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REVIEW 3 major objections 4 minor 59 references

Predicting the Curie temperature in substitutionally disordered alloys using a first-principles based model

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A four-parameter model fit to 32 known magnets reproduces Curie-temperature trends in seven untested alloy families and predicts a decrease in Tc for iron-technetium.

desk verdict Honest out-of-sample test of a fixed four-parameter TC model; trends hold in most systems, but the Cr/V manual exceptions and lack of error bars keep the 'broad applicability' claim from being fully proven. read the letter →

arxiv 2412.04920 v2 pith:7WJDXQLP submitted 2024-12-06 cond-mat.mtrl-sci

Marian Arale Brännvall , Rickard Armiento , Björn Alling This is my paper · ORCID
classification cond-mat.mtrl-sci MSC 82D40 PACS 75.30.Kz75.50.Bb71.15.Mb
keywords CurietemperaturesubstitutionaldisorderdisorderedlocalmomentsdensityfunctionaltheorymagneticentropyspecialquasirandomstructuresHeusleralloysiron-technetium
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 a four-parameter physics model, fit once to 32 known magnets in Ref. 20, transfers to substitutionally disordered alloys it never trained on. The model uses the density-functional energy difference between the disordered-local-moments (DLM) paramagnetic state and the magnetic ground state, the magnetic entropy of the DLM state, and the number of nearest magnetic neighbors. Applied to Fe$_{1-x}$Co$_x$, Fe$_{1-x}$Cr$_x$, Fe$_{1-x}$V$_x$, Ni-based Heusler alloys, Ti$_{1-x}$Cr$_x$N, and Co$_{1-x}$Al$_x$, it reproduces the qualitative composition trends of the measured Curie temperature and often lands within the model's stated mean absolute error of about 126 K. The same fixed-parameter model predicts a monotonic decrease of $T_\text{C}$ with solute content in the experimentally unexplored bcc alloy Fe$_{1-x}$Tc$_x$, matching the pattern seen in Fe-Mo and Fe-Re analogues.

What carries the argument

The load-bearing machinery is the DLM supercell representation of the paramagnetic state together with Eq. (1). In one DLM run, atomic spin directions are fixed in near-random orientations with short-range order close to zero using the constraint method of Ref. 29, while magnitudes relax; the magnetic ground state comes from a non-collinear ground-state search (Ref. 23), and substitutional disorder is encoded in special quasirandom structures (Ref. 28). From these calculations the paper extracts $\Delta E = E_\text{DLM} - E_\text{GS}$, the magnetic entropy $S_\text{mag} = k_B \sum_i \ln(m_i+1)/N_\text{mag}$ over constrained moment magnitudes $m_i$ in Bohr magnetons, and $N_N$, the number of nearest magnetic neighbors defined by a 0.75 $\mu_B$ ground-state moment threshold. The empirical factor $(1 - B/N_N^C)$ is the model's correction for short-range-order effects that matter when the magnetic energy is distributed over few neighbors, and $D$ sets a 124 K floor.

What would settle it

Measure the Curie temperature of a bcc Fe$_{0.9}$Tc$_{0.1}$ sample; a value above rather than below the pure-Fe prediction would contradict the claimed monotonic decrease, and a cheaper check is to recompute one Fe-V or Fe-Cr composition with several independent SQS cells and DLM configurations to see whether the scatter exceeds the trend the model attributes to composition.

Watch

Extended reading notes

Core claim

The central claim is that Eq. (1), with the fixed constants $A=0.85$, $B=0.69$, $C=0.14$, and $D=124$ K, is generally capable of reproducing the qualitative dependence of the Curie temperature on alloy composition across diverse chemistries and crystal structures, and in several systems the absolute values are close to experiment. None of the seven alloys studied here belongs to the 32 materials used to fit those constants, so the agreement is presented as a transferability test. The formula $T_\text{C} = A(\Delta E/S_\text{mag})(1 - B/N_N^C) + D$ K ties the ordering temperature to the energy penalty for magnetic disorder, divided by the magnetic entropy, corrected by the number of nearest magnetic neighbors, and offset by a constant floor. The paper's own agreement ranges from roughly 20-80 K for the Fe binaries to within about 170 K for the Heusler alloys, while fcc Co$_{1-x}$Al$_x$ clearly fails and Ti$_{1-x}$Cr$_x$N is overestimated because its low $T_\text{C}$ approaches the model's 124 K lower limit.

Load-bearing premise

The load-bearing premise is that one DLM supercell with near-zero spin short-range order, a fixed 0.75 $\mu_B$ threshold for constraining moments, and the four fitted constants faithfully represent the paramagnetic state of every tested chemistry; the paper's own hand-adjusted exemptions for chromium and vanadium moments show where that premise is strained.

Editorial extensions

If this is right

  • For the six families with experimental data, the model returns the correct sign of $\partial T_\text{C}/\partial x$ in every case, so it can rank compositions by magnetic ordering temperature before synthesis.
  • The fixed parameters mean each new alloy family is an independent test; the observed agreement within about 170 K across Heusler alloys and Fe binaries indicates the model is not being re-fit per system.
  • The failure on fcc Co$_{1-x}$Al$_x$ and the too-high values for Ti$_{1-x}$Cr$_x$N delimit the method's domain: robust local moments and $T_\text{C}$ well above the 124 K floor.
  • For Fe$_{1-x}$Tc$_x$, the predicted drop in $T_\text{C}$ with technetium content is a concrete, testable experimental target, despite the radioactivity of Tc.

Reading between the lines

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

  • A natural next stress test is an ordered intermetallic or a strongly localized-moment oxide, where the single-DLM-configuration approximation is less demanding; if Eq. (1) holds there, the entropy and neighbor-count terms are doing genuinely physical work rather than absorbing the fit.
  • The predicted Fe$_{1-x}$Tc$_x$ curve could be sharpened by repeating one composition with several independent SQS cells and DLM configurations; if the scatter exceeds the roughly 50 K drop the model predicts, the trend is not yet a robust target.
  • The manual exemptions for Cr and V moments suggest a principled extension: an itinerancy-aware constraint threshold, or a separately parameterized DLM moment magnitude, could remove the convergence-related exceptions and let the model speak for systems like Fe-V and Co-Al.
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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 / 4 minor

Summary. This paper applies a previously developed four-parameter model, Eq. (1), to predict the Curie temperature of seven substitutionally disordered alloy systems (Fe-Co, Fe-Cr, Fe-V, Ni-Cu-MnSb, Ni-MnSb, Ti-Cr-N, and Co-Al), comparing the predictions with experimental values and also presenting a prediction for the experimentally unexplored Fe-Tc system. The model, with parameters A=0.85, B=0.69, C=0.14, and D=124 K fitted to 32 known magnets in an earlier work (Ref. 20), uses the DLM-ground-state energy difference, a magnetic-entropy term, and the number of nearest magnetic neighbors. The authors report qualitative agreement with the composition dependence of TC in most systems, some quantitative agreement, and explicitly discuss cases where the model fails (Co-Al) or where the standard workflow had to be altered (unconstrained Cr/V moments in Fe-Cr and Fe-V, modified λ schedule for Co-Al). The central claim is that the method is broadly applicable with less hands-on adjustment than competing approaches.

Significance. If the central claim is supported, the model provides a computationally efficient, out-of-sample screening tool for alloy Curie-temperature trends, complementing more expensive Heisenberg-based methods and potentially guiding experimental alloy design. The work has several strengths: none of the tested alloys are in the 32-material fitting set, so the test is genuinely out-of-sample; the authors are unusually honest in reporting the Co-Al failure and the workflow modifications; the Fe-Tc prediction is a falsifiable experimental target; and the Python scripts for data extraction are openly available. The main reservation is that the evidence for 'broad applicability requiring less hands-on adjustments' is weakened by the very exceptions the paper acknowledges, and at least one of the claimed qualitative successes (Fe-V) does not actually reproduce the experimental composition trend.

major comments (3)
  1. [Sec. V and Table I] The central claim that the model reproduces 'the qualitative effect on TC of altering the alloy composition' is contradicted by the Fe1-xVx results. From x=0.125 to x=0.25, the experimental TC decreases (1111 K to 1053 K), while the predicted TC increases (1053 K to 1091 K). The text in Sec. V states that 'our method correctly predicts this observation' and attributes the discrepancy to the changes being 'minimal,' but the predicted slope has the opposite sign to the experimental slope. This is a qualitative failure, not a quantitative offset. The discussion should explicitly acknowledge this and explain why the model nevertheless is considered to capture the trend.
  2. [Sec. IV A and Sec. V] The unconstrained Cr and V moments in Fe1-xCrx and Fe1-xVx break the prescribed workflow of Sec. II C, and the good agreement for these systems is therefore not a clean out-of-sample test of Eq. (1). Because Cr and V are not constrained in the DLM runs, they are excluded from the magnetic entropy in Eq. (2), while their moment collapse (e.g., Cr from 1.3 to 0.2 μB at x=0.125) contributes to the energy difference ΔE in a way that a constrained run would not. A control calculation with constrained Cr/V moments, or a sensitivity analysis showing how TC depends on the choice of constraint, is needed to establish that the agreement is not fortuitous.
  3. [Abstract and Sec. V] The abstract's claim that the method requires 'less hands-on adjustments compared to other theoretical approaches' is overstated given the manual interventions described in the paper: the 0.75 μB moment threshold is relaxed for Cr and V in Fe-Cr and Fe-V, and the λ schedule is modified for Co-Al. These are exactly the type of system-specific adjustments the method aims to avoid. Please either soften the claim to accurately reflect the observed level of intervention, or provide a quantitative measure of the manual tuning needed per system.
minor comments (4)
  1. [Fig. 3 caption] The word 'cobolt' in the caption of Fig. 3 should be 'cobalt'.
  2. [Sec. II A] The description of the parameter fit states that 'A linear fit to the experimental TC subsequently gives the parameters A and D,' but it does not specify which experimental data are used; a cross-reference to Ref. 20 would clarify the procedure.
  3. [Sec. IV A] The legend in Fig. 1 lists 'This work' three times, which is redundant and could be simplified to a single entry or a note explaining that all filled symbols are from this work.
  4. [Sec. III] The details of the SQS supercells (size, number of configurations, and generated k-points) are not fully specified, which limits reproducibility; providing the SQS parameters or a reference to the generation code would be helpful.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model is a fixed, previously fitted formula applied out-of-sample.

full rationale

The paper does not derive Eq. (1) in this work; it applies a fixed model whose parameters A=0.85, B=0.69, C=0.14, and D=124 K were fitted in Ref. 20 to a disjoint set of materials. The paper explicitly states: "None of the alloys investigated in the present work are included among the 32 systems used to obtain the fitting parameters of Eq. (1) and can thus be seen as a critical test of its generality." Each predicted TC is therefore an out-of-sample evaluation of a fixed formula, built from DFT-derived inputs (Delta E, S_mag, N_N) that are computed for the alloy in question and compared against independent experimental data. The self-citation to Ref. 20 is load-bearing for the model form, but that prior publication is independently published and externally calibrated, and no uniqueness theorem or unverified same-author result is invoked to force the present choice. The acknowledged limitations in Sec. V, namely the unconstrained Cr/V moments in Fe-Cr and Fe-V, the 124 K lower bound for Ti-Cr-N, and the itinerant-magnetism failure for Co-Al, are stated caveats that weaken specific comparisons but do not make the predictions identical to their inputs or to the fitted data. No step in the derivation chain reduces, by construction, to the fitted parameters or to the experimental TC values being reproduced.

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

The predictions rest entirely on four constants fitted in prior work (A, B, C, D), on the hand-set 0.75 μB threshold, and on the modeling assumptions that a single DLM/SQS configuration is representative and that the mean-field-plus-SRO-correction form transfers. No new physical entities are introduced. The paper does not re-derive the SRO correction factor from first principles.

free parameters (5)
  • A = 0.85
    Scale factor in Eq. (1), fitted to 32 known magnetic materials in Ref. 20 via a linear fit to experimental TC. The current paper's predictions inherit this value.
  • B = 0.69
    Multiplicative constant in the SRO correction factor (1 - B/NN^C), fitted to 32 materials using the Nelder-Mead method in Ref. 20.
  • C = 0.14
    Exponent in the SRO correction factor, fitted to 32 materials using Nelder-Mead in Ref. 20.
  • D = 124 K
    Additive constant in Eq. (1), fitted to 32 materials via a linear fit. Gives the model a lower bound of 124 K and causes overestimation for low-TC systems like Ti1-xCrxN.
  • Magnetic moment threshold = 0.75 μB
    Hand-set threshold for defining magnetic atoms in the ground state, used to determine NN and Smag. The paper relaxes this threshold for Cr in Fe1-xCrx and V in Fe1-xVx to achieve SCF convergence, so it is an adjustable workflow choice.
assumptions (5)
  • domain assumption DFT with the PBE functional and PAW potentials gives accurate total energies and magnetic moments for the studied alloys.
    Invoked throughout Sec. III and IV as the foundation for all ΔE and Smag inputs.
  • domain assumption A single DLM supercell with SRO close to zero adequately represents the paramagnetic state.
    Section II C states only one DLM configuration is used; the representativeness of a single configuration is assumed, and no statistically averaged ensemble is tested.
  • domain assumption SQS supercells represent substitutional disorder at each composition.
    Section II C and III use SQS without checking convergence of properties with respect to different SQS realizations.
  • standard math The mean-field relation TC ∝ (EDLM - EFM)/Smag is a valid approximation for the studied systems.
    Equation (4) and Sec. II B rely on a free-energy argument and neglect short-range order, which is only partially corrected by the fitted factor.
  • ad hoc to paper The functional form (1 - B/NN^C) transfers to alloy systems outside the 32-material fitting set.
    This factor is an empirical correction fitted in Ref. 20; the current paper applies it without re-derivation, assuming the same SRO correction holds in the new chemistries and structures.

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Cite this review

Pith. "Pith review of Predicting the Curie temperature in substitutionally disordered alloys using a first-principles based model." pith.science (2026). https://pith.science/paper/7WJDXQLP

@misc{pith2026241204920,
  author       = {Pith},
  title        = {Pith review of: Predicting the Curie temperature in substitutionally disordered alloys using a first-principles based model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7WJDXQLP}},
  note         = {Machine review of arXiv:2412.04920}
}
abstract

When exploring new magnetic materials, the effect of alloying plays a crucial role for numerous properties. By altering the alloy composition, it is possible to tailor, e.g., the Curie temperature ($T_\text{C}$). In this work, $T_\text{C}$ of various alloys is investigated using a previously developed technique [Br\"{a}nnvall et al. Phys. Rev. Mat. (2024)] designed for robust predictions of $T_\text{C}$ across diverse chemistries and structures. The technique is based on density functional theory calculations and utilizes the energy difference between the magnetic ground state and the magnetically disordered paramagnetic state. It also accounts for the magnetic entropy in the paramagnetic state and the number of nearest magnetic neighbors. The experimentally known systems, Fe$_{1-x}$Co$_x$, Fe$_{1-x}$Cr$_x$, Fe$_{1-x}$V$_x$, NiMnSb-based Heusler alloys, Ti$_{1-x}$Cr$_x$N, and Co$_{1-x}$Al$_x$ are investigated. The experimentally unexplored system Fe$_{1-x}$Tc$_x$ is also tested to demonstrate the usefulness of the developed method in guiding future experimental efforts. This work demonstrates the broad applicability of the developed method across various systems, requiring less hands-on adjustments compared to other theoretical approaches.

Figures

Figures reproduced from arXiv: 2412.04920 by the authors.

Figure 1
Figure 1. Predicted and experimental Curie temperatures as a function of composition are shown for the following alloy systems: bcc [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Predicted and experimental Curie temperatures of fcc [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Distribution of the magnetic moment magnitudes of cobolt, aluminum, and iron in both fcc Co [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: The predicted Curie temperatures of bcc Fe [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 1
Figure 1. Figure 1: System x-value T Model C (K) T Exp. C (K) Fe1−xCox 0.0 1023 1043 0.125 1080 1064 0.25 1151 1230 0.375 1293 - 0.75 1143 1178 0.9 1365 1308 1.0 1418 1388 Fe1−xVx 0.05 1062 1083 0.125 1053 1111 0.25 1091 1053 Fe1−xCrx 0.1 1049 1023 0.125 1032 1010 0.25 919 906 0.375 847 7…

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Pith tools

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