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REVIEW 4 major objections 5 minor 60 references

Effect of applied pressure on the non-relativistic spin-splitting (NRSS) of FeSb2 altermagnet: A first-principles study

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Applied pressure flips the anomalous Hall response of the altermagnet FeSb2 from positive to negative while the lattice stays dynamically stable up to 10 GPa.

desk verdict Solid, straightforward DFT+U pressure study with a potentially interesting AHC sign change, but the abstract has a factual slip and the central transport claim needs a U-sensitivity check. read the letter →

arxiv 2507.22018 v1 pith:DLLYNAG3 submitted 2025-07-29 cond-mat.str-el cond-mat.mtrl-sci

Shalika R. Bhandari , R. Tamang , Keshav Shrestha , Samy Brahimi , Samir Lounis , D. P. Rai This is my paper
classification cond-mat.str-elcond-mat.mtrl-sci
keywords altermagnetismFeSb2non-relativisticspinsplittinganomalousHallconductivityhydrostaticpressureBerrycurvaturefirst-principlesDFT
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 argues that FeSb2, a collinear antiferromagnet with zero net magnetization, is a pressure-tunable altermagnet. Its spin-polarized band structure shows spin-up and spin-down bands crossing at the $\Gamma$ and $A$ points, producing non-relativistic spin splitting along $M'$-$\Gamma$-$M$ and $A$-$Z$-$A'$. Under hydrostatic pressure up to 10 GPa the lattice remains dynamically stable, but the splitting shrinks (band 26 from roughly 0.57 to 0.37 eV), the band-24 Fermi pocket disappears, and the anomalous Hall conductivity changes from a sharp positive response near +400 S/cm to a broad negative response around -150 S/cm at the Fermi level. If these results hold, pressure alone can switch the sign of Berry-curvature-driven transport in a compensated magnet and reshape its Fermi surface without chemical doping.

What carries the argument

The load-bearing object is the altermagnetic spin-group symmetry of FeSb2: the two Fe sites are related by a twofold rotation around [010] followed by half a unit-cell translation ($[C_2||C_{2y}t]$), and the combination with time-reversal symmetry ($\mathcal{T}$) lifts the spin degeneracy without spin-orbit coupling, producing the non-relativistic spin splitting that defines an altermagnet. The transport response is carried by the Berry curvature $\Omega_n^z(k)$, obtained from Wannier-interpolated bands and integrated in linear response theory to give the anomalous and spin Hall conductivities. Pressure enters by shifting band crossings near the Fermi level, which redistributes the Berry curvature and with it the sign and spectral shape of the Hall response.

What would settle it

Measure the anomalous Hall conductivity of FeSb2 under hydrostatic pressure up to 10 GPa in a diamond-anvil cell, or recompute the 10 GPa spectrum with U varied from 1 to 3 eV; if the negative sign does not survive a realistic U scan, the sign flip is an artifact of the fixed on-site interaction.

Watch

Extended reading notes

Core claim

The paper's central claim is that FeSb2 is a dynamically stable altermagnet whose non-relativistic spin splitting and anomalous Hall response are controllable by hydrostatic pressure up to 10 GPa. At ambient pressure the spin-up and spin-down bands cross exactly at the $\Gamma$ and $A$ symmetry points, and the splitting $|\Delta E|$ along $\Gamma$-$M$ and $A$-$Z$ is 0.23 eV and 0.57 eV for bands 24 and 26. Compression moves the band-24 node below the Fermi level, suppresses the splitting, and reconstructs the Fermi surface; the anomalous Hall conductivity at the Fermi level goes from about +130 S/cm at ambient pressure to about -150 S/cm at 10 GPa, with the spectrum broadening and turning negative because pressure-induced band crossings redistribute Berry curvature. The spin Hall conductivity remains 2-2.5 times smaller than the anomalous Hall conductivity in the -1 to 1 eV window. The paper concludes that FeSb2 offers a pathway to strain-engineered Hall responses in compensated magnetic systems.

Load-bearing premise

The load-bearing premise is that the on-site Coulomb parameter U = 2.0 eV chosen at ambient pressure remains valid at 10 GPa, since the predicted magnitudes of spin splitting and the sign change of the anomalous Hall conductivity depend on it.

Editorial extensions

If this is right

  • Hydrostatic pressure up to 10 GPa can switch the anomalous Hall conductivity of FeSb2 from about +130 S/cm to about -150 S/cm at the Fermi level, giving a pressure knob on Berry-curvature transport.
  • The band-24 Fermi pocket present at 0.25 GPa disappears by 10 GPa, so quantum-oscillation measurements under pressure should see a marked change in the extremal orbits.
  • Band-26's non-relativistic spin splitting drops from 0.57 eV to 0.37 eV while band-24's drops from 0.23 eV to 0.18 eV, so angle-resolved photoemission under pressure should see the two spin channels converge.
  • Because the spin Hall conductivity runs 2-2.5 times below the anomalous Hall conductivity in the -1 to 1 eV window, pressure can also tune spin-to-charge conversion without destabilizing the lattice.
  • The absence of imaginary phonon modes at 10 GPa means the predicted transport changes can in principle be measured in a diamond-anvil cell without a structural transition intervening.

Reading between the lines

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

  • If the fixed on-site U is relaxed in a U-scan from 1 to 3 eV, the 10 GPa sign change may weaken or disappear; the paper does not test this, so that scan is the first check on the claim.
  • Applying the same protocol to other Pnnm (space group 58) altermagnets would show whether pressure-induced anomalous Hall sign flips are generic to this symmetry class or specific to FeSb2.
  • Because the anomalous Hall effect in altermagnets depends on the Néel-vector orientation, a natural extension is to compute how pressure changes the magnetic anisotropy energy, which the paper does not calculate.
  • High-pressure Hall and resistivity measurements on FeSb2 would directly test the predicted semimetallic transition and negative anomalous Hall response, including the spectral broadening that accompanies it.
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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 first-principles DFT+U, DFPT phonon, and Wannier-based transport calculations for the altermagnet FeSb2 under hydrostatic pressure from 0 to 10 GPa. The main claims are that FeSb2 remains dynamically stable across this pressure range, that the non-relativistic spin splitting (NRSS) of bands near the Fermi level is progressively suppressed under pressure, and that the anomalous Hall conductivity (AHC) evolves from a sharp positive peak at ambient pressure (about +130 S/cm at the Fermi level) to a broadened negative value at 10 GPa (about -150 S/cm), accompanied by a spin Hall conductivity (SHC) that is described as 2-2.5 times smaller than the AHC. The authors interpret these results as evidence that FeSb2 is a pressure-tunable altermagnet.

Significance. If the central claims hold, the paper provides a useful extension of altermagnet research by demonstrating pressure as a control knob for both spin-splitting and Berry-curvature-driven transport in a compensated magnet. The phonon stability result is a concrete, falsifiable prediction, and the comparison of the ambient-pressure AHC with the published value (Ref. 48) is a good benchmarking step. However, the quantitative transport conclusions, especially the pressure-induced AHC sign change, rest on fixed Hubbard-U and unverified Wannier/Berry-curvature convergence, which weakens the robustness of the central claim. The paper's strength is its clear documentation of band-structure evolution under pressure; its weakness is the absence of sensitivity checks for the parameters that control the Berry curvature near the Fermi level.

major comments (4)
  1. [Section III.C, Fig. 6] The central claim of a pressure-induced AHC sign change is not tested against the Hubbard U value, even though the AHC at the Fermi level changes by roughly 280 S/cm between ambient pressure and 10 GPa (+130 to -150 S/cm). The Berry curvature near the Fermi level is controlled by band crossings in Fe-3d states, and the paper uses U=2.0 eV taken from ambient-pressure work (Ref. 30) without any U-dependence study. Since screening can change under compression, the effective U at 10 GPa may differ. I request a U-sensitivity analysis (for example U = 1.5, 2.5, and 3.0 eV) or a clear physical justification for keeping U fixed across the entire pressure range.
  2. [Section II, computational details] The Wannier-based AHC/SHC calculations lack convergence and interpolation-quality checks. The paper states a dense 150x150x150 k-mesh for the Berry curvature integral, but provides no comparison with coarser meshes (e.g., 60^3, 100^3) to demonstrate convergence of the AHC values. It also reports no Wannier interpolation quality metrics such as frozen-window settings, band-spread values, or a plot comparing the Wannier-interpolated bands to the DFT bands. Without these checks, the AHC values, and in particular the sign change at 10 GPa, cannot be considered quantitatively reliable.
  3. [Abstract and Section III.C] The abstract states that 'the values of spin hall conductivity (SHC) are around 2-2.5 times lower as compared to AHC,' but Fig. 6(a) shows SHC at the Fermi level of about +220 S/cm exceeding AHC of about +130 S/cm at ambient pressure. The statement is only consistent with the 1 GPa and 10 GPa panels if one compares magnitudes and ignores signs. The authors should correct the abstract and text to specify whether the comparison is by magnitude and at which pressures, or revise the claim so that it is not contradicted by their own figure.
  4. [Section II, computational details] There is an inconsistency between the use of a 'scalar non-relativistic pseudopotential' for the electronic structure calculations and the statement that 'full-relativistic DFT calculation' is used for the Wannier90 transport calculations. Anomalous and spin Hall conductivities require spin-orbit coupling, so the paper must clarify how SOC is included and which pseudopotential was used for the transport calculations. This is not a minor detail, because the AHC values in Fig. 6 are the basis for the main pressure-tunability claim.
minor comments (5)
  1. [Eq. (1)] Equation (1) contains typographical errors: '-2, Im' should be '-2 Im', and the expression 'Ωz n(k is' is missing a closing parenthesis. Please correct the Berry curvature formula.
  2. [Abstract and Section I] The phrase 'broken time-reversal (PT) symmetry' is physically imprecise. Altermagnetic NRSS arises from broken combined parity-time (PT) symmetry in the collinear magnetic state, while time-reversal symmetry itself is broken by the magnetic order. Please rephrase for accuracy.
  3. [Fig. 2] The phonon dispersion panels in Fig. 2 have repeated 'States/eV' labels that appear to be artifacts of the figure layout; the y-axis of the dispersion should be labeled 'Frequency (cm^-1)' only. Please clean up the figure.
  4. [References] References 53 and 58 are duplicates (both cite Sinova et al., Rev. Mod. Phys. 87, 1213 (2015)). Please merge them.
  5. [Data availability statement] The data availability statement says data are available in the article or supplementary material, but no link or repository identifier is provided. Please either add a DOI or repository link, or state where the supplementary material can be obtained.

Circularity Check

0 steps flagged · score 2.0 of 10

No construction-level circularity: NRSS and AHC results are new DFT outputs; the self-cited inputs (U and AFM order) are not fitted to the predicted quantities.

full rationale

The paper's claimed results—phonon stability up to 10 GPa, pressure-induced suppression of NRSS (band-24 |ΔE| from ~0.23 eV to ~0.18 eV; band-26 from ~0.57 eV to ~0.37 eV), and the AHC evolution from +130 S/cm to -150 S/cm—are all computed quantities obtained from self-consistent DFT+U band structures, DFPT phonons, Wannier interpolation, and Kubo-formula Berry curvature integration (Eqs. 1-3). No parameter appearing in those equations is fitted to the AHC or NRSS outputs, so the central predictions are not equivalent to an input by construction. The model does inherit U=2.0 eV and the AFM spin arrangement from the authors' earlier Ref. 30, and the altermagnetic label is motivated by that prior work; however, the current paper recomputes the spin-resolved bands, checks the AFM ground state by total-energy comparison (Fig. S2), and presents the pressure dependence as new output. The ambient AHC benchmark (130 S/cm) is compared to an independent prior calculation by Mazin et al. (Ref. 48), not used as a fitting target. The fixed-U assumption is a legitimate robustness/correctness concern—no U-sweep is provided and screening could change under pressure—but that is a parameter-sensitivity issue rather than a circular reduction. Because the self-citations supply model setup rather than the predicted results, no circular step is identified; score 2 reflects only the minor, non-load-bearing reliance on the authors' prior work for the starting Hamiltonian, not any construction-level circularity.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The central claims rest on standard DFT/DFPT methodology plus two domain assumptions: the validity of GGA+U with a fixed U, and the persistence of collinear AFM order under pressure. No new particles, forces, or conserved quantities are introduced. The only free parameter is the Hubbard U, which is taken from prior work and not re-fit.

free parameters (1)
  • Hubbard U on Fe 3d orbitals = 2.0 eV
    Chosen from prior FeSb2 study (Ref 30), not re-fit at each pressure. It controls the exchange splitting and band positions, so it directly affects the reported NRSS magnitudes and the AHC sign change.
assumptions (3)
  • domain assumption DFT/GGA+U accurately describes the electronic structure of FeSb2 across 0 to 10 GPa
    The entire study relies on this. No experimental verification under pressure is provided, and the fixed U is not tested for pressure dependence.
  • domain assumption Collinear antiferromagnetic order between Fe1 and Fe2 remains the ground state across the studied pressure range
    AFM coupling is set following prior reports (Refs 30, 48). The paper does not search for a magnetic phase transition under pressure, so a pressure-induced magnetic reorientation would invalidate the NRSS and AHC results.
  • standard math The Kubo linear response formula in the clean limit gives the intrinsic AHC and SHC
    Standard formalism used per Ref 50, but it neglects disorder, finite temperature, and vertex corrections, which could affect the quantitative values.

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Cite this review

Pith. "Pith review of Effect of applied pressure on the non-relativistic spin-splitting (NRSS) of FeSb2 altermagnet: A first-principles study." pith.science (2026). https://pith.science/paper/DLLYNAG3

@misc{pith2026250722018,
  author       = {Pith},
  title        = {Pith review of: Effect of applied pressure on the non-relativistic spin-splitting (NRSS) of FeSb2 altermagnet: A first-principles study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DLLYNAG3}},
  note         = {Machine review of arXiv:2507.22018}
}
read the original abstract

We have investigated the pressure-dependent electronic structure, phonon stability, and anomalous Hall response of the recently discovered altermagnet FeSb2 from density functional theory (DFT) and Wannier function analysis. From density functional perturbation theory (DFPT) calculations, we have found that FeSb2 remains dynamically stable up to 10 GPa, evidenced by positive phonon frequencies. Our spin-polarised band structure shows that the node of band crossing between spin-up and spin-down bands around the Fermi energy exactly lies at the Gamma and A-symmetry points. The Fermi crossing is mostly exhibited by band-24, band-25 and band-26. The non-relativistic spin-splitting (NRSS) along M'-Gamma-M and A-Z-A' symmetry is attributed to the broken time-reversal (PT ) symmetry. There are significant changes in the band profile under applied pressure, as one can see the shifting of the node of band-24 and band-26 towards the lower energy side. The NRSS exhibited by band-24 along M'-Gamma-M symmetry is notably small. Although the strength of NRSS of band-26 along A-Z-A' symmetry is significant but reduces under applied pressure. The anomalous Hall conductivity (AHC) values are prominent in -1 to 1 eV range. A sharp peaked and positive AHC values at ambient pressure, becomes spectrally broadened and negative at 10 GPa due to pressure-induced band crossings and redistribution of Berry curvature near the Fermi level. We have observed that the values of spin hall conductivity (SHC) are around 2-2.5 times lower as compared to AHC and prominent in between -1.0 eV to 1.0 eV. Our results establish FeSb2 as a tunable altermagnetic candidate where pressure can modulate both topological transport and dynamic stability, offering opportunities for strain-engineered Hall responses in compensated magnetic systems.

Figures

Figures reproduced from arXiv: 2507.22018 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Unit cell structure of FeSb [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (Color online) Phonon dispersion relations and [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Fig.3. Under ambient conditions, FeSb [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (4 more)
Figure 3
Figure 3. Figure 3: FIG. 3. Spin-resolved electronic band structures of FeSb [PITH_FULL_IMAGE:figures/full_fig_p004_3.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a) First Brillouin-zone with high symmetry points [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Anomalous Hall conductivity (Scaling on the left side) and Spin Hall conductivity (Scaling on the right side) of [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 3
Figure 3. Figure 3: Fig.3. Fig. 6(b) shows the result of the AHC and SHC at [PITH_FULL_IMAGE:figures/full_fig_p006_3.png]

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.