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REVIEW 4 major objections 6 minor 94 references

Observation of pseudogap in Cr_{1-x}Y_xN magnetic alloy and its impact on the Seebeck coefficient by ab-initio calculations

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read First-principles calculations show that in Cr$_{1-x}$Y$_x$N the Seebeck coefficient and figure of merit are governed by a pseudogap in both spin channels and by the Fermi level sitting on a steep descending density-of-states slope, with…

desk verdict First CrYN Seebeck/zT screening is worth a look, but the 800 K zT=0.35 rests on a hypothetical magnetic state and zero phonon conductivity, so the quantitative claim should not be taken at face value. read the letter →

arxiv 2506.00687 v1 pith:IMU7LCAG submitted 2025-05-31 cond-mat.mtrl-sci cond-mat.str-elphysics.comp-ph

Luis Felipe Leon-Pinzon , Elisabeth Restrepo-Parra , Andres Manuel Garay-Tapia This is my paper
classification cond-mat.mtrl-scicond-mat.str-elphysics.comp-ph
keywords CrYNalloythermoelectricfigureofmeritSeebeckcoefficientpseudogapdensityfunctionaltheoryspecialquasirandomstructurestransitionmetalnitridesmagneticstructure
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 tries to establish a design rule for thermoelectric performance in the transition-metal nitride alloy Cr$_{1-x}$Y$_x$N: a large Seebeck coefficient and figure of merit require a pseudogap (a deep dip in the density of states just above the Fermi level) in both electron-spin channels, and the Fermi level must lie on a steep descending slope of the number of states. The authors test this rule with density functional theory on special quasirandom supercells at x = 0.25, 0.5, and 0.75, seeded from different magnetic orders of CrN, and evaluate the Seebeck coefficient and zT with a Boltzmann transport calculation. Their headline number is zT = 0.35 at 800 K for Cr$_{0.75}$Y$_{0.25}$N built from the AFM1 magnetic configuration, with several other structures above 0.25. If the rule holds, it gives materials chemists a concrete electronic-structure fingerprint for screening nitride thermoelectrics before synthesis.

What carries the argument

The central objects are cubic supercells built as special quasirandom structures (SQS), a way to approximate a random Cr/Y distribution in a small periodic cell, relaxed with density functional theory. The argument is carried by the density of states (DOS) and its relation to the Seebeck coefficient through Mott's approximation, $S \propto \partial \ln \sigma(E)/\partial E$: a steep decreasing DOS at the Fermi level makes the logarithmic conductivity slope large, and a pseudogap in both spin channels preserves that slope while limiting the states available to carriers. A Boltzmann transport calculation then converts those electronic features into Seebeck coefficient and zT values.

What would settle it

Measure the thermal conductivity of Cr$_{0.75}$Y$_{0.25}$N at 800 K and separate the electronic and lattice contributions; if the lattice part is comparable to or larger than the electronic part, the reported zT = 0.35 is an overestimate. A second check is to measure the Seebeck coefficient of the same composition as a function of doping or temperature and see whether it tracks the predicted Fermi-level position on the steep density-of-states slope.

Watch

Extended reading notes

Core claim

The central claim is that the thermoelectric performance of Cr$_{1-x}$Y$_x$N is governed by two coexisting electronic features. In the computed densities of states, high Seebeck coefficients appear when a pseudogap is present in both spin channels and when the Fermi level lies on a steep decreasing slope of the density of states; through the Mott-type relation $S \propto \partial \ln \sigma(E)/\partial E$, that slope directly boosts S. The calculation finds metallic behavior in all structures, small indirect gaps in the x = 0.5 alloys, and no retention of the initial magnetic configurations after relaxation. The relaxed cells are mostly ferrimagnetic, and the resulting position of the Fermi level relative to the pseudogap is what the authors link to the Seebeck coefficient. Large octahedral deformations are associated with suppressed thermoelectric properties, as in the Cr$_{0.75}$Y$_{0.25}$N-AFM2 case, which lacks a clear pseudogap.

Load-bearing premise

The load-bearing premise is that phonons carry negligible heat in these alloys, so every reported zT value is an upper bound; if the lattice thermal conductivity is not very small, the zT numbers drop.

Editorial extensions

If this is right

  • At 800 K, Cr$_{0.75}$Y$_{0.25}$N-AFM1 reaches zT = 0.35, and four other Cr-Y-N structures exceed 0.25, placing the alloys close to previously reported Cr-Sc-N and Cr-V-N values.
  • The 50% Cr alloys combine pseudogaps with small indirect band gaps, which the authors suggest may be observable as optical effects in synthesized samples.
  • Most 50% and 75% Cr structures have Seebeck coefficients above YN, while Cr$_{0.75}$Y$_{0.25}$N-AFM2, which lacks a clear pseudogap, stays below YN, providing the internal comparison that supports the two-feature criterion.
  • Because none of the initial magnetic configurations survives relaxation, the magnetic template acts as a practical tuning parameter for the Fermi-level position relative to the pseudogap and therefore for zT.

Reading between the lines

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

  • Beyond the paper: the same two-feature fingerprint—a pseudogap in both spin channels plus a Fermi level on a steep falling density of states—could be screened cheaply from density of states in other rock-salt transition-metal nitride alloys before computing transport.
  • Beyond the paper: because the functional used here tends to overestimate magnetic moments and the Cr states are highly correlated, adding Hubbard U or spin-orbit coupling could shift the Fermi level relative to the pseudogap and change the ordering of magnetic configurations; the 0.35 value should be treated as a DFT-level estimate.
  • Beyond the paper: the octahedral-deformation analysis points to a strain or synthesis strategy—suppressing Jahn-Teller and tetragonal distortions—as a way to protect the pseudogap and raise zT.
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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 / 6 minor

Summary. The paper reports first-principles SCAN calculations for the ternary alloy Cr1-xYxN at x = 0.25, 0.5, and 0.75, built as special quasirandom structures from three initial CrN magnetic orderings (AFM1, AFM2, FM). It analyzes lattice parameters, magnetic moments, octahedral distortions, second-neighbor distributions, densities of states, and band structures, and computes Seebeck coefficients and zT via BoltzTrap2. The central claim is that high Seebeck coefficient and high zT require a pseudogap in both spin channels with the Fermi level on a steep decreasing slope of the DOS, and the most specific quantitative result is a zT of 0.35 at 800 K for Cr0.75Y0.25N-AFM1.

Significance. If the central design rule is correct, the paper would provide a useful qualitative guideline for thermoelectric engineering in magnetic transition-metal nitride alloys and constitutes the first ab initio thermoelectric study of CrYN. The work is largely parameter-free on the transport side: the Seebeck coefficients come from BoltzTrap2 with no parameter fitted to the target S or zT values, and the proposed pseudogap/slope correlation is in principle falsifiable by experiment or by higher-level calculations. The structural and magnetic characterization is extensive, and the authors honestly report that the relaxed alloys do not retain their initial magnetic configurations. However, the quantitative zT claims are built on two optimistic assumptions - zero lattice thermal conductivity and an ordered magnetic state that is admitted to be hypothetical above room temperature - and the YN reference electronic structure disagrees with established band-gap values. These issues prevent the quantitative conclusions from being accepted as they stand.

major comments (4)
  1. [Thermoelectric properties, Eq. (8), Figs. 21-23] The assumption that the lattice thermal conductivity is negligible is unjustified for transport at 100-800 K. The sentence 'since we are working at 0K, the phonon thermal conductivity will be considered negligible' contradicts the temperature range of the plotted Seebeck and zT values; phonon thermal conductivity is a finite-temperature quantity and cannot be discarded because the DFT cell is relaxed at 0 K. All reported zT values, including the headline 0.35 at 800 K for Cr0.75Y0.25N-AFM1, are therefore upper bounds. Unless a finite kappa_latt is estimated from a phonon/lattice-dynamics calculation or the zT claims are explicitly reframed as purely electronic upper bounds, the quantitative figure-of-merit statements are not supported.
  2. [Thermoelectric properties, Table I, Fig. 23] The 800 K zT claim is computed for an ordered magnetic state that the paper itself labels 'hypothetical above room temperature' in the thermoelectric section. The relaxed Cr0.75Y0.25N-AFM1 cell is actually not AFM but ferrimagnetic (magnetization M = 6.00 μB per cell in Table I), and CrN magnetic order is known to disappear near room temperature. No paramagnetic high-temperature electronic structure or explicit finite-temperature magnetic treatment is provided, so the 800 K zT = 0.35 describes a hypothetical ordered phase rather than the material at 800 K. This undermines the high-temperature conclusion in the abstract and conclusions, independent of the kappa_latt issue.
  3. [Electronic properties, Table III, Figs. 12 and 21] The calculated YN electronic structure is semimetallic with no gap, which disagrees with the established YN band gap of roughly 0.7 eV, as evidenced by the cited theoretical values in Table III (220-1070 meV). Since YN serves as the reference endpoint for the alloy comparisons and the YN-ScN similarity motivates the study, this discrepancy should be resolved or explicitly explained. Without a validated YN reference, the alloy DOS analysis and the derived pseudogap design rule rest on a questionable electronic-structure baseline.
  4. [Electronic properties, Table III] The reported energy gaps of 0.1-1.5 meV (e.g., Cr0.5Y0.5N-AFM1 Bg-up = 0.2 meV and Cr0.75Y0.25N-AFM2 Bg = 0.1 meV) are two to three orders of magnitude below the thermal energy at the temperatures of interest (about 25 meV at 300 K) and are comparable to numerical uncertainties in the band-structure interpolation. The claim that 'small indirect energy gaps are present' should be substantiated by a convergence test (k-point mesh, interpolation parameters, or band-unfolding resolution) or removed.
minor comments (6)
  1. [Conclusions and throughout] There are several typographical issues: 'Vegaard's law' should be 'Vegard's law', 'BoltzTrap2' is the code name and should be spelled consistently, 'Jhan-Teller' should be 'Jahn-Teller', and the section header 'RESUL TS AND DISCUSSION' contains a spacing error.
  2. [Figure 4 caption] The caption for Figure 4 says 'Cr0.75Y0.75N', but the composition should presumably be Cr0.75Y0.25N, matching the other 75% Cr structures.
  3. [Structural results and Electronic properties] Several cross-references to tables appear as unresolved 'Table ??' placeholders, including references to Table I and Table II in the structural and electronic sections. These should be fixed.
  4. [Thermoelectric properties, Eq. (9)] Equation (9) states S proportional to the energy derivative of ln sigma(E), but the text immediately equates this with 'the density of state can be related to the Seebeck coefficient' and with 'high DOS slopes'. The Mott expression involves the energy derivative of the transport distribution, not the DOS itself. Please clarify the relationship between the DOS features shown in the figures and the calculated Seebeck values.
  5. [Analysis of octahedrons, Fig. 11] The sentence describing the symmetric distribution at 50% Cr is repeated verbatim, and panels (g)-(i) are all labeled 'FM' in the subcaptions even though the surrounding text indicates they correspond to different magnetic structures. Please correct the labels and remove the duplicate sentence.
  6. [Thermoelectric properties] The phrase 'since we are working at 0K' is confusing because all transport results are plotted at 100-800 K; this should be reworded to state that the DFT band structure is computed at 0 K while transport coefficients are evaluated at finite temperature within the constant relaxation-time approximation.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity; the Seebeck and zT values are BoltzTrap2 outputs from DFT band structures, and the pseudogap/slope criterion is a post-hoc interpretation. Only a minor, non-load-bearing self-citation to the first author's thesis appears.

full rationale

The paper computes Seebeck coefficients and zT with BoltzTrap2 from DFT band structures; no parameter is fitted to the reported Seebeck or zT values. Mott's approximation (Eq. 9) is used as an interpretive lens to connect DOS slopes to S, but the actual S values come from the independent transport calculation. The claimed correlation between pseudogaps/steep DOS slopes and high S is observed post-hoc, not forced by construction. Setting the phonon thermal conductivity to zero is an acknowledged approximation that overestimates zT, but it is not a circular input. The only self-citation is reference [29], the first author's thesis, cited for magnetic structure models and SQS correlation-function details; however, the magnetic structures originate from experimental work [36] and the SQS method is implemented via standard ATAT software, so this self-citation is not load-bearing. Comparisons against experimental lattice parameters, Seebeck data, and zT values of other alloys provide external anchoring. Therefore no circular step reduces the central claims to their inputs.

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

The calculated zT values depend on the zero-lattice-conductivity assumption, and the Seebeck interpretation depends on Mott's approximation. No new physical entities are introduced.

free parameters (1)
  • Lattice thermal conductivity (kappa_latt) = 0 W/m/K (set to zero)
    The paper assumes phonon thermal conductivity is negligible, which directly inflates the computed zT. No phonon calculation or experimental value is used.
assumptions (4)
  • domain assumption SCAN meta-GGA functional gives accurate lattice parameters and band structures for CrN and YN.
    The paper states SCAN fits experiments better than PBE/LDA, but does not validate against the YN gap discrepancy.
  • domain assumption Constant relaxation time approximation in BoltzTrap2.
    Seebeck is independent of relaxation time, but sigma and kappa_el require it; zT with kappa_latt=0 is independent of it. The assumption is standard but unstated.
  • domain assumption 64-atom SQS supercells represent random CrYN alloys at the three compositions.
    The paper uses SQS as a reliable model for disordered phases, citing [24,37], but does not test convergence with larger supercells.
  • domain assumption Mott's approximation relating Seebeck coefficient to DOS slope.
    Equation (9) is used to interpret the correlation between DOS features and Seebeck coefficients.

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Cite this review

Pith. "Pith review of Observation of pseudogap in Cr_{1-x}Y_xN magnetic alloy and its impact on the Seebeck coefficient by ab-initio calculations." pith.science (2026). https://pith.science/paper/IMU7LCAG

@misc{pith2026250600687,
  author       = {Pith},
  title        = {Pith review of: Observation of pseudogap in Cr_1-xY_xN magnetic alloy and its impact on the Seebeck coefficient by ab-initio calculations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IMU7LCAG}},
  note         = {Machine review of arXiv:2506.00687}
}
read the original abstract

Thermoelectric materials require high electronic conductivity and low thermal conductivity. CrN has been shown to have low phononic thermal conductivity, making it a potential candidate for thermoelectric applications. In addition, similarities have been observed between YN and ScN suggesting that the CrYN alloy may have interesting thermoelectric properties. As CrYN has not been studied in detail at the level of thermoelectric properties, the first study on CrYN alloy of Seebeck coefficient and zT figure of merit is proposed in this study. For this purpose, cubic special quasirandom structures were constructed at values of x = 0.25, 0.5 and 0.75 in the alloy Cr_{1-x}Y_xN starting from different magnetic structures. After analyzing lattice parameters, Cr magnetic moments, octahedron deformation, second neighbors distribution around metals, density of states and band structures, it was concluded that to obtain high values of Seebeck coefficient and zT, it is necessary the presence of a pseudo gap in both spin channels and it is also necessary that the Fermi level is on a steep decreasing slope of number of states, since due to Motts approximation, the value of this slope is proportional to the Seebeck coefficient. Density of states of all the structures shows a metallic behavior. In structures with x=0.5, the presence of small indirect energy gaps is observed. Although no structure retains the initial magnetic configuration, there is a possible influence of this on the electronic structure. Considerable deformations in octahedra can suppress thermoelectric properties.

Figures

Figures reproduced from arXiv: 2506.00687 by the authors.

Figure 1
Figure 1. Model magnetic structures of CrN and YN in FCC phase obtained from [ [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Cr0.25Y0.75N a c b (a) AFM1 [100] a c b (b) AFM2 [110] a c b (c) FM [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Cr0.5Y0.5N structures (SQS) [37] was used using the ATAT software [38] for the construction of the correlation functions (for details of these functions, see the study [29]). This method has been shown in different theoretical studies on ternary CrN alloys with transition metals to be a reliable thermodynamic model for disordered phases and provides a considerably simpler and (a) AFM1 [100] (b) AFM2 [110] (c) FM [P… view at source ↗
Figures from the paper (20 more)
Figure 4
Figure 4. Figure 4: Cr0.75Y0.75N 6 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Lattice parameter with respect to the percentage of Cr composition for the [PITH_FULL_IMAGE:figures/full_fig_p038_5.png]
Figure 6
Figure 6. Figure 6: Average lattice parameter with respect to the free energy of each magnetic [PITH_FULL_IMAGE:figures/full_fig_p039_6.png]
Figure 7
Figure 7. Figure 7: Magnetic moment with respect to the percentage of Cr composition for the [PITH_FULL_IMAGE:figures/full_fig_p040_7.png]
Figure 8
Figure 8. Figure 8: Average magnetic moment with respect to the free energy of each magnetic [PITH_FULL_IMAGE:figures/full_fig_p041_8.png]
Figure 9
Figure 9. Figure 9: Formation enthalpy 0.00 0.25 0.50 0.75 1.00 YN x(Cr) at CrN 1.0 0.8 0.6 0.4 0.2 0.0 0.2 ¢ H mix ( e V = a t ) AFM1 [100] AFM2 [110] FM [PITH_FULL_IMAGE:figures/full_fig_p041_9.png]
Figure 10
Figure 10. Figure 10: Mixing enthalpy 41 [PITH_FULL_IMAGE:figures/full_fig_p041_10.png]
Figure 11
Figure 11. Figure 11: Bond distances, distortion angle and number of octahedra with respect to [PITH_FULL_IMAGE:figures/full_fig_p042_11.png]
Figure 12
Figure 12. Figure 12: YN DOS and band structure [PITH_FULL_IMAGE:figures/full_fig_p043_12.png]
Figure 13
Figure 13. Figure 13: CrN NM DOS and band structure 43 [PITH_FULL_IMAGE:figures/full_fig_p043_13.png]
Figure 14
Figure 14. Figure 14: CrN AFM1 [100] DOS and band structure [PITH_FULL_IMAGE:figures/full_fig_p044_14.png]
Figure 15
Figure 15. Figure 15: CrN AFM2 [110] DOS and band structure 44 [PITH_FULL_IMAGE:figures/full_fig_p044_15.png]
Figure 16
Figure 16. Figure 16: CrN FM DOS and band structure [PITH_FULL_IMAGE:figures/full_fig_p045_16.png]
Figure 17
Figure 17. Figure 17: CrN PM DOS and band structure 45 [PITH_FULL_IMAGE:figures/full_fig_p045_17.png]
Figure 18
Figure 18. Figure 18: Cr25Y75N DOS and band structure 46 [PITH_FULL_IMAGE:figures/full_fig_p046_18.png]
Figure 19
Figure 19. Figure 19: Cr50Y50N DOS and band structure 47 [PITH_FULL_IMAGE:figures/full_fig_p047_19.png]
Figure 20
Figure 20. Figure 20: Cr75Y25N DOS and band structure 48 [PITH_FULL_IMAGE:figures/full_fig_p048_20.png]
Figure 21
Figure 21. Figure 21: Figure of merit zT and Seebeck coefficient with respect to temperature (T) for [PITH_FULL_IMAGE:figures/full_fig_p049_21.png]
Figure 22
Figure 22. Figure 22: Seebeck coefficient (S) with respect to temperature (T) for each of the different [PITH_FULL_IMAGE:figures/full_fig_p049_22.png]
Figure 23
Figure 23. Figure 23: Figure of merit zT with respect to temperature (T) for each of the different [PITH_FULL_IMAGE:figures/full_fig_p050_23.png]

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Pith tools

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