikuta , Hiroaki Ikeda This is my paper · ORCID
classification cond-mat.mtrl-sci PACS 71.18.+y75.50.Ee71.20.-b
keywords altermagnetismCrSbquantumoscillationsFermisurfacespinsplittingShubnikov-deHaaseffectdeHaas-vanAlphenDFT+U
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

The paper sets out to verify, in the bulk, the altermagnetic band structure of CrSb, a collinear antiferromagnet whose up- and down-spin sublattices are related by rotation and whose bands should be spin-split with g-wave symmetry. Using Shubnikov–de Haas and magnetic-torque measurements in fields up to 41.5 T, combined with DFT+U calculations including spin-orbit coupling, it identifies five quantum-oscillation frequency branches and assigns each to extremal orbits on four spin-non-degenerate bands. The central result is that the measured frequencies are consistently explained by the calculated altermagnetic Fermi surface, with bands 1 and 2 forming outer tubular sheets along ΓA plus new closed pockets at A, band 3 contributing ring-like and general-point orbits, and band 4 ellipsoidal pockets at M. This matters because it gives definitive bulk measurement, as opposed to surface-sensitive photoemission, of altermagnetic spin splitting, and it settles the Fermi-surface topology of a prototypical altermagnet.

What carries the argument

The key machinery is the Onsager relation F=(ħ/2πe)A, connecting each measured frequency to an extremal Fermi-surface cross-section, and the Lifshitz–Kosevich formula for fitting amplitudes. The calculated Fermi surface comes from fully relativistic DFT+U (U=0.01 Ry on Cr d orbitals) with spin-orbit coupling, giving four spin-split bands. To match the dominant α frequency, the Fermi levels of bands 1–2 are shifted up by 0.046 eV and bands 3–4 down by 0.007 eV; the comparison of these shifted calculations with the measured angle-dependent branches is the load-bearing evidence.

What would settle it

Treat the rigid band shifts and the Hubbard U as free parameters and simultaneously fit all five measured branches across both rotation planes; if no single set of shifts reproduces the observed angular dependences of α, β, δ, ε, and ζ, the altermagnetic Fermi-surface assignment fails. Alternatively, angle-resolved photoemission at the wave vectors of the 3-gp orbits (around kz ≈ 0.21·2π/c) should directly image the band-3 pockets assigned to the β branch; their absence would falsify that assignment.

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Extended reading notes

Core claim

The measured quantum-oscillation frequencies in CrSb—α, β, δ, ε, and ζ—are each assigned to extremal orbits of a DFT+U Fermi surface in which four bands cross the Fermi level and are spin-split by altermagnetic order. Bands 1 and 2 each contribute an outer tubular sheet along Γ-A and an inner closed pocket at A, which explains the δ branch near B∥c and corrects earlier open-tube or dogbone proposals. Band 3 provides the general-point orbits behind the β and high-angle δ branches and the T-line orbit behind ζ; band 4 gives ellipsoidal pockets at M that explain ε. Effective masses are only moderately enhanced over band masses, and no Zeeman-driven frequency splitting is seen; the paper present

Load-bearing premise

The comparison between experiment and theory relies on rigidly shifting the calculated Fermi energies—up 0.046 eV for bands 1–2 and down 0.007 eV for bands 3–4—to fit the dominant α frequency; if those shifts, or the Hubbard U=0.01 Ry, misrepresent the true band structure, the orbit assignments, especially for the band-3 general-point orbits and the band-1/2 A pockets, could be wrong.

Editorial extensions

If this is right

  • CrSb's Fermi-surface topology is now pinned down by a bulk probe: bands 1 and 2 carry inner closed pockets at A plus outer tubular sheets, ruling out the earlier open-tube and dogbone proposals.
  • Quantum oscillations are shown to be a workable bulk tool for detecting altermagnetic spin splitting in metals, complementing surface-sensitive photoemission.
  • The assignment of the β branch and the high-angle δ branch to band-3 general-point orbits rounds out the experimental picture of the higher bands, which previous studies had not addressed.
  • Effective masses only moderately exceed band masses (m*/m_band ≈ 1.3–1.8), indicating that electron correlations are not strong in CrSb and that the DFT+U description is a credible starting point.
  • Derived mobilities (roughly 400–700 cm²/Vs) are consistent with the high-mobility multicarrier transport reported for CrSb, tying the Fermi-surface picture to bulk transport behavior.

Reading between the lines

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

  • The same measurement strategy could be applied to other metallic altermagnet candidates: predicted momentum-dependent spin splitting should appear as a characteristic multiplicity of frequency branches, and its absence would test the altermagnetic assignment.
  • Because the α branch is a sum of two nearly degenerate orbits (1-A-o and 2-A-o), a careful beat analysis at higher fields could separate the two and directly reveal the spin-orbit-induced splitting between them—a finer check than the frequency assignment itself.
  • If the inner A pockets are real, measurements beyond 41.5 T should reveal additional low-frequency branches; detecting or failing to detect them is a concrete extension of this work.
  • The predicted Zeeman-driven merging and re-splitting of altermagnetic frequency branches is a natural next experiment at 60 T or higher: confirming the predicted behavior would further validate the altermagnetic band structure.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper reports a quantum-oscillation (SdH and dHvA) study of the altermagnetic metal CrSb, combining high-field transport and torque measurements with DFT+U calculations including spin-orbit coupling. Multiple frequency branches (α, β, δ, ε, ζ) are tracked over wide angular ranges and assigned to extremal orbits on the calculated four-band Fermi surface. The authors conclude that their results provide definitive bulk-sensitive evidence for the altermagnetic spin-split Fermi surface and that bands 1 and 2 consist of tubular sheets plus A-centered pockets, with band-3 and band-4 orbits explaining the remaining branches. They also argue that the Berry phase of the α oscillation cannot be reliably inferred because α is a sum of two near-degenerate orbits.

Significance. If the assignments are correct, the paper would be an important bulk-sensitive confirmation of altermagnetic spin splitting in CrSb, complementing surface-sensitive ARPES studies. The experimental work is substantial: high-quality crystals, multiple techniques, wide angular tracking, and careful treatment of the Lifshitz–Kosevich analysis. The paper is also honest about the ambiguity in the Berry-phase determination. However, the central claim of definitive evidence is weakened by the explicit use of adjustable rigid Fermi-level shifts to match the dominant α frequency and by the sensitivity of the band-3 Fermi-surface topology to the chosen Hubbard U. Those points need to be addressed before the conclusion can be accepted at face value.

major comments (4)
  1. [Supplemental, 'Band structure calculations'] The α frequency is reproduced by rigidly shifting the Fermi level of bands 1 and 2 by +0.046 eV and of bands 3 and 4 by −0.007 eV. Thus the agreement of the calculated 1-A-o orbit with the experimental α branch is not an independent prediction but a least-squares-style fit. The paper should state the unshifted DFT+U frequency for this orbit, quantify the discrepancy, and justify the shift independently (e.g., by comparison with ARPES or with a self-consistent renormalization). Without this, the agreement for α is a tuning result and cannot be cited as evidence for the altermagnetic calculation.
  2. [Supplemental, 'Band structure calculations'] The band-3 Fermi surface is explicitly reconstructed by the introduction of U = 0.01 Ry, which 'breaks the complex connectivity ... generating several small pockets.' The β and δ (|θ| ≥ 40°) branches are assigned to the 3-gp1 and 3-gp2 orbits on these reconstructed pockets. Because no systematic scan over U or over double-counting schemes is presented, it is possible that the existence and shape of these pockets are artifacts of a single chosen value of U. This is load-bearing: β and δ are the only branches assigned to band-3, and the paper uses them to claim comprehensive Fermi-surface coverage. A U-dependence study or an independent check of the pocket sizes (e.g., via carrier densities or ARPES) is needed.
  3. [Abstract vs. main text, p. 2] The abstract states that 'bands 1 and 2 form closed pockets centered at the A point, rather than the tubular c-axis-open sheets ... proposed in previous studies.' This directly contradicts the main text, which says each band-1 and band-2 Fermi surface 'consists of an outer tubular sheet along the ΓA line and an inner closed pocket at the A point.' The abstract must be corrected; as written, it misstates the paper's own calculated and argued Fermi-surface topology and could mislead readers about the central result.
  4. [General comparison with a spin-degenerate calculation] The paper compares the measured frequencies only to a spin-polarized DFT+U calculation that contains the known altermagnetic order. It does not provide a comparison with a spin-degenerate (nonmagnetic or artificially paramagnetic) calculation. Since the magnetic order is already established by neutron diffraction and the DFT+U calculation builds it in, the observation of multiple frequencies does not by itself demonstrate altermagnetic spin splitting. A direct comparison with a nonmagnetic calculation would clarify which frequency branches are specifically attributable to the spin splitting, rather than to the underlying band structure. This comparison is needed to support the 'definitive evidence' claim.
minor comments (5)
  1. [Title] Typo: 'quantum os cillation' should be 'quantum oscillation'.
  2. [Fig. 1, caption and text] The sentence 'the lowest frequency peaks ... correspond to oscillations with periods of 1.5 or lower within the measured field range' is unclear. Presumably the frequencies are below about 1.5 T, corresponding to long periods; please rephrase to avoid confusion between frequency and period.
  3. [Supplemental, Eq. (S2) and following] The assumption A1 = A2 and ϕB,1 = −ϕB,2 for the two α components is introduced without comment. Since this assumption underlies the explanation of the near-zero intercept, it should be explicitly justified or at least flagged as an assumption that cannot be independently verified from the present data.
  4. [Fig. 2 and Table SI] The experimental branches are shown with different symbols for different samples/field windows, but no legend appears in Fig. 2(a). Adding a legend or a clear table matching symbols to conditions would improve readability.
  5. [References] References [33] and [34] are parallel studies; the paper compares frequencies with them. It would be helpful to state explicitly which of their samples/methods are being compared, and whether the differences in field windows could affect the frequency resolution.

Circularity Check

1 steps flagged · score 4.0 of 10

One quantum-oscillation frequency (α) is used to calibrate the DFT+U Fermi level, so that branch is partly explained by construction; the remaining branches retain independent content.

  1. fitted input called prediction [Supplemental Material, 'Band structure calculations'; main-text Fig. 2(a), Table S I, and Conclusion]
    "To reproduce the experimentally observed oscillation frequency α with the extremal orbit 1-A-o of the band-1 Fermi surface obtained in the DFT+U calculation, the Fermi levels of bands 1 and 2 were shifted upward by 0.046 eV."

    The α frequency is the target used to set the Fermi-level shift of the calculated bands. Therefore the later agreement of the calculated 1-A-o orbit with the measured α branch at B∥c is imposed by construction, not independently tested. When the paper concludes that the DFT+U Fermi surface 'provides an excellent explanation for the experimentally observed quantum-oscillation frequencies', one of the included branches (α) is explained only because the calculation was adjusted to match it. However, the assignments of β, δ, ε, and ζ to band-3 and band-4 orbits are not individually fitted, and the angular dependence of the calculated orbits is not forced by this single shift.

full rationale

The paper is largely self-contained and transparent about its one calibration step: the Supplemental Material explicitly states that the band-1/2 Fermi level was shifted upward by 0.046 eV to reproduce the α frequency, with a smaller compensating shift for bands 3/4. This makes the α branch a fit point rather than a prediction, which is a genuine but limited circular component. It does not by itself force the other assignments: β and δ are matched to general-point orbits on the band-3 pocket, ε and ζ to band-4/band-3 orbits, and the angular shapes of these branches are compared over wide field-rotation ranges, not set by the α shift. The band-3 reconstruction is attributed to the externally chosen Hubbard U=0.01 Ry, cited to a previous non-self study; no U-scan is shown, so the β/δ assignments are sensitive to that modeling choice, but the paper does not fit U to the data, making this a correctness/robustness concern rather than a circularity. The altermagnetic spin-split conclusion is also supported by independently established collinear magnetic order and by ARPES studies of bands 1/2, so the central claim does not reduce solely to the fitted calculation. Self-citations are present but not load-bearing: [34] includes a coauthor but is used for comparison/disagreement, and [35]/[SM7] concern crystal growth and LK conventions. Overall the circular content is partial and confined to one calibration branch, so the score is moderate.

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

The central interpretation rests on a DFT+U Fermi surface that is adjusted with two rigid Fermi-level shifts and a Hubbard U chosen from prior literature. The Onsager and Lifshitz–Kosevich relations are standard. No new particles, forces, or conserved quantities are introduced; the 'orbits' are features of the calculated Fermi surface.

free parameters (3)
  • Fermi level shift for bands 1 and 2 = +0.046 eV
    Shifted upward to reproduce the experimental α frequency (orbit 1-A-o) in the DFT+U calculation.
  • Fermi level shift for bands 3 and 4 = -0.007 eV
    Shifted downward to compensate the carrier-number change from the bands 1-2 shift; affects band-3/4 frequencies.
  • Hubbard U on Cr d orbitals = 0.01 Ry (~1.36 eV)
    Adopted from prior work (ref SM16); enlarges band-1/2 volumes and reconstructs the band-3 Fermi surface. Not fitted in this paper but a tunable model input.
assumptions (6)
  • standard math Onsager relation F = (ℏ/2πe)A relates quantum-oscillation frequency to Fermi-surface cross-sectional area
    Used to convert measured frequencies to areas; well-established.
  • domain assumption Lifshitz–Kosevich formula describes quantum-oscillation amplitude with temperature and Dingle factors
    Standard fermiology; assumes non-interacting quasiparticles and extremal orbits (Supplemental Eq. S1).
  • domain assumption PBE+U with AMF double-counting and U=0.01 Ry describes the CrSb electronic structure near the Fermi level
    Implemented in Wien2k; U value taken from ref SM16; affects Fermi-surface topology.
  • ad hoc to paper Rigid-band Fermi-level shifts are valid for interpreting quantum-oscillation frequencies
    Used to match α; implicitly assumes the band structure is unchanged by a doping-like energy shift.
  • ad hoc to paper For B ∥ c, the α oscillation is a sum of two near-degenerate orbits with equal amplitudes and opposite phases (A1=A2, ϕB1=−ϕB2)
    Supplemental Eqs. S2-S3; used to explain the near-zero Landau-fan intercept and the ambiguity of the Berry-phase determination.
  • domain assumption CrSb has altermagnetic order with Cr moments up/down along c, ordered moment ~3 μB
    From prior neutron diffraction; used as input to the DFT calculation.

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Pith. "Pith review of Altermagnetic spin-split Fermi surfaces in CrSb revealed by quantum oscillation measurements." pith.science (2026). https://pith.science/paper/DVLWZDCA

@misc{pith2026260119105,
  author       = {Pith},
  title        = {Pith review of: Altermagnetic spin-split Fermi surfaces in CrSb revealed by quantum oscillation measurements},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DVLWZDCA}},
  note         = {Machine review of arXiv:2601.19105}
}
abstract

We report a comprehensive quantum oscillation study of the prototypical altermagnet CrSb, combining high-field magnetotransport and torque measurements with DFT + $U$ calculations including spin-orbit coupling. Multiple quantum oscillation frequencies were observed and tracked over wide angular ranges. The measured frequency branches are consistently explained by the spin-split Fermi surfaces arising from the altermagnetic electronic structure. Our determined Fermi surface reveals that bands 1 and 2 form closed pockets centered at the A point, rather than the tubular $c$-axis-open sheets or $\Gamma$-centered closed pockets proposed in previous studies. Our findings establish the Fermi-surface topology of CrSb and provide a firm basis for exploring emergent phenomena in altermagnetic materials.

Figures

Figures reproduced from arXiv: 2601.19105 by the authors.

Figure 1
Figure 1. FIG. 1. Quantum oscillations in CrSb. (a) Magnetic field depen [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Fermi surface in CrSb. Magnetic-field-direction dependen [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Temperature and magnetic-field dependences of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Band splitting in the altermagnet CrSb

    cond-mat.str-el 2026-02 unverdicted novelty 5.0 of 10

    The proposed spin–orbit band splitting for CrSb (Eq. 10) is not invariant under the paper's own magnetic group (Eq. 9), and the abstract's toroid-altermagnet result is absent from the text.

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Works this paper leans on

51 extracted references · 2 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Cvetkovic and O

    V. Cvetkovic and O. Vafek, Space group symmetry, spin- orbit coupling, and the low-energy effective Hamiltonian for iron-based superconductors, Phys. Rev. B 88, 134510 (2013)

    2013

  2. [2]

    Nakatsuji, N

    S. Nakatsuji, N. Kiyohara, and T. Higo, Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature, Nature 527, 212 (2015)

    2015

  3. [3]

    Takagi, R

    R. Takagi, R. Hirakida, Y. Settai, R. Oiwa, H. Tak- agi, A. Kitaori, K. Yamauchi, H. Inoue, J.-i. Yamaura, D. Nishio-Hamane, S. Itoh, S. Aji, H. Saito, T. Nakajima, T. Nomoto, R. Arita, and S. Seki, Spontaneous Hall ef- fect induced by collinear antiferromagnetic order at room temperature, Nat. Mater. 24, 63 (2025)

    2025

  4. [4]

    L´ opez-Moreno, A

    S. L´ opez-Moreno, A. H. Romero, J. Mej ´ ıa-L´ opez, A. Mu˜ noz, and I. V. Roshchin, First-principles study of electronic, vibrational, elastic, and magnetic properties of FeF2 as a function of pressure, Phys. Rev. B 85, 134110 (2012)

    2012

  5. [5]

    Y. Noda, K. Ohno, and S. Nakamura, Momentum- dependent band spin splitting in semiconducting MnO 2: a density functional calculation, Phys. Chem. Chem. Phys. 18, 13294 (2016)

    2016

  6. [6]

    K.-H. Ahn, A. Hariki, K.-W. Lee, and J. Kuneˇ s, Antifer- romagnetism in RuO 2 as d-wave pomeranchuk instability, Phys. Rev. B 99, 184432 (2019)

    2019

  7. [7]

    M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Mo- tome, and H. Seo, Spin current generation in organic an- tiferromagnets, Nat. Commun. 10, 4305 (2019)

    2019

  8. [8]

    Hayami, Y

    S. Hayami, Y. Yanagi, and H. Kusunose, Momentum- dependent spin splitting by collinear antiferromagnetic ordering, J. Phys. Soc. Jpn. 88, 123702 (2019)

    2019

Show all 51 references
  1. [9]

    ˇSmejkal, R

    L. ˇSmejkal, R. Gonz´ alez-Hern´ andez, T. Jungwirth, and J. Sinova, Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets, Sci. Adv. 6, eaaz8809 (2020)

    2020

  2. [10]

    L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and A. Zunger, Giant momentum-dependent spin splitting in centrosymmetric low- Z antiferromagnets, Phys. Rev. B 102, 014422 (2020)

    2020

  3. [11]

    I. I. Mazin, K. Koepernik, M. D. Johannes, R. Gonz´ alez- Hern´ andez, and L.ˇSmejkal, Prediction of unconventional magnetism in doped FeSb 2, Proc. Natl. Acad. Sci. USA 118, e2108924118 (2021)

    2021

  4. [12]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Beyond conven- tional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X 12, 031042 (2022)

    2022

  5. [13]

    Mazin, Altermagnetism then and now, Physics 17, 4 (2024)

    I. Mazin, Altermagnetism then and now, Physics 17, 4 (2024)

    2024

  6. [14]

    Hiraishi, H

    M. Hiraishi, H. Okabe, A. Koda, R. Kadono, T. Muroi, D. Hirai, and Z. Hiroi, Nonmagnetic ground state in RuO2 revealed by muon spin rotation, Phys. Rev. Lett. 132, 166702 (2024)

    2024

  7. [15]

    Keßler, L

    P. Keßler, L. Garcia-Gassull, A. Suter, T. Prokscha, Z. Salman, D. Khalyavin, P. Manuel, F. Orlandi, I. I. Mazin, R. Valent ´ ı, and S. Moser, Absence of magnetic order in RuO 2: insights from µSR spectroscopy and neu- tron diffraction, npj Spintronics 2, 50 (2024)

    2024

  8. [16]

    Z. Wu, M. Long, H. Chen, S. Paul, H. Matsuki, O. Zhe- liuk, U. Zeitler, G. Li, R. Zhou, Z. Zhu, D. Graf, T. I. Weinberger, F. M. Grosche, Y. Maeno, and A. G. Eaton, Fermi surface of RuO2 measured by quantum oscillations, Phys. Rev. X 15, 031044 (2025)

    2025

  9. [17]

    Krempask´ y, L

    J. Krempask´ y, L. ˇSmejkal, S. W. D’Souza, M. Ha- jlaoui, G. Springholz, K. Uhl ´ ıˇ rov´ a, F. Alarab, P. C. Constantinou, V. Strocov, D. Usanov, W. R. Pudelko, R. Gonz´ alez-Hern´ andez, A. Birk Hellenes, Z. Jansa, H. Reichlov´ a, Z. ˇSob´ aˇ n, R. D. Gonzalez Betancourt, P...

    2024

  10. [18]

    S. Lee, S. Lee, S. Jung, J. Jung, D. Kim, Y. Lee, B. Seok, J. Kim, B. G. Park, L. ˇSmejkal, C.-J. Kang, and C. Kim, Broken kramers degeneracy in altermagnetic MnTe, Phys. Rev. Lett. 132, 036702 (2024)

    2024

  11. [19]

    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. B 109, 115102 (2024)

    2024

  12. [20]

    A. I. Snow, Neutron diffraction investigation of the atomic magnetic moment orientation in the antiferro- magnetic compound CrSb, Phys. Rev. 85, 365 (1952)

    1952

  13. [21]

    W. J. Takei, D. E. Cox, and G. Shirane, Magnetic struc- tures in the MnSb-CrSb system, Phys. Rev. 129, 2008 (1963). 6

    2008

  14. [22]

    Reimers, L

    S. Reimers, L. Odenbreit, L. ˇSmejkal, 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. Kl¨ aui, J. Sinova, and M. Jourdan, Direct observation of altermag...

    2024

  15. [23]

    G. Yang, Z. Li, S. Yang, J. Li, H. Zheng, W. Zhu, Z. Pan, Y. Xu, S. Cao, W. Zhao, A. Jana, J. Zhang, M. Ye, Y. Song, L.-H. Hu, L. Yang, J. Fujii, I. Vobornik, M. Shi, H. Yuan, Y. Zhang, Y. Xu, and Y. Liu, Three- dimensional mapping of the altermagnetic spin splitting in CrSb, ...

    2025

  16. [24]

    Zeng, M.-Y

    M. Zeng, M.-Y. Zhu, Y.-P. Zhu, X.-R. Liu, X.-M. Ma, Y.- J. Hao, P. Liu, G. Qu, Y. Yang, Z. Jiang, K. Yamagami, M. Arita, X. Zhang, T.-H. Shao, Y. Dai, K. Shimada, Z. Liu, M. Ye, Y. Huang, Q. Liu, and C. Liu, Observation of spin splitting in room-temperature metallic antiferro-...

    2024

  17. [25]

    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

  18. [26]

    W. Li, W. Li, M. Zou, Y. Yin, H. Li, G. Qu, Y. Huang, R. Yu, H. Yang, and B. Wang, Large anisotropic x-ray magnetic circular dichroism in altermagnetic CrSb with collinear antiferromagnetic structure at room tempera- ture, Phys. Rev. B 111, 224417 (2025)

    2025

  19. [27]

    C. Li, M. Hu, Z. Li, Y. Wang, W. Chen, B. Thiagara- jan, M. Leandersson, C. Polley, T. Kim, H. Liu, C. Fulga, M. G. Vergniory, O. Janson, O. Tjernberg, and J. van den Brink, Topological Weyl altermagnetism in CrSb, Com- mun. Phys. 8, 311 (2025)

    2025

  20. [28]

    C. R. Whitsett, Oscillatory magnetoresistance in mer- curic selenide, Phys. Rev. 138, A829 (1965)

    1965

  21. [29]

    L. M. Roth, S. H. Groves, and P. W. Wyatt, Inver- sion asymmetry effects on oscillatory magnetoresistance in HgSe, Phys. Rev. Lett. 19, 576 (1967)

    1967

  22. [30]

    J. R. Anderson and A. V. Gold, de Haas-van Alphen effect and internal field in iron, Phys. Rev. Lett. 10, 227 (1963)

    1963

  23. [31]

    A. S. Joseph and A. C. Thorsen, de Haas-van Alphen effect and Fermi surface in nickel, Phys. Rev. Lett. 11, 554 (1963)

    1963

  24. [32]

    A. V. Gold, Fermi-surface studies in iron and nickel, J. Appl. Phys. 39, 768 (1968)

    1968

  25. [33]

    and approximate those estimated from multicarrier analyses of the magnetotransport data of major carri- ers with carrier densities of 10 20 cm−3 or larger [35, 36]. These multicarrier analyses suggested the existence of high-mobility minor carriers with mobilities above 2000 c...

    2000

  26. [35]

    M. Long, T. I. Weinberger, Z. Wu, M. F. Hansen, R. Tao, M. Shrestha, D. Graf, Y. Skourski, F. M. Grosche, and A. G. Eaton, 3D bulk-resolved g-wave magnetic order parameter symmetry in the metallic altermagnet CrSb, arXiv:2601.14526 (2026)

    2026 arXiv

  27. [36]

    Urata, W

    T. Urata, W. Hattori, and H. Ikuta, High mobility charge transport in a multicarrier altermagnet CrSb, Phys. Rev. Mater. 8, 084412 (2024)

    2024

  28. [37]

    X. Peng, Y. Wang, S. Zhang, Y. Zhou, Y. Sun, Y. Su, C. Wu, T. Zhou, L. Liu, H. Wang, J. Yang, B. Chen, Z. Fang, J. Du, Z. Jiao, Q. Wu, and M. Fang, Scaling behavior of magnetoresistance and Hall resistivity in the altermagnet CrSb, Phys. Rev. B 111, 144402 (2025)

    2025

  29. [38]

    See Supplemental Material at [URL] for the crys- tal growth procedure, Lifshitz-Kosevich formula, band- structure calculations, Landau-fan plot of α oscillations, and experimental and calculated Fermi surface parame- ters, which includes Refs. 38–51

  30. [39]

    Blaha, K

    P. Blaha, K. Schwarz, F. Tran, R. Laskowski, G. K. H. Madsen, and L. D. Marks, WIEN2k: An APW+lo pro- gram for calculating the properties of solids, J. Chem. Phys. 152, 074101 (2020)

    2020

  31. [40]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996)

    1996

  32. [41]

    Momma and F

    K. Momma and F. Izumi, VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011)

    2011

  33. [42]

    Z.-X. Li, H. Zhou, X. Wan, and W. Chen, Diagnosing al- termagnetic phases through quantum oscillations, Phys. Rev. B 111, 125119 (2025)

    2025

  34. [43]

    F. E. Richards, Investigation of the magnetoresistance quantum oscillations in magnesium, Phys. Rev. B 8, 2552 (1973)

    1973

  35. [44]

    Shoenberg, Magnetic Oscillations in Metals (Cam- bridge University Press, Cambridge, 1984)

    D. Shoenberg, Magnetic Oscillations in Metals (Cam- bridge University Press, Cambridge, 1984)

    1984

  36. [45]

    G. P. Mikitik and Y. V. Sharlai, Semiclassical energy levels of electrons in metals with band degeneracy lines, Soviet Physics–JETP 87, 747 (1998)

    1998

  37. [46]

    Alexandradinata and L

    A. Alexandradinata and L. Glazman, Fermiology of topo- logical metals, Annu. Rev. Condens. Matter Phys. 14, 261 (2023)

    2023

  38. [47]

    H. Aoki, N. Kimura, and T. Terashima, Fermi surface properties, metamagnetic transition and quantum phase transition of CeRu 2Si2 and its alloys probed by the dHvA effect, J. Phys. Soc. Jpn. 83, 072001 (2014)

    2014

  39. [48]

    A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Density-functional theory and strong interactions: Or- bital ordering in Mott-Hubbard insulators, Phys. Rev. B 52, R5467 (1995)

    1995

  40. [49]

    A. B. Shick, A. I. Liechtenstein, and W. E. Pickett, Implementation of the LDA+U method using the full- potential linearized augmented plane-wave basis, Phys. Rev. B 60, 10763 (1999)

    1999

  41. [50]

    A. G. Petukhov, I. I. Mazin, L. Chioncel, and A. I. Licht- enstein, Correlated metals and the LDA + U method, Phys. Rev. B 67, 153106 (2003)

    2003

  42. [51]

    Marzari and D

    N. Marzari and D. Vanderbilt, Maximally localized gen- eralized Wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997)

    1997

  43. [52]

    Kuneˇ s, R

    J. Kuneˇ s, R. Arita, P. Wissgott, A. Toschi, H. Ikeda, and K. Held, Wien2wannier: From linearized augmented plane waves to maximally localized Wannier functions, Comput. Phys. Commun. 181, 1888 (2010) . verSM3 Supplemental Material: Altermagnetic spin-split Fermi surfaces in ...

    2010 arXiv

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