Shape of temperature dependence of spontaneous magnetization of various ferromagnets

A. Perevertov

REVIEW 3 major objections 3 minor 1 references

The reduced spontaneous-magnetization curve of ferromagnets is well described by a Lamé superellipse whose squareness generally rises with Curie temperature.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-13 12:28 UTC pith:TAMFPLPH

load-bearing objection Modest empirical Lamé survey of M(T) shapes; the abstract is clear, but the full text we have is unreadable, so the fits and TC trend cannot be checked. the 3 major comments →

arxiv 2604.03704 v2 pith:TAMFPLPH submitted 2026-04-04 cond-mat.mtrl-sci

Shape of temperature dependence of spontaneous magnetization of various ferromagnets

A. Perevertov This is my paper

classification cond-mat.mtrl-sci

keywords spontaneous magnetizationCurie temperaturesuperellipseLamé curveferromagnetsmagnetization curve shapesquareness

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper argues that the full temperature shape of spontaneous magnetization, plotted as M/Ms versus T/Tc, can be captured for a wide range of ferromagnets by a single-parameter superellipse (the Lamé curve). Fitting roughly forty materials yields a squareness (power) parameter between about 1.4 and 3.0: pure iron is the most square, while certain antiferromagnets and the dilute alloy Ni55Cu45 are the least. Among metallic alloys the squareness tends to increase with Curie temperature, cobalt being a clear exception that tracks nickel’s curve despite a much higher Tc. Adding other metals—magnetic or not—to iron or nickel systematically lowers the squareness, yet thermal expansion has no visible effect: zero-expansion Invar still follows a standard Lamé shape. A sympathetic reader cares because the result supplies a simple, quantitative ranking of the entire M(T) curve across chemically diverse magnets instead of relying only on Tc or local critical exponents.

Core claim

For about forty ferromagnetic materials the reduced spontaneous-magnetization curves M(T)/Ms versus T/Tc are well described by the Lamé superellipse equation. The single free power parameter that sets the squareness of the curve ranges from 1.4 to 3.0; iron exhibits the largest squareness and antiferromagnets together with Ni55Cu45 the smallest. In metallic alloys the squareness generally increases with Curie temperature, the sole clear exception being cobalt, which collapses onto the same reduced curve as nickel. Dilution of iron or nickel by other metals decreases squareness, while zero-expansion Invar still follows a standard Lamé form, showing that the thermal-expansion coefficient does

What carries the argument

The Lamé superellipse (superellipse equation) used as a one-parameter fit to the full reduced M(T) curve; its power coefficient is adopted as the numerical measure of squareness.

Load-bearing premise

That a single-parameter Lamé superellipse is an adequate and physically meaningful description of the entire magnetization curve for chemically diverse materials, without systematic residual comparison to standard magnetic models.

What would settle it

High-precision M(T) data sets for several pure metals and alloys that leave large, systematic residuals when fit by the best Lamé curve (especially near Tc or at low T) while a Brillouin function or a two-parameter Bloch-plus-critical form fits markedly better would falsify the claim that Lamé usefully captures squareness.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

Squareness of the full reduced M(T) curve can be ranked across materials by a single number lying between roughly 1.4 and 3.0.
Metallic alloys with higher Curie temperature tend to display squarer magnetization curves.
Alloying iron or nickel, whether with magnetic or non-magnetic metals, systematically softens the reduced M(T) shape.
Thermal expansion coefficient does not dictate the form of the magnetization curve; zero-expansion Invar still follows a standard Lamé shape.
Cobalt and nickel share essentially the same reduced magnetization curve despite very different Curie temperatures.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

A universal Lamé description would allow materials databases to store one squareness number for first-order comparisons instead of full tabulated M(T) curves.
The cobalt–nickel coincidence implies that crystal structure or exchange mechanism can override the simple Tc–squareness correlation.
Mapping systematic residuals of Lamé fits against Brillouin or Bloch forms would isolate which temperature regime (spin-wave or critical) drives the observed squareness trends.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

Modest empirical Lamé survey of M(T) shapes; the abstract is clear, but the full text we have is unreadable, so the fits and TC trend cannot be checked.

read the letter

The only clean part of this package is the abstract. It reports a straightforward empirical job: take reduced spontaneous magnetization curves for about forty ferromagnets, fit them with a Lamé superellipse, extract a squareness (power) parameter between 1.4 and 3.0, and look at how that tracks Tc for metallic alloys. Iron is most square; cobalt is the named exception that tracks nickel; alloying iron or nickel softens the shape; Invar does not look special. That is a usable packaging of known M(T) data for people who screen alloys or need a one-number shape index. It is not a theory paper and does not claim to be.

What is actually new is the multi-material survey and the reported Tc–squareness tendency with the cobalt exception. The superellipse itself is classical; the contribution is the compilation and the correlation. On the abstract alone that is honest, limited-scope materials work.

The soft spot is not subtle: the full manuscript body in the source is almost entirely corrupted (replacement glyphs, then unrelated Schrödinger/author text). We cannot see equations, material list, data sources, residuals, error bars, or any comparison to Brillouin/mean-field, Bloch T^{3/2}, or critical-power forms. So “good agreement” and the 1.4–3.0 range remain assertions. The reader’s concern that a single free power is being treated as an adequate physical model without baselines is fair and uncheckable from what we have. Circularity risk is low; the work is descriptive fitting, not a prediction loop.

Who it is for: experimental magnetism and alloy people who want a compact shape index. Not for theorists looking for a new mechanism. If a clean PDF exists with tables, figures, and residual stats, it deserves a serious referee and light-to-moderate revision pressure on baselines and data provenance. As the text stands here, it is not evaluable. I would not bring the garbled version to reading group; I would not cite it until I can read the fits. Send a clean manuscript to peer review; do not desk-reject the idea on abstract merit alone.

Referee Report

3 major / 3 minor

Summary. The manuscript analyzes the temperature dependence of spontaneous magnetization for about forty ferromagnetic materials by fitting reduced M(T)/Ms versus T/Tc curves to a single-parameter Lamé (superellipse) form. It reports that the squareness (power) parameter ranges from about 1.4 to 3.0, is largest for iron and smallest for some antiferromagnets and Ni55Cu45, and for metallic alloys generally increases with Curie temperature (with cobalt as a noted exception that tracks nickel in reduced coordinates). Alloying of Fe or Ni is said to reduce squareness, and zero-expansion Invar is reported to follow a standard Lamé shape, implying no special role for thermal expansion.

Significance. If the fits and trends hold under proper residual analysis and comparison to standard baselines, the work would offer a compact phenomenological ranking of M(T) shapes across a broad materials set, which could be useful for materials comparison and for organizing empirical data. The contribution is descriptive rather than a first-principles derivation: a free squareness parameter is fitted per material. Strengths claimed in the abstract (broad materials coverage, a simple closed-form shape descriptor, and a reported Tc trend with an explicit cobalt exception) would be of moderate interest to magnetism and materials communities, but only if goodness-of-fit, data provenance, and comparison to mean-field/Bloch/critical forms are made transparent.

major comments (3)

The supplied full manuscript body is almost entirely unreadable (pervasive replacement glyphs) and ends with unrelated text from a different work (semilinear Schrödinger equations and unrelated author block). Equations, tables, figures, material lists, fit residuals, and data sources cannot be inspected. The central claims of “good agreement,” the 1.4–3.0 range, and the Tc trend therefore cannot be audited from the manuscript as provided. A complete, correctly encoded version with all figures and tables is required before scientific review can proceed.
Abstract and intended Results: the premise that a single-parameter Lamé superellipse adequately characterizes the full reduced M(T) curve is load-bearing, but no systematic comparison to standard forms (mean-field Brillouin functions, low-T Bloch T^{3/2}, and critical power laws near Tc) or quantified residual statistics (e.g., RMS, R², or region-wise residuals) is available in the readable text. Without those, “good agreement for most materials” and the reported squareness ranking remain uncheckable assertions.
Abstract (Tc-trend claim): the reported increase of squareness with Tc for metallic alloys (cobalt excepted) depends on how Ms and Tc are fixed and on which alloys are included. The manuscript must state exclusion rules, error bars on the squareness parameter, and whether Ms and Tc were taken from the same datasets used in the fits or from independent literature, so that the trend is not an artifact of reduced-coordinate construction.

minor comments (3)

Abstract: the parenthetical “the power coefficient in the superellipse equation was found…” is missing a closing parenthesis and should define the Lamé exponent notation once and use it consistently.
When a readable version is supplied, please include a table of all materials with sources of M(T), adopted Ms and Tc, fitted squareness, and a goodness-of-fit metric so the “about forty” set can be reproduced.
Clarify whether antiferromagnets are included only for sublattice magnetization shape comparison, and how spontaneous magnetization is defined for those cases.

Circularity Check

0 steps flagged

Descriptive Lamé-curve fitting of experimental M(T); no derivation that reduces to its own inputs.

full rationale

The paper’s central activity is empirical: spontaneous magnetization curves for ~40 ferromagnets are fitted with a one-parameter superellipse (Lamé) form, the fitted squareness is reported (1.4–3.0), and trends versus TC and alloying are noted. That is characterization, not a first-principles chain in which a claimed prediction is forced by construction from the same fitted quantity. There is no self-definitional loop (squareness is not defined as the quantity it is said to predict), no “prediction” that is merely a re-expression of a fit residual, no load-bearing uniqueness theorem imported from the authors’ prior work, and no ansatz smuggled in via self-citation. The abstract’s “good agreement” and TC-trend statements are ordinary fit-and-correlate claims; they stand or fall on residual quality and data selection, which are correctness/audit issues, not circularity. The supplied body is largely corrupted, so equations and tables cannot be re-checked, but nothing in the readable abstract or remaining fragments exhibits a reduction of the form Eq. X ≡ fitted input. Score 0 is therefore the honest finding.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 0 invented entities

Central claims rest on treating published spontaneous-magnetization curves as comparable in reduced coordinates and on adopting the Lamé power as the shape metric. One free parameter per material (squareness) is fitted; no new physical entity is introduced. Domain assumptions about data quality and model adequacy carry the conclusions.

free parameters (1)

Lamé squareness / power coefficient n (per material) = 1.4–3.0 across materials
Fitted to each experimental M(T)/Ms vs T/Tc curve; abstract reports range 1.4–3.0. All shape comparisons and TC trends are statements about this fitted number.

axioms (3)

domain assumption Reduced spontaneous magnetization M/Ms versus reduced temperature T/Tc is the appropriate universal comparison across materials.
Standard in magnetism; required for cross-material squareness ranking and the cobalt–nickel comparison.
ad hoc to paper A single-parameter Lamé (superellipse) equation is a sufficient model of the full M(T) shape for ranking materials.
Choice of functional form is the paper’s methodological core; not derived from spin Hamiltonian or critical theory in the abstract.
domain assumption Literature spontaneous-magnetization data for the ~40 materials are accurate enough for shape fitting and TC correlation.
No new primary measurements are claimed in the abstract; conclusions inherit experimental uncertainties of the source curves.

pith-pipeline@v1.1.0-grok45 · 7560 in / 2454 out tokens · 32547 ms · 2026-07-13T12:28:47.673775+00:00 · methodology

0 comments

read the original abstract

The shape of the temperature dependence of spontaneous magnetization was analyzed for about forty ferromagnetic materials. The squareness of the shape was determined by fitting the magnetization curves with the superellipse equation (Lame curve). The agreement between the Lame curve fits and the experimental data was good for most materials. The squareness parameter (the power coefficient in the superellipse equation was found to range from 1.4 to 3.0. The largest squareness was observed for iron, whereas the smallest was found for antiferromagnetic materials and the Ni55Cu45 alloy. The squareness parameter was studied as a function of the Curie temperature, TC. For metallic alloys, a general tendency was observed: the squareness increased with increasing Curie temperature. The only exception was cobalt, which exhibited the same magnetization curve in reduced coordinates as nickel despite having a Curie temperature twice as high. The addition of either ferromagnetic or nonferromagnetic metals to iron or nickel led to a decrease in squareness. No influence of the thermal expansion coefficient on the magnetization curve was observed: zero-expansion Invar exhibited a standard shape following the Lame curve.

Review history (2 revisions) →

discussion (0)

Reference graph

Works this paper leans on

1 extracted references

[1]

Cazenave, Semilinear Schrödinger equations, vol

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2003

[1] [1]

Cazenave, Semilinear Schrödinger equations, vol

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2003