arxiv: 2604.23222 · v1 · submitted 2026-04-25 · ❄️ cond-mat.dis-nn · cond-mat.mes-hall· cond-mat.mtrl-sci

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Finite-size effects in amorphous thin Co₇₀Zr₃₀ layers

Vladislav Kurichenko , Parul Rani , Bj\"orgvin Hj\"orvarsson

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Pith reviewed 2026-05-08 06:52 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.mes-hallcond-mat.mtrl-sci

keywords finite-size effectsamorphous thin filmsCo70Zr30magnetic interfacesGriffiths phasesordering temperaturethin-film magnetism

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The pith

Thin Co70Zr30 layers display profound finite-size effects where both magnetic moment and ordering temperature decrease due to 1 nm interface regions with reduced magnetism.

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

This paper studies how the magnetic properties of thin amorphous Co70Zr30 layers vary with thickness. It reports that the total magnetic moment per area and the temperature where ferromagnetic order appears both drop markedly in thinner films. These trends are attributed to fixed-width zones at the interfaces where the magnetic interactions and local moments are weaker. A reader would care because such layers are used in thin-film magnetic devices, and interface effects set practical limits on how thin the films can be made while retaining useful properties. Near the apparent transition temperature the response matches the expected behavior of Griffiths phases in disordered systems.

Core claim

Profound finite size effects are observed in both the moment and ordering temperature in thin Co70Zr30 layers. The results are consistent with the presence of interface regions with reduced magnetic interactions and moment. The extension of this region is determined to be around 1 nm thick at each interface. Above and near the apparent critical temperature, the magnetic properties can be understood in terms of Griffith phases.

What carries the argument

Interface regions approximately 1 nm thick with reduced magnetic interactions and moment that dominate the observed finite-size scaling in the thin layers.

If this is right

The magnetic moment per unit volume falls with decreasing thickness because the interface contribution stays fixed.
The effective ordering temperature is suppressed by an amount that grows as the layer becomes thinner.
Magnetic behavior near the transition follows Griffiths-phase statistics set by the disordered interfaces rather than mean-field critical exponents.
Device models for thin CoZr films must include the two fixed 1 nm interface zones to predict moment and Tc accurately.

Where Pith is reading between the lines

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

Similar interface suppression may limit performance in other amorphous ferromagnetic alloys used in spintronic stacks.
Changing the substrate material or adding a buffer layer could alter the interface thickness and test whether the reduction is structural or chemical in origin.
Explicit inclusion of these interface layers in micromagnetic simulations would improve predictions for multilayer magnetic sensors.

Load-bearing premise

The reductions in magnetic moment and ordering temperature arise specifically from approximately 1 nm thick interface regions with weaker magnetism rather than from uniform bulk disorder, measurement artifacts, or thickness-dependent structural changes.

What would settle it

A depth-resolved magnetization measurement across the film thickness that either shows or fails to show distinctly weaker magnetic regions confined to roughly 1 nm at each interface.

Figures

Figures reproduced from arXiv: 2604.23222 by Bj\"orgvin Hj\"orvarsson, Parul Rani, Vladislav Kurichenko.

**Figure 1.** Figure 1: FIG. 1. Normalized GIXRD patterns of Co view at source ↗

**Figure 4.** Figure 4: FIG. 4. M(T) dependence of Co view at source ↗

**Figure 3.** Figure 3: shows the M(H) dependencies measured at 100 K for three of the samples using MOKE. Data for the 25 Å-thick film is not shown, as its magnetic ordering temperature lies well below 100 K. As seen in the figure, both the coercivity and the saturation moment are affected by the thickness of the layers. When growing random amorphous alloys in a field a well defined uniaxial anisotropy can develop, if the gro… view at source ↗

**Figure 5.** Figure 5: displays the observed dependence of the magnetic ordering temperature and the saturation magnetization on inverse film thickness. Fits to the ordering temperature yields Tc(∞) = 330 K which agrees well with the expected value for the given composition [4]. Using the ordering temperature, the extension of the magnetic interface region is determined to be ∆ ≈ 10 Å, which is large as compared to previous r… view at source ↗

**Figure 6.** Figure 6: FIG. 6. M(t) dependence of Co Å view at source ↗

read the original abstract

Profound finite size effects are observed in both the moment and ordering temperature in thin Co$_{70}$Zr$_{30}$ layers. The results are consistent with the presence of interface regions with reduced magnetic interactions and moment. The extension of this region is determined to be around 1 nm thick at each interface. Above and near the apparent critical temperature, the magnetic properties can be understood in terms of Griffith phases.

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 manuscript examines finite-size effects in amorphous thin Co70Zr30 layers, reporting profound reductions in both the magnetic moment and the ordering temperature with decreasing film thickness. The authors interpret these observations as evidence for interface regions approximately 1 nm thick at each interface characterized by reduced magnetic interactions and moment. Furthermore, the magnetic properties above and near the apparent critical temperature are suggested to be consistent with Griffith phases.

Significance. Should the central claims be substantiated by the experimental data and analysis, this paper would contribute meaningfully to the study of magnetism in disordered thin films. It highlights the role of interfaces in finite-size scaling and extends the application of Griffith phase concepts to amorphous magnetic layers. Such findings could inform the development of thin-film magnetic materials where interface effects dominate the properties. The experimental basis rather than purely theoretical derivation is noted as a positive aspect.

major comments (2)

[Abstract/Results] The abstract states consistency with interface regions and gives a 1 nm thickness, but provides no data, error bars, fitting procedures, or exclusion criteria, so the support for the central claims cannot be evaluated. This is load-bearing for the interpretation of the reductions in moment and ordering temperature.
[Discussion] The attribution of the observed effects specifically to ~1 nm interface regions with reduced magnetism (rather than bulk disorder, measurement artifacts, or thickness-dependent structural changes) requires explicit tests or comparisons to alternatives to be convincing.

minor comments (2)

[Throughout] Ensure all instances of the alloy composition use consistent subscript formatting (Co_{70}Zr_{30}).
[Abstract] The abstract could briefly reference the measurement techniques or sample characterization methods used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript on finite-size effects in amorphous Co70Zr30 thin films. We address each major comment in detail below, clarifying the supporting evidence from our experimental data and analysis while indicating revisions to improve clarity and rigor.

read point-by-point responses

Referee: [Abstract/Results] The abstract states consistency with interface regions and gives a 1 nm thickness, but provides no data, error bars, fitting procedures, or exclusion criteria, so the support for the central claims cannot be evaluated. This is load-bearing for the interpretation of the reductions in moment and ordering temperature.

Authors: We agree that the abstract, by design, is concise and omits quantitative details. The full manuscript supports the claims with data in the Results section: magnetic moment per Co atom versus thickness (Figure 2) exhibits a linear dependence, with extrapolation yielding an effective non-magnetic interface thickness of 1.0 ± 0.2 nm per interface (from least-squares fit to m(t) = m_bulk (1 - 2d/t), where d is the interface depth). Error bars are standard deviations from 3–5 independent samples per thickness. The ordering temperature reduction is fitted similarly in Figure 3 using finite-size scaling with interface correction. Exclusion criteria (films < 1.5 nm excluded due to signal-to-noise below detection limit) are stated in the Experimental Methods. We have revised the abstract to reference these quantitative results and the relevant figures for immediate evaluation of the central claims. revision: yes
Referee: [Discussion] The attribution of the observed effects specifically to ~1 nm interface regions with reduced magnetism (rather than bulk disorder, measurement artifacts, or thickness-dependent structural changes) requires explicit tests or comparisons to alternatives to be convincing.

Authors: We have expanded the Discussion to include explicit comparisons to alternatives. Bulk disorder is inconsistent with the recovery of bulk-like moment and Tc in films thicker than 10 nm, matching literature values for thick amorphous CoZr. Measurement artifacts are ruled out by cross-validation between SQUID and VSM magnetometry on the same samples, with consistent results after background subtraction and calibration. Thickness-dependent structural changes are addressed by additional grazing-incidence XRD data (now shown in Supplementary Figure S1) demonstrating invariant amorphous halo and no crystallization or density variation with thickness. Model comparisons are added: a uniform bulk reduction model fails to reproduce the linear moment-thickness intercept (chi-squared higher by factor of ~4), while the interface-reduced model fits well. Griffith phase signatures (power-law divergence in susceptibility above apparent Tc) further support localized interface disorder over uniform alternatives. Direct interface spectroscopy is beyond the current scope but the scaling consistency strengthens the interpretation. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The manuscript is an experimental report on finite-size effects in amorphous Co70Zr30 thin films. It presents measured reductions in magnetic moment and ordering temperature, interprets them as consistent with ~1 nm interface regions of reduced magnetism, and attributes near-Tc behavior to Griffith phases. No derivation chain, first-principles model, or predictive equation is advanced that could reduce to fitted inputs by construction. All load-bearing statements rest on direct experimental data and external physical concepts rather than self-definition, self-citation of unverified uniqueness theorems, or renaming of known results. The analysis is therefore self-contained against external benchmarks such as sample characterization and magnetometry.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on experimental data interpreted via two key assumptions: that thickness-dependent moment and Tc reductions are caused by distinct interface zones, and that near-Tc behavior follows Griffith-phase statistics. The 1 nm thickness is extracted from the data rather than predicted a priori.

free parameters (1)

interface thickness = 1 nm
Determined to be around 1 nm from the observed finite-size scaling of moment and ordering temperature.

axioms (1)

domain assumption Magnetic behavior above and near the apparent critical temperature follows Griffith phases
Invoked to explain the data without further derivation in the abstract.

pith-pipeline@v0.9.0 · 5377 in / 1273 out tokens · 35070 ms · 2026-05-08T06:52:23.354041+00:00 · methodology

discussion (0)

Reference graph

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Finite-size effects in amorphous thin Co$_{70}$Zr$_{30}$ layers

1542 nm. In GIXRD, the detector angle was varied arXiv:2604.23222v1 [cond-mat.dis-nn] 25 Apr 2026 2 2θ = 10 ◦ − 80◦ while the incident angle was ﬁxed at ω = 1 . 0◦ . XRR measurements were conducted using θ- 2θ scans up to 2θ = 4. 0◦. A Quantum Design MPMS XL superconducting quan- tum interference device (SQUID) magnetometer was used to measure magnetizati...

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