Study of the structural and electronic properties of the Heusler Co2FeGe alloy by DFT approach

A. Jabar; A. Jamraoui; L. Bahmad; Y. Selmani

REVIEW 5 major objections 5 minor 20 references

Study of the structural and electronic properties of the Heusler Co2FeGe alloy by DFT approach

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Using density functional theory with the GGA approximation, this paper argues that the full Heusler compound Co2FeGe is a ferromagnetic metal whose magnetization is carried mainly by cobalt and iron d states, making it a candidate for…

desk verdict Routine GGA run on Co2FeGe that is internally inconsistent on structure and on the metal/semiconductor claim; not publishable as written. read the letter →

arxiv 2505.24836 v1 pith:F57SOMJL submitted 2025-05-30 cond-mat.mtrl-sci

A. Jamraoui , Y. Selmani , A. Jabar , L. Bahmad This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords HeusleralloyCo2FeGedensityfunctionaltheoryGGAapproximationferromagnetismmetallicbandstructurespintronicsKorringa-Kohn-Rostoker

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 tries to establish that the full Heusler compound Co2FeGe is, at equilibrium, a ferromagnetic metal rather than a half-metal or semiconductor. The authors model the crystal with density functional theory in the GGA approximation, optimize the lattice parameter, and compute spin-resolved band structures and densities of states. Their central claims are that both spin channels have electronic states at the Fermi level, that the magnetic moment comes mainly from the d orbitals of Co and Fe, and that this combination makes Co2FeGe a promising spintronics material. If true, the result gives a concrete electronic-structure fingerprint for a magnetic electrode candidate.

What carries the argument

The central objects are the spin-resolved band structure and density of states obtained from a density functional theory calculation in the Korringa–Kohn–Rostoker Green's function scheme with the GGA exchange-correlation functional. The argument works by comparing the two spin channels: asymmetry in the partial d-electron density of states of Co and Fe is read as the signature of ferromagnetism, and the presence of states at the Fermi level in both channels is read as the signature of metallicity. The lattice parameter is optimized by minimizing total energy as a function of volume, and all electronic conclusions are drawn at that equilibrium geometry.

What would settle it

A converged plane-wave or full-potential DFT calculation at the experimental lattice parameter 5.738 Å, using the same Fm-3m Heusler ordering, would settle the claim: if the minority-spin density of states at the Fermi level comes out zero (half-metal), or if the calculated total moment disagrees with the measured 5.54 μB by more than a few tenths of a Bohr magneton, then the paper's metallic-ferromagnet classification and its Co/Fe origin-of-magnetism statement would need revision.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that Co2FeGe is a metallic ferromagnet: both the spin-up and spin-down band structures show bands crossing the Fermi level, and the total density of states is asymmetric between majority and minority spins, producing a net magnetic moment. The partial densities of states attribute the magnetism almost entirely to the d states of Co and Fe, while Ge contributes little and its spin-up and spin-down densities are symmetric. The paper therefore classifies Co2FeGe as a conventional metallic ferromagnet and explicitly distinguishes it from a perfect half-metal, because the minority-spin density of states at the Fermi level is small but not zero.

Load-bearing premise

The results stand or fall with the assumed crystal structure and lattice parameter used to build the unit cell: the paper specifies an Fm-3m arrangement with Fe at the origin, Co on tetrahedral sites, and Ge on octahedral sites, and it lists two inconsistent lattice constants (4.057 Å in the input appendix versus 5.700 Å optimized and 5.738 Å experimental); if the geometry fed into the calculation is wrong, the band structure, density of states, and magnetic attribution would all be invalid.

Editorial extensions

If this is right

If the central claim is correct, Co2FeGe should be treated as a metallic ferromagnet, not as a half-metal, for applications that rely on bulk spin-polarized transport.
The calculated origin of magnetism in Co and Fe d states implies that substitutions on the Co or Fe sites would be the natural handles for tuning the magnetic moment, while Ge-site substitutions would have little direct magnetic effect.
Since the material has a measured Curie temperature of 1060 K and a measured total moment of 5.54 μB, a correct GGA description should be consistent with both when the experimental lattice parameter is used.
The paper's spintronics recommendation rests on the coexistence of robust ferromagnetism with metallic conductivity, which would support spin injection or spin-transport applications rather than half-metallic switching behavior.

Reading between the lines

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

The paper's own DOS analysis leaves open a testable boundary: with a different treatment of electron correlation, such as GGA+U, the small minority-spin weight at the Fermi level could vanish and Co2FeGe could become half-metallic, so the metallic-versus-half-metallic classification is likely sensitive to the exchange-correlation approximation.
The appendix lists a lattice parameter of 4.057 Å while the main text reports an optimized 5.700 Å and an experimental 5.738 Å; resolving which geometry actually entered the production calculation is a necessary reproducibility step before the quantitative results can be used.
A natural extension would be to compute the total magnetic moment per formula unit from the spin-resolved DOS and compare it directly with the experimental 5.54 μB, since the paper does not report a numerical calculated moment.
The T=0 K DFT result says nothing about thermal stability or spin dynamics; reproducing the measured 1060 K Curie temperature would require a statistical or Monte Carlo treatment built on the calculated magnetic exchanges.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

This is a routine GGA calculation of Co2FeGe that probably reproduces the known metallic ferromagnetism, but the manuscript as written cannot support it. The structural input is inconsistent, and the text contradicts itself on the central electronic property.

What's new: very little. Ref. [14], with overlapping authors, already studied Co2FeGe with DFT and Monte Carlo and reported half-metallic behavior. Here the only new element is a GGA-only run in AKAI-KKR, with no new mechanism, no quantitative prediction, and no spin polarization value. The paper does show the standard workflow—structural optimization, band structure, DOS—but that's routine.

Soft spots, in order of severity:

1. The structural input is wrong as printed. Section 2(a) puts Fe at (0,0,0), Co on 8c, and Ge on four sites that are a mix of 4a and 4b. For L21 Co2FeGe you need four Fe on 4a, four Ge on 4b, and eight Co on 8c. As written, the cell is Co8FeGe4, not Co2FeGe. The Appendix also states an input lattice constant of 4.057 Å, while Table 2 reports optimized 5.700 Å and experimental 5.738 Å. The 4.057 value looks like 5.738/√2, but the text never explains the conversion. If the code was fed that cell and lattice constant, all results in Figs. 3–5 belong to an off-stoichiometric structure. That's the load-bearing problem.

2. The band structure section first reports a clear gap in both spin channels and calls the material a semiconductor, then states there is overlap and the material is metallic. The DOS section also waffles between 'metallic ferromagnet' and 'not a perfect half-metal.' The reader can't tell which the authors believe.

3. Missing quantitative results. No magnetic moments, no spin polarization at the Fermi level, no DOS values. For a spintronics claim, that's the minimum needed.

4. Minor: Co2FeGe is a full-Heusler (ternary), not quaternary. The novelty overlap with ref. [14] is substantial.

Bottom line: the broad conclusion is probably correct in reality, but this paper doesn't demonstrate it. The computational record is internally inconsistent. I wouldn't send it to peer review. If the authors supply the actual input file and fix the contradictions, it might be a different story.

Referee Report

5 major / 5 minor

Summary. The paper reports density-functional-theory calculations for the full-Heusler compound Co2FeGe using the AKAI-KKR code with the GGA approximation. The authors present a volume optimization, band structures for both spin channels, and total and partial densities of states. On the basis of these calculations they claim that Co2FeGe is a metallic ferromagnet, that the magnetism originates mainly from the Co and Fe d states, and that the material is a promising candidate for spintronics applications. The manuscript also includes an appendix describing the construction of the AKAI-KKR input file.

Significance. If the calculations were correct and properly documented, the paper would provide a routine GGA confirmation that Co2FeGe is a metallic ferromagnet, which is a plausible but not novel result given the existing literature on this compound. The work has the strength of being a direct numerical calculation with no fitted target observable and no circular reasoning. However, as submitted, the significance is undercut by serious internal inconsistencies: the structural model appears off-stoichiometric, the stated lattice input conflicts with the optimization results, and the band-structure section contradicts itself on the metallic versus semiconducting character. No quantitative magnetic moments are reported. Because these issues affect the central claims, the manuscript is not publishable in its current form.

major comments (5)

[§2(a), Fig. 1, Appendix] The structural model described for Co2FeGe appears off-stoichiometric. In the L21 Fm-3m structure, the conventional cell has Fe on the 4a sites and Ge on the 4b sites, with Co on the 8c sites. The manuscript places Fe only at (0,0,0) and places Ge at (1/2,1/2,1/2), (1/2,1/2,0), (1/2,0,1/2), and (0,1/2,1/2); three of those Ge sites occupy positions that belong to the Fe 4a sublattice. The resulting cell therefore has composition Co8FeGe4, i.e. Co2Fe0.25Ge, rather than Co2FeGe. Unless the actual AKAI-KKR input file is supplied and shown to correspond to the stoichiometric L21 cell, the electronic and magnetic results in Figs. 3-5 cannot be attributed to Co2FeGe.
[Appendix, Table 2, Fig. 2] The lattice-parameter input is inconsistent. The Appendix states a=b=c=4.057 Å, while Table 2 reports an optimized GGA value of 5.700 Å and an experimental value of 5.738 Å, and the energy minimum in Fig. 2 occurs at a volume of about 190-200 Å³, which corresponds to a conventional lattice parameter near 5.7 Å. The value 4.057 Å is 5.738/√2, suggesting a primitive-cell convention, but then the stated atomic coordinates and the volume-optimization curve are not in the same convention. The lattice constant used as input must be reconciled with the cubic cell description and with the optimization result.
[§2(b), Fig. 3] The band-structure discussion is self-contradictory. For both spin-up and spin-down, the text first states that there is a clear energy gap around the Fermi level and that the material is a semiconductor with an indirect gap, and then states that the valence and conduction bands overlap and that the material is metallic for both spin orientations. Since the central claim of the paper is metallic behavior, the text must be corrected to a single consistent classification, with the actual band edges or Fermi-level crossings identified.
[§2(b), Figs. 4-5, Conclusion] No quantitative magnetic data are reported. The claims that Co2FeGe is magnetic and that the magnetization comes mainly from Co and Fe are supported only by qualitative asymmetry of the density of states; no total magnetic moment per formula unit, no atom-resolved magnetic moments, and no spin polarization at the Fermi level are given. These numbers are directly obtainable from the same calculation and are necessary to substantiate the abstract and conclusion.
[Appendix] The calculation is reported with only 15 k-points and 520 iterations, but no convergence study is presented. For a metallic system, 15 k-points are generally too coarse to converge the Fermi level and the density of states at EF reliably. The authors should provide a k-point convergence test and state the final converged k-point mesh and iteration criteria.

minor comments (5)

[Abstract, Conclusion] Co2FeGe is a full-Heusler (ternary) compound, not a quaternary Heusler compound; the paper repeatedly uses the term 'quaternary' and should be corrected.
[Figs. 4-5 and text] Several figure labels and text passages refer to 'Ga' instead of Ge, for example 'Fig. 4(Ga)' and 'the Ga element is non-magnetic.' This appears to be an element-label typo that should be fixed throughout.
[Fig. 2 and Table 2] The text states the minimum energy is approximately -12274.5 Ry, while Table 2 lists -12274.47513 Ry; the values should be made consistent.
[§2(a)] The text says Ge occupies 'all 12 octahedral sites' but only four Ge positions are listed and the conventional cell contains only four Ge sites; this wording should be corrected.
[References] Several references appear mismatched, such as [17] citing Heusler's 1934 paper for the experimental magnetic moment of Co2FeGe and [19] citing a Mössbauer study of Co2TiSn as a DFT method reference; the citation list should be carefully re-checked.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the DFT results are generated from the stated inputs rather than fitted to or defined in terms of the conclusions.

full rationale

The central claims of the paper—metallic character, magnetism, and the dominant role of Co and Fe d-states—are direct outputs of the AKAI-KKR GGA calculation, not quantities fitted to those claims or defined in terms of them. No equation or procedure in the manuscript identifies a predicted quantity as equal to an input by construction. The single self-citation (ref. [14], sharing authors Selmani and Bahmad) is used only as literature context for a GGA+U semi-metallic study and is not load-bearing for the present GGA result, which indeed differs from that cited semi-metallic conclusion. The reported inconsistencies in the stated atomic positions or lattice constants (e.g., one Fe at (0,0,0) versus a full L21 cell, and 4.057 Å versus the optimized 5.700 Å in Table 2) are correctness and reproducibility concerns, not circularity. The derivation chain is therefore self-contained in the circularity sense, and no circular step is present.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

No fitted physical constants and no invented entities. The only chosen numerical parameter is the k-point count; the central physics rests on standard DFT/GGA assumptions and on the assumed Heusler crystal structure.

free parameters (1)

k-point count = 15
Chosen by hand in the AKAI-KKR input; the DOS at the Fermi level, which determines the metallic character claim, depends on this mesh, and no convergence test is reported.

assumptions (4)

domain assumption DFT with the GGA approximation gives a correct ground state and electronic structure for Co2FeGe.
Invoked in Sections 2 and 3 via ref [18] without benchmarking against experiment or higher-level methods.
domain assumption The compound crystallizes in the cubic Fm-3m Heusler structure with the listed atomic positions.
Section 2(a) and the Appendix state the space group and coordinates; no other orderings, such as the XA structure, or disorder are considered.
domain assumption The equilibrium volume is found by fitting total energy versus volume and corresponds to the T=0 K ground state.
Section 2(a) minimizes E(V); no thermal or pressure effects are included.
ad hoc to paper The AKAI-KKR calculation with 15 k-points and 520 iterations is converged.
Stated in the Appendix without a convergence study; this is a numerical assumption specific to this paper.

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Cite this review

Pith. "Pith review of Study of the structural and electronic properties of the Heusler Co2FeGe alloy by DFT approach." pith.science (2026). https://pith.science/paper/F57SOMJL

@misc{pith2026250524836,
  author       = {Pith},
  title        = {Pith review of: Study of the structural and electronic properties of the Heusler Co2FeGe alloy by DFT approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F57SOMJL}},
  note         = {Machine review of arXiv:2505.24836}
}

read the original abstract

In this work we reported the structural and electronic properties of the Heusler compound Co2FeGe using the AKAI-KKR code under the GGA approximation. We established that this material presents not only magnetic character but also has a metallic behavior. Our calculations have been conducted using the DFT method in the framework of the AKAI-KKR code. This study enabled us to define certain characteristics and initial parameters for creating a model of the system. The method used allowed us to apply fundamental concepts to the studied system in the form of modeling. The main results, of the studied Heusler compound Co2FeGe are: i) this material is magnetic; ii) The band structure of the material predicts a metallic character; iii) the origin of magnetism comes mainly from the transition metals Co and Fe atoms. These results, assure that the studied quaternary Heusler Co2FeGe stands for a strong candidate for different spintronics applications.

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Reference graph

Works this paper leans on

20 extracted references · 19 canonical work pages

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M. Mouatassime, Y. Selmani, S. Idrissi, L. Bahmad, F. Goumrhar, H. Labrim,A. Benyoussef, Magnetic properties and half metallic behavior of the Full-Heusler Co2FeGe alloy:DFT and Monte Carlo studies, Journal of Solid State Chemistry (2021), doi: https://doi.org/10.1016/ j.jssc.2021.122534

arXiv 2021
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set lattice parameter

H.C. Kandpal, G.H. Fecher, C. Felser, arXiv:cond-mat/0611179v1 (2006). Appendix: Input preparation for the Co2FeGe Heusler: We create our AKAI KKR input using the Xband software. We start by choosing the system creation method. In our case, we opted to create the crystal syste...

2006 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [14]

Mouatassime, Y

M. Mouatassime, Y. Selmani, S. Idrissi, L. Bahmad, F. Goumrhar, H. Labrim,A. Benyoussef, Magnetic properties and half metallic behavior of the Full-Heusler Co2FeGe alloy:DFT and Monte Carlo studies, Journal of Solid State Chemistry (2021), doi: https://doi.org/10.1016/ j.jssc.2021.122534

arXiv 2021

[2] [1]

Chinese Journal of Physics, 2016

Bouabça, A., et al., Half-metallic completely compensated ferrimagnets in Cr doped BaP. Chinese Journal of Physics, 2016. 54(4): p. 489-494

work page 2016

[3] [2]

Springborg, M., Methods of electronic-structure calculations: from molecules to solids2000

work page

[4] [3]

Physical Review B, 1990

Rappe, A.M., et al., Optimized pseudopotentials. Physical Review B, 1990. 41(2): p. 1227

work page 1990

[5] [4]

Physical Review B, 1989

Shirley, E.L., et al., Extended norm -conserving pseudopotentials. Physical Review B, 1989. 40(6): p. 3652

work page 1989

[6] [5]

Physical Review B, 2003

Ritchie, L., et al., Magnetic, structural, and transport properties of the Heusler alloys Co 2 MnSi and NiMnSb. Physical Review B, 2003. 68(10): p. 104430

work page 2003

[7] [6]

Physical review letters, 1997

Nishino, Y., et al., Semiconductorlike behavior of electrical resistivity in Heusler-type Fe 2 VAl compound. Physical review letters, 1997. 79(10): p. 1909

work page 1997

[8] [7]

Electrochimica acta, 2007

Morcrette, M., et al., Influence of electrode microstructure on the reactivity of Cu2Sb with lithium. Electrochimica acta, 2007. 52(17): p. 5339-5345

work page 2007