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arxiv: 2605.08920 · v1 · submitted 2026-05-09 · ❄️ cond-mat.mtrl-sci · physics.app-ph

Recognition: 2 theorem links

· Lean Theorem

Thermodynamic Approach for Deciphering Magneto-Structural Phase Transitions: Proof of Concept in Heusler Alloys

Eleonora Rusconi , Lorenzo Gallo , Victor A. L'vov , Anna Kosogor , Simone Fabbrici , Giovanna Trevisi , Francesco Cugini , Massimo Solzi
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Thomas Schrefl Franca Albertini
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Pith reviewed 2026-05-12 02:42 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.app-ph
keywords Heusler alloysmagneto-structural transitionsCurie temperaturethermodynamic analysismartensitic transformationmagnetic susceptibilityNi-Mn-Ga
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The pith

Thermodynamic model shows structural transitions shift Curie temperatures by 50 K or more between phases in Heusler alloys

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

The paper develops a thermodynamic analysis of magnetization and susceptibility data measured on Ni-Mn-Cu-Ga Heusler alloys whose copper content is varied in small steps. This variation produces three distinct patterns: martensitic transformation inside the ferromagnetic phase, a coupled magneto-structural transition from paramagnetic austenite to ferromagnetic martensite, and martensitic transformation inside the paramagnetic phase. By including the effect of the structural change on the spin-exchange parameter, the model extracts separate Curie temperatures for the austenite and martensite structures and finds a gap of at least 50 K between them. A reader would care because these overlapping transitions control large caloric and magnetic responses, yet their characteristic temperatures are difficult to assign from routine curves without such a separation.

Core claim

The theoretical analysis of experimental data revealed that this impact results in a large difference (≥ 50 K) between the Curie temperatures computed for the austenitic and martensitic states of each alloy.

What carries the argument

Thermodynamic model that incorporates the modification of the spin-exchange parameter by the martensitic structural transition when fitting temperature-dependent magnetization and susceptibility data to extract phase-specific Curie temperatures.

If this is right

  • The positions of extrema in dM/dT and χ(T) correlate with the actual Curie and martensitic temperatures in ways that depend on the specific type of transformational behavior.
  • The method extracts characteristic temperatures that cannot be measured directly from standard magnetization curves.
  • The framework applies to ferromagnetic Heusler systems and other multiferroic ferromagnetic materials with coupled transitions.

Where Pith is reading between the lines

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

  • If the extracted gap holds, lattice distortion must strongly tune the magnetic exchange, offering a route to engineer the overlap between structural and magnetic transitions.
  • The same fitting procedure could be applied to pressure-dependent or field-dependent data to map how the exchange parameter varies with lattice spacing.
  • Independent checks with phase-stabilized specimens or microscopic magnetic probes would test whether the 50 K difference survives when the phases are isolated over wide temperature windows.

Load-bearing premise

The structural transition affects the spin-exchange parameter in a manner that a thermodynamic model can capture to separate the austenite and martensite Curie temperatures from bulk M(T) and χ(T) data alone.

What would settle it

Direct measurement of magnetic ordering in stabilized pure austenite and pure martensite phases, for example by neutron diffraction or local probes on composition-tuned samples, showing the difference between those Curie temperatures is substantially less than 50 K.

Figures

Figures reproduced from arXiv: 2605.08920 by Anna Kosogor, Eleonora Rusconi, Franca Albertini, Francesco Cugini, Giovanna Trevisi, Lorenzo Gallo, Massimo Solzi, Simone Fabbrici, Thomas Schrefl, Victor A. L'vov.

Figure 1
Figure 1. Figure 1: Magnetization curves measured under a satu [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Magnetic susceptibility computed for the [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Experimental temperature dependences of m [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
read the original abstract

Ferromagnetic solids acquire nontrivial magnetic and caloric properties when the temperature of the structural phase transition approaches the Curie point. Deciphering magneto-structural transitions, i.e. determining their characteristic temperatures and elucidating the related properties, remains challenging. In the present paper, three types of transformational behaviour of Ni50Mn25-xCuxGa25 (x = 6.25, 6.5, 6.75, 7) and Ni50.5Mn18.5Cu6.5Ga24.5 alloys have been identified, arising from small variations in chemical composition: (i) structural martensitic transformation (MT) in the ferromagnetic phase; (ii) magneto-structural phase transition from paramagnetic austenite to ferromagnetic martensite; (iii) MT in paramagnetic phase. The temperature-dependent values of magnetization, M(T), and of magnetic susceptibility, $\chi(T)$, were measured for each alloy. A novel thermodynamic analysis was used to determine the Curie points and MT temperatures. The novelty lies in considering the interplay between structural and magnetic characteristics of the alloys through the impact of the structural transition on the spin-exchange parameter. The theoretical analysis of experimental data revealed that this impact results in a large difference ($\geq$ 50 K) between the Curie temperatures computed for the austenitic and martensitic states of each alloy. The characteristic temperatures, corresponding to the extrema of the dM(T)/dT and $\chi(T)$ functions, were calculated. The correlation of these temperatures with the Curie temperatures and the MT temperatures is not straightforward and depends strongly on the type of transformational behaviour (i) - (iii). The proposed approach provides a robust framework for extracting unmeasurable characteristic temperatures from standard magnetization data, applicable to ferromagnetic Heusler systems and other multiferroic ferromagnetic materials.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper reports measurements of M(T) and χ(T) on Ni50Mn25-xCuxGa25 (x = 6.25, 6.5, 6.75, 7) and Ni50.5Mn18.5Cu6.5Ga24.5 Heusler alloys and classifies three distinct magneto-structural transformational regimes arising from small composition changes. A thermodynamic model is introduced that incorporates the effect of the martensitic transition on the spin-exchange parameter; this model is used to extract separate Curie temperatures for the austenitic and martensitic states, yielding a reported difference of at least 50 K. Characteristic temperatures are also obtained from extrema of dM/dT and χ(T) and their correlation with the transition type is discussed.

Significance. If the separation of austenite and martensite Curie temperatures can be shown to be robust and independent of fitting assumptions, the approach would supply a practical route to obtain otherwise inaccessible characteristic temperatures from routine bulk magnetization data. This would be useful for the design of Heusler alloys exhibiting coupled transitions and large caloric effects. The classification of three behavioral types as a function of composition is also of direct materials interest.

major comments (2)
  1. [thermodynamic analysis section] Thermodynamic analysis (the section introducing the model that accounts for the structural transition’s impact on the spin-exchange parameter): the manuscript states that the structural change produces a ≥50 K shift in Tc but does not supply the explicit free-energy expressions, the functional form chosen for the J shift, or the fitting protocol used to deconvolve the superimposed M(T) curves. Without these details it is impossible to determine whether the reported difference is an independent result or is largely fixed by the assumed functional form.
  2. [results section] Results and discussion of the extracted Curie temperatures: no cross-validation against local probes (e.g., NMR, neutron diffraction, or composition-tuned single-phase specimens) or against independent measurements on the same alloys is presented. Given that the measured magnetization is a superposition near the coupled transition, the magnitude of the claimed ≥50 K difference remains under-constrained without additional constraints or external checks.
minor comments (2)
  1. [abstract and introduction] The abstract and introduction refer to “the extrema of the dM(T)/dT and χ(T) functions” without specifying whether these are local maxima, minima, or inflection points; a brief clarification of the precise definition used would improve reproducibility.
  2. [figures and discussion] Figure captions and text occasionally interchange “Curie temperature” and “characteristic temperature” without explicit mapping; consistent terminology would reduce ambiguity when the correlation between the two is discussed.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful and constructive review. The comments highlight important aspects of clarity and validation that we address point by point below. We will revise the manuscript to improve transparency while maintaining the focus on the thermodynamic approach applied to bulk data.

read point-by-point responses

  1. Referee: [thermodynamic analysis section] Thermodynamic analysis (the section introducing the model that accounts for the structural transition’s impact on the spin-exchange parameter): the manuscript states that the structural change produces a ≥50 K shift in Tc but does not supply the explicit free-energy expressions, the functional form chosen for the J shift, or the fitting protocol used to deconvolve the superimposed M(T) curves. Without these details it is impossible to determine whether the reported difference is an independent result or is largely fixed by the assumed functional form.

    Authors: We agree that the explicit details of the model were insufficiently elaborated. The thermodynamic framework is a Landau expansion coupling the structural order parameter to the magnetic exchange J, with J taking distinct values in the austenite and martensite phases. The shift in J is taken as a step change at the martensitic transition temperature, and the total magnetization is obtained by weighting the contributions from each phase according to the temperature-dependent phase fraction. Fitting is performed by least-squares minimization against the measured M(T) curves, with Tc^A and Tc^M as adjustable parameters. In the revised manuscript we will add the full free-energy expression, the precise functional form for the J shift, and a step-by-step description of the fitting protocol in a new appendix. We will also include a brief sensitivity test using an alternative (linear) coupling form to show that the ≥50 K difference remains required to reproduce the data. revision: yes

  2. Referee: [results section] Results and discussion of the extracted Curie temperatures: no cross-validation against local probes (e.g., NMR, neutron diffraction, or composition-tuned single-phase specimens) or against independent measurements on the same alloys is presented. Given that the measured magnetization is a superposition near the coupled transition, the magnitude of the claimed ≥50 K difference remains under-constrained without additional constraints or external checks.

    Authors: We concur that independent validation would strengthen the quantitative claim. The present study is restricted to standard bulk magnetization and susceptibility measurements; no local-probe or single-phase data were acquired. The model is constrained by the observed shapes of M(T) and χ(T) together with the independently measured structural transition temperatures. In the revision we will add an explicit paragraph discussing this limitation, noting that the large Tc difference is required to fit the distinct magnetic regimes on either side of the coupled transition and that the consistency across the four compositions provides internal support. We cannot, however, supply new experimental cross-validation within the scope of this work. revision: partial

standing simulated objections not resolved
  • Cross-validation of the extracted Curie temperatures against local probes (NMR, neutron diffraction) or independent measurements on single-phase specimens, as such data were not collected in the present study.

Circularity Check

1 steps flagged

Tc(austenite) vs Tc(martensite) difference obtained by fitting thermodynamic model with assumed J jump to the same M(T)/χ(T) curves

specific steps
  1. fitted input called prediction [Abstract]
    "The novelty lies in considering the interplay between structural and magnetic characteristics of the alloys through the impact of the structural transition on the spin-exchange parameter. The theoretical analysis of experimental data revealed that this impact results in a large difference (≥ 50 K) between the Curie temperatures computed for the austenitic and martensitic states of each alloy."

    The model incorporates the structural transition's effect on the spin-exchange parameter as an adjustable feature; the reported ≥50 K Tc difference is then computed from the same M(T) and χ(T) data to which the model is fitted. The difference is therefore forced by the chosen functional form and parameter adjustment rather than emerging as an independent result.

full rationale

The paper's central result (≥50 K difference) is obtained by fitting a thermodynamic model that encodes the structural transition's effect on the spin-exchange parameter directly to the measured magnetization and susceptibility curves. The extracted difference is therefore a direct output of the fit parameters rather than an independent prediction or external verification. No cross-check against local probes or single-phase samples is described, so the magnitude is not shown to be robust to alternative functional forms.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach rests on standard thermodynamic relations between magnetization and exchange interactions plus the assumption that the structural transition produces a discrete jump in the exchange parameter; no new entities are introduced.

free parameters (1)
  • spin-exchange parameter shift
    Magnitude of the change in exchange interaction across the structural transition is inferred from data to produce the reported >=50 K Curie difference.
axioms (1)
  • domain assumption Magnetization and susceptibility extrema correspond to characteristic transition temperatures in a manner that depends on the relative ordering of magnetic and structural transitions.
    Invoked when correlating dM/dT and χ(T) extrema with Curie and MT temperatures for the three behavioral types.

pith-pipeline@v0.9.0 · 5680 in / 1351 out tokens · 45859 ms · 2026-05-12T02:42:31.390887+00:00 · methodology

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