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REVIEW 3 major objections 3 minor 58 references

Competition between local magnetic disorder and altermagnetism in doped FeSb$_2$

T0 review · 3 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read First-principles calculations say Co-doped FeSb2 is an altermagnetic metal, while Cr-doped FeSb2 is a locally disordered, spin-compensated magnet.

desk verdict A genuinely useful workflow for magnetic alloy searches, with a global ground-state claim that slightly overreaches its sampled configurational space. read the letter →

arxiv 2608.11089 v1 pith:JLLWMYGS submitted 2026-08-11 cond-mat.mtrl-sci

Enrico Di Lucente , Michele Simoncelli This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords altermagnetismFeSb2DFT+Umagneticdisordervirtual-crystalapproximationsupercellHubbardUdopedsemiconductor
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 uses first-principles calculations to determine what happens magnetically when the narrow-gap semiconductor FeSb2 is doped with cobalt or chromium. It argues that Co0.15Fe0.85Sb2 is an altermagnetic metal, with opposite-spin sublattices related by symmetry and no net moment, while Cr0.15Fe0.85Sb2 is instead a locally disordered, spin-compensated state that breaks the altermagnetic symmetry but keeps local antiparallel correlations. If correct, this explains why the Co-doped crystal shows altermagnetic-like optical signatures while the Cr-doped crystal behaves as a short-range or disordered magnet. The paper also introduces a way to search magnetic states without preselecting a magnetic class, using an approximate averaged-potential calculation to seed explicit supercell calculations.

What carries the argument

The load-bearing construction is a 120-atom $4\times1\times5$ supercell (Fe$_{34}M_6$Sb$_{80}$) that is the smallest cell at $x=0.15$ supporting an exact altermagnetic operation. Because exhaustive relaxation of all 7,992 compensated non-altermagnetic configurations is out of reach, the authors sample only the subset lying on shortest atomic-swap paths between converged low-energy AFMo endpoints; the lowest-energy such non-AFMo interior state is the LDSC motif. A single same-spin Fe–dopant occupation swap converts the AFMo minimum into the LDSC minimum.

What would settle it

A calculation that relaxes all 7,992 compensated non-AFMo configurations for Cr0.15Fe0.85Sb2 at the same Hubbard U and finds one lower than the LDSC minimum would falsify the central claim; so would an experiment that fails to find the predicted AFMo splitting pattern in Co-doped crystals.

Watch

Extended reading notes

Core claim

The central result is that the two dopants push the same host into different magnetic ground states. For Co0.15Fe0.85Sb2, the lowest-energy explicit supercell configuration found is AFMo, an altermagnetic state in which a symmetry operation exchanges the fully spin-polarized sublattices and the total moment vanishes. For Cr0.15Fe0.85Sb2, the lowest-energy state is the LDSC configuration, obtained from the AFMo minimum by one same-spin Fe-dopant swap; this removes every global spin-sublattice-exchanging operation while preserving most local antiparallel Fe–Fe and Fe–Cr environments, so it is formally compatible with Néel's fully compensated L-type ferrimagnetism. The authors conclude that long-range altermagnetic order is unlikely in the Cr-doped compound at low temperature.

Load-bearing premise

The search assumes that the true low-energy non-altermagnetic states all appear on shortest atomic-swap paths between low-energy altermagnetic states, so the 7,992 unsearched non-altermagnetic configurations cannot hide a state lower than the sampled LDSC minimum.

Editorial extensions

If this is right

  • If the Co result is right, Co$_{0.15}$Fe$_{0.85}$Sb$_2$ is a zero-temperature altermagnetic metal, in line with its nearly compensated magnetization and optical-conductivity comparison.
  • If the Cr result is right, Cr$_{0.15}$Fe$_{0.85}$Sb$_2$ has no long-range altermagnetic order at low temperature; its nearly compensated, disordered magnetism is captured by the LDSC motif rather than by a conventional antiferromagnet.
  • The virtual-crystal approximation by itself is misleading for these alloys: at the computed Hubbard U it predicts a weak ferrimagnetic ground state for Co doping that does not survive in explicit supercells, so approximate and explicit simulations need to be used together.
  • The swap-based bridge sampling provides a tractable way to explore compensated magnetic disorder in doped magnets, reducing 7,992 classes to a handful of physically motivated configurations.
  • The LDSC motif's low energy means that local chemical disorder can disrupt altermagnetic coherence even at zero temperature, a consideration for any candidate altermagnet where dopant placement is quenched.

Reading between the lines

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

  • The bridge assumption is the main unproven step: non-altermagnetic states that are not on shortest swap paths between low-energy AFMo endpoints are never relaxed. A full enumeration or a genetic search over the 7,992 classes could either confirm the LDSC minimum or reveal a deeper state.
  • The same local-disorder mechanism may explain why other predicted altermagnets fail to show spin-split bands in experiment: quenched dopant disorder could realize LDSC-like motifs even when the ordered altermagnetic state is lower in energy.
  • The approximate configurational free energy for Co doping crosses near 25 K because LDSC has many more realizations; if such configurations can be frozen during growth, samples might display finite-temperature disorder signatures even though the zero-temperature ground state is altermagnetic.
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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

3 major / 3 minor

Summary. The manuscript studies the magnetic ground states of Co- and Cr-doped FeSb2 at x=0.15 using DFT+U with a first-principles DFPT Hubbard parameter, combined with the Romeo occupation-matrix search in the virtual-crystal approximation and explicit 120-atom supercell calculations. In the VCA, the lowest-energy solution is ferrimagnetic for Co doping and altermagnetic for Cr doping at U=5 eV, but this ordering is nonmonotonic in U. In explicit supercells, the authors enumerate 342 symmetry-inequivalent AFMo-compatible decorations and 7,992 compensated non-AFMo classes, and they sample the latter along shortest atomic-swap paths between low-energy AFMo states. For Co doping, the lowest-energy sampled state is AFMo, about 3 meV per 120-atom cell below the lowest LDSC state; for Cr doping, the lowest sampled state is an LDSC configuration, about 8.5 meV per cell below the lowest sampled AFMo state. The paper argues that the Cr LDSC state is compatible with Néel's L-type fully compensated ferrimagnetism and consistent with the experimental short-range disordered magnetism, whereas Co doping stabilizes altermagnetism.

Significance. If the central claim holds, the paper resolves an apparent contradiction between altermagnetic predictions and experimentally observed disordered magnetism in Cr-doped FeSb2, and it provides a practical protocol for combining VCA-based magnetic-state searches with explicit alloy supercells. The work has notable strengths: the Hubbard U is obtained from DFPT rather than fitted, the explicit supercell enumeration is symmetry-based and independently verified with AMCheck, the numerical energy convergence is carefully controlled with a stated 0.01 meV error bar, and the limitations are discussed transparently, including the periodic-supercell caveat and the restricted sampling of non-AFMo configurations. The main risk to the central claim is the incompleteness of the non-AFMo search and the single value of the common Hubbard U used for the explicit comparisons.

major comments (3)
  1. [Supplemental Sec. SIV.A; main text Figs. 2-3] The Cr ground-state claim rests on the unproven assumption that every low-energy non-AFMo compensated configuration lies on a shortest atomic-swap path between low-energy AFMo decorations. The paper itself states that the bridge search 'does not enumerate or relax that full set' of 7,992 non-AFMo classes, and the main text carefully says 'lowest-energy state identified within our explicit-alloy search.' However, the abstract and conclusions state without qualification that the ground state is LDSC for Cr doping. Since the Cr LDSC-vs-AFMo separation is only 8.5 meV per 120-atom cell (Fig. 3), an off-path non-AFMo decoration could overturn the ordering. The three SQS references are single macrostates that do not bound the remaining 7,989 classes. No argument is given that low-energy non-AFMo states must be geodesic intermediates between low-energy AFMo states, and the restriction to same-spin-sublattice swaps excludes clustered or chemically reorganized dopant arrangements. Please either provide a physical or statistical argument bounding the off-path states, or consistently phrase the central claim as 'lowest-energy state identified within our explicit-alloy search' and state the resulting uncertainty for the Cr interpretation.
  2. [Supplemental Sec. SI and SIII.C; Table S1] The explicit-supercell comparisons use a common Hubbard U = 5 eV for Fe and the dopant, justified by DFPT values of about 5.1 eV (Co) and 5.3 eV (Cr) for the AFMo VCA states. The VCA landscape is itself nonmonotonic in U (Figs. S7-S8), and the Cr explicit ordering depends on an energy difference of only 8.5 meV per cell. The only species-dependent Hubbard test in explicit supercells is for Co doping (Table S1, with U_Fe,U_Co = 3.5,3.5 and 3.5,5.0 eV); no analogous test is provided for Cr. At minimum, the paper should report the Cr AFMo and LDSC energies for at least two additional U values or provide a clear argument for why the Cr LDSC-vs-AFMo ordering is robust to U. As written, the sensitivity of the central Cr conclusion to the common-U choice is untested.
  3. [Conclusions; main text around Figs. 4-5] The statement that Cr doping 'makes long-range altermagnetism unlikely' extrapolates from a single low-energy LDSC motif in a 120-atom periodic cell. The paper correctly notes that the supercell is an ordered computational snapshot and does not determine a magnetic correlation length, but the conclusion goes beyond the evidence: a periodic LDSC motif does not exclude the possibility that other low-energy disordered or partially ordered configurations could support long-range AFMo coherence, nor does it exclude a state with multiple nearby defects. I recommend softening the conclusion to say that the sampled low-energy LDSC motif is the lowest-energy configuration found in this search and is consistent with, but does not prove, the absence of long-range altermagnetic order.
minor comments (3)
  1. [Main text, Fig. 2 caption] The caption states 'Nswaps w.r.t. min-E AFMo config.' and 'Nswaps w.r.t. min-E LDSC config.' without defining 'w.r.t.'; please spell out 'with respect to' or use a notation that is immediately clear to the reader.
  2. [Supplemental Sec. SVI, Fig. S11] The caption of Fig. S11 refers to curves for AFMo, LDSC, and SQS macrostates, but the plot axes and the meaning of the crossing near 25 K would benefit from an explicit statement that the crossing does not imply an equilibrium transition because atomic exchange is frozen; the main text already explains this, but the caption alone is ambiguous.
  3. [Main text, Sec. on VCA-Romeo] The sentence 'We therefore discard this FM state' is slightly abrupt; since the discard is based on a known DFT+U high-spin bias and experimental consistency, please add a sentence explaining that this branch is not used in the explicit-supercell initializations and why it cannot be the physical ground state.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the explicit-alloy energy comparisons are independent of the cited inputs, and the unproven sampling-coverage assumption is a completeness limitation, not a circular reduction.

full rationale

The paper's central claims are computed, not fitted: the Hubbard U is obtained from first-principles DFPT, and the AFMo-vs-LDSC ordering in the explicit 120-atom supercells comes from directly computed DFT+U total energies, with the magnetic classes independently verified by AMCheck. The LDSC configuration is not defined as the answer; it is the specific non-AFMo state found lowest on a physically motivated swap path, and the Cr LDSC minimum lies below the sampled AFMo state by an explicitly quoted energy margin. The VCA high-spin FM branch is discarded because it conflicts with experiment and known DFT+U spin-state bias, but this exclusion is disclosed and is not the basis for the central predictions; independent U scans and a U=3.5 eV explicit-cell test support the Co conclusion. The main substantive limitation is the unproven assumption in Supplemental Sec. SIV that the 7,992 non-AFMo compensated classes need not be relaxed because low-energy states lie on shortest swap paths between low-energy AFMo endpoints. That is a completeness/robustness gap, not a definitional equivalence or a fitted parameter renamed as a prediction, so it does not constitute circularity under the strict standard required here. The Romeo and FeSb3 self-citations are to a search algorithm and a DFT+U pathology analogy, respectively; neither imports an unverified uniqueness theorem nor supplies the central result. The paper is therefore self-contained against its own computed benchmarks and warrants a circularity score of zero.

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

No new particles, forces, or fields are postulated; LDSC is a descriptive label for a spin-configuration class rather than a new physical entity. The main free parameters are the common Hubbard U and the analysis choices for spectral broadening; the central energy ordering depends most strongly on U, which is partly mitigated by sensitivity tests. The weakest structural assumption is the swap-path sampling of non-AFMo configurations.

free parameters (3)
  • Hubbard U (common) = 5 eV (rounded from DFPT values 5.1 eV for Co and 5.3 eV for Cr)
    A single U = 5 eV is applied to Fe and dopant in all final explicit-supercell comparisons. The VCA magnetic landscape changes nonmonotonically with U (Figs. S7, S8), so this parameter is consequential for the energy hierarchy. It is not fitted to the experimental target states, and a partial robustness check at U = 3.5 eV for Co keeps AFMo lowest among the tested states.
  • Centroid energy window = [-0.5, +0.5] eV relative to EF
    Hand-chosen window used to define the spin-resolved spectral centroid and the splitting measure |∆µ(k)| in Eq. (1). The window is applied consistently to both AFMo and LDSC states and does not enter the total-energy ordering, but it shapes the reported electronic-structure comparison.
  • Gaussian broadening for unfolding = 0.01 eV for spectral maps, 0.03 eV for centroids
    Gaussian broadenings chosen for visualization and for the centroid calculation; standard choices that affect only the presentation of the spectral functions, not the energy ordering.
assumptions (5)
  • domain assumption PBE+U with linear-response DFPT Hubbard parameters provides an accurate enough description of the magnetic energy ordering in FeSb2-based alloys.
    All conclusions rest on DFT+U. The paper itself shows the VCA ground state switches with U (Figs. S7, S8), so the electronic structure method carries real uncertainty; this is discussed in Secs. SI and SII.
  • domain assumption The 4x1x5 supercell with six dopants is representative of the x = 0.15 alloy, and the periodic cell is a valid proxy for the disorder ensemble.
    The authors acknowledge that the periodic supercell is an ordered computational snapshot and does not determine a magnetic correlation length, but the energy ordering relies on this cell choice.
  • ad hoc to paper Low-energy non-AFMo states lie on shortest atomic-swap paths between low-energy AFMo decorations.
    Supplemental Sec. SIV: the bridge construction samples only states on minimum-swap paths between converged AFMo endpoints; no proof covers the other 7,992 non-AFMo classes. This is the main gap in establishing the global ground state.
  • domain assumption Uncompensated spin configurations cannot host the ground state; VCA-motivated FiM initializations cover this space.
    The exhaustive enumeration only covers compensated configurations (20 up, 20 down spins). The FiM initializations from VCA all either reclassified or remained high in energy, but the full uncompensated space was not enumerated.
  • domain assumption The Romeo algorithm finds all relevant local minima of the unconstrained DFT+U functional.
    The conclusions about the VCA landscape rely on Romeo sampling states in full generality without preselecting a magnetic class. As with any heuristic search, completeness is assumed.

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Pith. "Pith review of Competition between local magnetic disorder and altermagnetism in doped FeSb$_2$." pith.science (2026). https://pith.science/paper/JLLWMYGS

@misc{pith2026260811089,
  author       = {Pith},
  title        = {Pith review of: Competition between local magnetic disorder and altermagnetism in doped FeSb$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JLLWMYGS}},
  note         = {Machine review of arXiv:2608.11089}
}
abstract

Recent experimental reports suggest that the narrow-gap nonmagnetic semiconductor FeSb$_2$ can be transformed into an altermagnetic metal through Co doping (Co$_{0.15}$Fe$_{0.85}$Sb$_2$), or into a magnetically disordered or short-range-ordered state through Cr doping (Cr$_{0.15}$Fe$_{0.85}$Sb$_2$). Here we explore the energy landscape and magnetic states of these doped systems from first principles, relying on Hubbard-augmented density-functional theory (DFT+U) combined with the Romeo ground-state search algorithm. Within the established virtual-crystal approximation (VCA), we show that \texttt{Romeo} finds several non-trivial magnetic states, which inform targeted explicit simulations of doping in supercells. We rely on these findings to discuss strengths and limitations of the VCA-Romeo approach versus the explicit-doping supercell approach, and how they can be used in synergy. Overall, our simulations suggest that the ground state of the Cr-doped system is a Locally Disordered Spin-Compensated (LDSC) configuration, formally compatible with N\'eel's L-type fully compensated ferrimagnetism, whereas the ground state of the Co-doped system is found to be altermagnetic (AFMo). This work shows how approximate and explicit simulations of magnetic alloys can be mutually informative, and establishes a protocol for studying candidate metallic altermagnets.

Figures

Figures reproduced from arXiv: 2608.11089 by the authors.

Figure 1
Figure 1. DFT+U+VCA magnetic-energy landscapes. Self-consistent solutions obtained with Romeo [31] for (a) Co0.15Fe0.85Sb2 and (b) Cr0.15Fe0.85Sb2 at U = 5 eV com￾puted from first principles [34]. Each point represents a local minimum of the unconstrained DFT+U+VCA functional. The vertical axis gives the energy per atom relative to the lowest￾energy solution of the corresponding composition, while the horizontal axis gives th… view at source ↗
Figure 2
Figure 2. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Energy landscape for Cr0.15Fe0.85Sb2. Absolute DFT+U total energies of converged AFMo (red) and LDSC (blue) configurations, ordered by the minimum number of atomic swaps from their respective family energy minima. The upper and lower annotations give the swap distances, and the inset compares the two lowest-energy states. The LDSC minimum lies below the lowest sampled AFMo state. composition, the numbers of spin-up … view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Electronic structure for Co0.15Fe0.85Sb2. (a,b) Spin-up and spin-down unfolded spectral weights of the lowest￾energy AFMo supercell; the overlaid red curves are the U = 5 eV VCA bands of the lowest-energy AFMo state in [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: Electronic structure for Cr0.15Fe0.85Sb2. (a,b) Spin-up and spin-down unfolded spectral weights of the lowest￾energy LDSC supercell; the overlaid blue curves are the U = 5 eV VCA bands of the lowest-energy AFMo state in [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.