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REVIEW 2 major objections 6 minor 38 references

Direction-Dependent Conduction Polarity in Altermagnetic CrSb

T0 review · 2 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read CrSb conducts holes along its c-axis and electrons in the ab-plane, a direction-dependent polarity confirmed by Hall and Seebeck measurements.

desk verdict Solid experimental evidence for direction-dependent conduction polarity in CrSb, with a DFT mechanism that is plausible but partly post hoc because the Fermi-energy shift is fitted. read the letter →

arxiv 2502.02231 v2 pith:M46CRUW6 submitted 2025-02-04 cond-mat.mtrl-sci

Banik Rai , Krishnendu Patra , Satyabrata Bera , Sk Kalimuddin , Kakan Deb , Mintu Mondal , Priya Mahadevan , Nitesh Kumar This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords direction-dependentconductionpolarityaltermagnetismCrSbHalleffectSeebeckcoefficientFermisurfacegeometrymulticarriertransportholedoping
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 reports that the altermagnetic metal CrSb carries current by holes along its hexagonal c-axis and by electrons within the ab-plane, an effect it calls direction-dependent conduction polarity (DDCP). The evidence is two independent probes: the low-field Hall coefficient and the Seebeck thermopower, both of which keep opposite signs in the two directions over the whole measured temperature range. The authors use density-functional band calculations to trace the effect to a multicarrier Fermi surface, with two hole-like pockets and one electron-like pocket whose direction-averaged effective masses make in-plane conduction electron-dominated and cross-plane conduction hole-dominated. They predict the effect lives in a narrow energy window near the Fermi level, and they confirm that prediction by showing that substituting 2% vanadium (about 0.04 added holes per unit cell) removes it and drives the material p-type in all directions.

What carries the argument

The load-bearing object is the Fermi surface of CrSb at the shifted Fermi energy $E'_F$, computed with density-functional band theory. Its three sheets, two hyperboloid-like hole pockets ($\alpha$, $\beta$) that include small electron-like hemispherical sub-pockets and one bead-like electron pocket ($\gamma$), are analyzed through the inverse effective-mass tensor $m^{*-1}_{ij}$, essentially the curvature of the band at each Fermi-surface point. Averaged over the whole surface this tensor is positive for the in-plane directions $x$ and $y$ and negative for the cross-plane direction $z$, which is the mechanism that makes the Hall and Seebeck signs switch with current direction. The same Fermi surface, with its shape set by altermagnetic spin splitting, is what confines the effect to a narrow $\Delta E \approx 14$ meV energy window.

What would settle it

Measure the real Fermi surface of CrSb by quantum oscillations (Shubnikov–de Haas or de Haas–van Alphen) and compare the observed pocket cross-sections and carrier densities with the DFT bands at the unshifted and shifted Fermi levels; if the observed pockets match the unshifted Fermi level rather than $E'_F$, the proposed 100 meV shift and with it the theoretical mechanism would be falsified. A simpler check is to measure Hall and Seebeck on a thoroughly characterized stoichiometric crystal and see whether the sign switch persists.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that the sign of the dominant charge carrier in CrSb is set by crystal direction: Hall and Seebeck measurements both say electrons dominate in the $ab$-plane while holes dominate along $c$. Density-functional band theory at a Fermi energy shifted 100 meV below its nominal calculated position reproduces the sign pattern and attributes it to a multicarrier mechanism: two nearly hyperboloid hole pockets ($\alpha$, $\beta$) and one anisotropic electron pocket ($\gamma$) combine so that the average inverse effective-mass tensor is positive in-plane and negative along $z$. The calculation further locates DDCP in a window of roughly 14 meV around the shifted Fermi level and predicts suppression by modest hole doping; the measured loss of DDCP in $\mathrm{Cr}_{0.98}\mathrm{V}_{0.02}\mathrm{Sb}$ supports that prediction.

Load-bearing premise

The whole DFT account of DDCP rests on moving the Fermi level 100 meV below its unshifted calculated value (about 0.13 added holes per unit cell), and the paper's only in-text justification is that real crystals often deviate from perfect stoichiometry; its own composition analysis shows CrSb close to 1:1, so the shift is not directly evidenced.

Editorial extensions

If this is right

  • A single air-stable crystal of earth-abundant CrSb can act as both an electron conductor and a hole conductor depending on direction, so a device made from it can internalize p- and n-type functions without junctions.
  • Because DDCP survives in only a roughly 14 meV window near the Fermi level, small doping, strain, or compositional shifts can switch the material from DDCP to wholly p-type, as demonstrated with 2% vanadium substitution.
  • The magnetic point group of the A-type antiferromagnetic order enforces equal Hall coefficients $R_{zyx}=R_{xzy}$, and the measured equality supports the assigned magnetic symmetry while ruling out anomalous-Hall explanations for the nonlinear Hall response.
  • The coexistence of DDCP and altermagnetic spin splitting makes CrSb a single platform where direction-dependent conduction polarity and spin-polarized bands can be addressed together.

Reading between the lines

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

  • The 100 meV rigid-band shift adds about 0.13 holes per unit cell, yet the composition analysis shows near-1:1 stoichiometry; the shift is therefore an inference from Fermi-surface agreement with published ARPES data rather than a measured composition effect, and direct carrier-density or quantum-oscillation measurements would settle it.
  • By the same rigid-band logic, electron doping (for instance substituting Sb with Te or adding interstitial donors) should move the Fermi level the opposite way and might widen or relocate the DDCP window instead of destroying it; this is a testable extension the paper does not attempt.
  • Since the sign switch is controlled entirely by Fermi-surface geometry, other NiAs-type antiferromagnets with similar altermagnetic band splittings may show the same direction-dependent polarity; a symmetry-and-curvature search over isostructural compounds could find more candidates.
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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

2 major / 6 minor

Summary. This manuscript reports the experimental observation of direction-dependent conduction polarity (DDCP) in altermagnetic CrSb. Hall measurements in three geometries and Seebeck measurements along the in-plane and c-axis directions consistently show electron-dominated conduction in the ab-plane and hole-dominated conduction along the c-axis. Density functional theory (DFT) transport calculations attribute this behavior to a multicarrier mechanism involving two hole pockets and one electron pocket, but only after shifting the Fermi energy by -100 meV (about 0.13 holes per unit cell). The manuscript further reports that 2% V doping (Cr0.98V0.02Sb) suppresses DDCP, consistent with the DFT prediction of a narrow energy window.

Significance. The experimental detection of DDCP in an altermagnet is a new and potentially significant result, with implications for anisotropic thermoelectric and spintronic devices. The mutual consistency of the Hall and Seebeck signs and the agreement with the magnetic point group constraint Rzyx = Rxzy make the core experimental observation robust. The DFT mechanism, if independently confirmed, would demonstrate a concrete example of multicarrier-driven DDCP in an earth-abundant material and its tunability by doping. However, the theoretical prediction is contingent on an unmeasured Fermi-energy shift, and the doping experiment provides only directional support.

major comments (2)
  1. [Sec. 2, DFT paragraph (Fig. 4)] The DFT calculation of DDCP is not parameter-free: the Fermi energy is shifted by -100 meV (about 0.13 holes per unit cell), introduced with the statement 'Real crystals often deviate from perfect stoichiometry...'. This shift is required for the computed Seebeck and Hall coefficients (Fig. 4c,d) to match the experimental signs. The EDXS data in Table S1 give Cr1.0065Sb0.9935, which is slightly Cr-rich and would dope electrons rather than holes, so the stoichiometry argument is not directly supported. The appeal to ARPES Fermi-surface agreement (Refs. 25-27) is qualitative and does not uniquely determine the -100 meV value. Consequently, the 14 meV DDCP window in Fig. 4b and the predicted doping sensitivity are partly post hoc. The authors should either provide an independent measurement of the Fermi-level position (e.g., quantum oscillations or a calibrated ARPES energy scan) or explicitly present the calculation as a scenario calculation that assumes a particular shift.
  2. [Sec. 2, Fig. 6 paragraph] The Cr0.98V0.02Sb doping experiment gives qualitative support for the DFT prediction, but it does not quantitatively validate the assumed -100 meV offset or the 14 meV window. Because the model already contains a pre-existing shift of 0.13 holes/u.c., the additional 0.04 holes/u.c. introduced by 2% V doping tests only the direction of the predicted shift, not its magnitude. The statement that the experiment 'confirms' the narrow-energy-window prediction overstates the evidence; the experiment is consistent with the scenario but does not independently fix the offset.
minor comments (6)
  1. [Abstract and Sec. 2] The abstract contains the typo 'F urthermore' with an extra space, and Sec. 2 includes 'carrier denisty' instead of 'carrier density'.
  2. [Fig. 3g] The y-axis label of the Seebeck panel appears as 'Sii (mV/K)' but should be 'Sii (μV/K)' to match the units used in the text and in Fig. 4.
  3. [Sec. 2] The phrase 'the identical sign and magnitude of Rzyx and Rxzy' is stronger than the data support; the measurements are consistent with the symmetry constraint Rzyx = Rxzy within experimental uncertainty, so the wording should be softened accordingly.
  4. [Supporting Information, Fig. S6 caption] The caption refers to the 'experimental fermi energy', which should be capitalized as 'experimental Fermi energy' for consistency.
  5. [Sec. 2, Fig. 4b] The label 'DCP~14 meV' in Fig. 4b should read 'DDCP' to match the abbreviation used throughout the main text.
  6. [Supporting Information, Sec. S2] The parameters of the three-carrier fit in Table S2 are reported without error bars or a uniqueness analysis; adding these would strengthen the quantitative statements, although the qualitative sign conclusions do not depend on the fit.

Circularity Check

1 steps flagged · score 5.0 of 10

DFT mechanism for DDCP relies on a Fermi-energy shift chosen to reproduce the observed sign anisotropy; the theoretical DDCP 'prediction' is therefore partly calibrated, but the V-doping and ARPES checks provide independent content.

  1. fitted input called prediction [Section 2 (Results and Discussion), Fig. 4 paragraph; echoed in Abstract and Conclusion]
    "Real crystals often deviate from perfect stoichiometry, which changes the position of the Fermi energy. This must, however, be considered in the DFT calculations to capture the trends seen in the experiment. We find that adding a small number of holes per unit cell ( ∼ 0.13/u.c.) induces DDCP. In this case, the Fermi energy EF is shifted below by 100 meV to E′F, represented by the black dashed line in Figure 4(a) and 4(b)."

    The offset E′F is determined by requiring the DFT calculation to match the already observed DDCP signs ('to capture the trends seen in the experiment'; 'adding ... holes ... induces DDCP'). All subsequent theoretical statements that DDCP exists at E′F and in a ~14 meV window around it inherit this calibrated choice: the center of the window is where the fit placed it, so the existence of DDCP at that energy is guaranteed rather than independently predicted. The SI (Table S1) measures near-stoichiometric Cr1.0065Sb0.9935, so the assumed 0.13 holes/u.c. is not directly evidenced. The V-doping experiment and ARPES comparison are partial external checks, but they do not pin down the pre-existing offset independently.

full rationale

The experimental part of the paper is self-contained: opposite signs of the in-plane/cross-plane Seebeck coefficients and of the low-field Hall coefficients are mutually consistent, and the magnetic point-group constraint Rzyx = Rxzy is observed. No load-bearing self-citation or imported uniqueness argument is used. The circularity is confined to the DFT attribution: the Fermi level is shifted by -100 meV (0.13 holes/u.c.) explicitly 'to capture the trends seen in the experiment', and the DDCP at the shifted level is then reported as a DFT finding/prediction. This fits the fitted-input-called-prediction pattern. However, the paper has some independent content: the computed ~14 meV window width, the pocket decomposition of the inverse-effective-mass tensor, the qualitative ARPES Fermi-surface agreement from Refs 25-27, and especially the successful Cr0.98V0.02Sb doping experiment, which moves the system out of the DDCP window. These prevent the paper from being wholly circular, but the central theoretical mechanism is not parameter-free. A score of 5 reflects a partial circularity: one key prediction is constructed by the fitted shift, while external checks keep the result from being forced.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on two classes of inputs: direct transport measurements and DFT calculations with a fitted Fermi shift. The -100 meV shift is the most important free parameter; the three-carrier fit parameters are also fitted to data. The scattering-isotropy and no-AHE assumptions are needed for sign interpretation. No new particles, forces, or dimensions are introduced.

free parameters (2)
  • Fermi energy shift EF to E'F = -100 meV, about 0.13 added holes per unit cell
    Chosen so that DFT reproduces the experimentally observed DDCP signs. The calculated 14 meV DDCP window and doping sensitivity are evaluated relative to this shifted level.
  • Three-carrier fit densities and mobilities (nh, ne1, ne2, mu_h, mu_e1, mu_e2) = See SI Table S2, e.g. at 2 K: nh=1.45e21 cm^-3, ne1=6.39e20 cm^-3, ne2=1.75e19 cm^-3, mu_h=312 cm^2/Vs, mu_e1=480…
    Six-parameter fits to field-dependent longitudinal and Hall conductivities. Used to support the multicarrier picture and to assign carriers to Fermi pockets, but these are fitted values, not predictions.
assumptions (5)
  • domain assumption DFT-GGA with spin-orbit coupling gives a band structure accurate enough for transport polarity signs.
    All calculated Seebeck and Hall signs depend on the VASP band structure; exchange-correlation and self-interaction errors could shift band crossings.
  • domain assumption Constant relaxation-time and rigid-band approximations in BoltzTraP2 are valid.
    Stated in Methods: 'semiclassical Boltzmann transport equation... relaxation time and rigid band approximations.' Phonon drag and energy-dependent scattering are neglected.
  • ad hoc to paper Real CrSb crystals have a Fermi energy shifted by -100 meV due to off-stoichiometry.
    Invoked in the Fig 4 paragraph to match experiment. EDXS in the SI reports near 1:1 stoichiometry, so the 0.13 holes/u.c. shift is not independently measured.
  • domain assumption The scattering term (1/tau_ii)d(tau_ii)/dE in the Seebeck tensor has isotropic sign.
    Used to conclude that the sign anisotropy in S_ii comes from effective mass, not from scattering anisotropy. The authors argue this from isotropic resistivity, but it is an assumption about scattering physics.
  • domain assumption Anomalous Hall effect is absent for the given Neel vector orientation.
    Used to attribute the nonlinear Hall signal to multicarrier transport rather than anomalous Hall effect, citing Refs 17-20.

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Cite this review

Pith. "Pith review of Direction-Dependent Conduction Polarity in Altermagnetic CrSb." pith.science (2026). https://pith.science/paper/M46CRUW6

@misc{pith2026250202231,
  author       = {Pith},
  title        = {Pith review of: Direction-Dependent Conduction Polarity in Altermagnetic CrSb},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M46CRUW6}},
  note         = {Machine review of arXiv:2502.02231}
}
abstract

CrSb has recently gained immense attention as an altermagnetic candidate. This work reports on the experimental observation of direction-dependent conduction polarity (DDCP) in altermagnetic CrSb through Hall and Seebeck thermopower measurements. Conduction is dominated by holes along the c-axis and by electrons in the ab-plane of the hexagonal crystal of CrSb. Density functional theory (DFT) calculations indicate that DDCP in CrSb arises from a multicarrier mechanism, where electrons and holes living in distinct bands dominate conduction along different crystallographic directions. Furthermore, DFT predicts that DDCP exists within a narrow energy window near the Fermi level and is sensitive to small doping levels. This prediction is experimentally validated by the loss of DDCP in hole-doped Cr$_{0.98}$V$_{0.02}$Sb. These findings highlight the potential for tunable electronic behavior in CrSb, offering promising avenues for applications in devices that require both p-type and n-type functionalities within a single material.

Figures

Figures reproduced from arXiv: 2502.02231 by the authors.

Figure 1
Figure 1. FS geometries for DDCP via single carrier and multicarrier mechanisms. (a) Hyperboloid FS for [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Crystal structure and sublattice transposing symmetries of CrSb. (a) Magnetic unit cell of CrSb [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Electrical transport properties and Seebeck effect in CrSb. (a) Defining coordinate axes on the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Results of theoretical calculations on CrSb. a Band structure along high-symmetry paths (see inset) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: (a) Calculated Fermi pockets α, β, and γ associated with three distinct bands #1, #2, and #3, respectively, that cross E′ F . (b)-(d) The distribution of IEM strength on the Fermi pockets along (b) x-, (c) y-, and (d) z-directions. that cross E′ F . Although band #3 do…
Figure 6
Figure 6. Figure 6: Magnetic field dependent Hall resistivity of Cr [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

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