Magnetostriction and Temperature Dependent Gilbert Damping in Boron Doped Fe$_{80}$Ga$_{20}$ Thin Films

Axel Hoffmann; Haoyang Ni; Jian-Min Zuo; Jinho Lim; Zhixin Zhang

REVIEW 4 major objections 5 minor 36 references

Magnetostriction and Temperature Dependent Gilbert Damping in Boron Doped Fe$_{80}$Ga$_{20}$ Thin Films

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Pith's one-line read Boron at the 8–10% level makes Fe$_{80}$Ga$_{20}$ films amorphous, and this structural transition simultaneously raises saturation magnetostriction to 48.8 ppm while lowering Gilbert damping to about $6\times10^{-3}$; the authors tie the…

desk verdict A solid FeGaB thin-film optimization study whose boron-dependent magnetostriction and damping trends are credible, but the magnetoelastic explanation of the 40 K damping peak is a plausible correlation, not yet a proven mechanism. read the letter →

arxiv 2505.11472 v1 pith:USK537ZS submitted 2025-05-16 cond-mat.mtrl-sci

Zhixin Zhang , Jinho Lim , Haoyang Ni , Jian-Min Zuo , Axel Hoffmann This is my paper · ORCID

classification cond-mat.mtrl-sci PACS 75.80.+q76.50.+g75.70.-i

keywords magnetostrictionGilbertdampingFeGaBthinfilmsborondopingamorphoustransitionferromagneticresonancemagnetoelasticcouplinglow-temperature

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 claims that alloying boron into Fe$_{80}$Ga$_{20}$ thin films drives a crystalline-to-amorphous transition near 8% boron, and that this structural switch is what allows the material to combine high magnetostriction with low magnetic damping. At 10% boron the films show a saturation magnetostriction of $48.8 \pm 0.9$ ppm and a Gilbert damping of about $6\times10^{-3}$, a combination that matters for surface-acoustic-wave and magnetoelectric devices. The paper also reports that the low-temperature damping peak near 40 K, quantified by $\Delta\alpha/\alpha_{RT}$, is largest at 8% boron (55.7%) and tracks the magnetostriction trend, which it reads as evidence for a magnetoelastic contribution to damping. If the interpretation is right, FeGaB near 8–10% boron is a practical platform for devices needing both strong coupling and low loss.

What carries the argument

The load-bearing object is the alloy series $(\mathrm{Fe}_{80}\mathrm{Ga}_{20})_{1-x}B_x$ with boron content spanning the crystalline-to-amorphous boundary near 8%, and the new diagnostic parameter is $\Delta\alpha/\alpha_{RT}=(\alpha_{\mathrm{Max}}-\alpha_{RT})/\alpha_{RT}$, which isolates the relative height of the 40 K damping peak. The analysis chain combines cantilever-deflection magnetostriction measurements, using the standard conversion factor $E_f/(1+\nu_f)=50$ GPa, with ferromagnetic-resonance linewidth fits $\Delta H = (4\pi/\gamma)\alpha f + \Delta H_0$ to extract the Gilbert damping $\alpha$ and the inhomogeneous broadening $\Delta H_0$. A phonon-relaxation picture of magnetoelastic damping connects the peak height to magnetostriction, allowing the authors to compare a temperature-dependent loss feature across compositions.

What would settle it

Grow a FeGaB film with 8–10% boron but suppress or strongly reduce its magnetostriction, for example by doping with a non-magnetoelastic element or by clamping it to a stiff substrate, while keeping the amorphous structure; if the relative 40 K damping peak stays near 55%, the magnetoelastic attribution is wrong. Alternatively, measure $\Delta\alpha/\alpha_{RT}$ under applied tensile or compressive stress, since a magnetoelastic contribution should shift with the stress-dependent magnetostriction.

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Extended reading notes

Core claim

The paper establishes, for magnetron-sputtered $(\mathrm{Fe}_{80}\mathrm{Ga}_{20})_{1-x}B_x$ films with $x$ from 2 to 16%, a composition-driven structural transition: boron content near 8% moves the film from polycrystalline to amorphous, coercivity drops from about 76 Oe to 3 Oe, and the amorphous regime simultaneously improves magnetostriction and suppresses Gilbert damping. The optimum is near 10% boron, with saturation magnetostriction of 48.8 ppm and damping of about $6\times10^{-3}$. In temperature-dependent ferromagnetic resonance, every composition shows a damping peak near 40 K, and the authors define the relative increase $\Delta\alpha/\alpha_{RT}$ to quantify it; this quantity reaches 55.7% at 8% boron and follows the same boron-concentration trend as the room-temperature magnetostriction, while non-magnetostrictive permalloy shows no comparable peak. On this basis the authors associate the 40 K damping peak with magnetoelastic contributions to the damping, while noting that further experimental or theoretical work is needed to confirm the mechanism.

Load-bearing premise

The load-bearing premise is that the extra damping at 40 K is caused by magnetoelastic coupling, inferred from the correlation between $\Delta\alpha/\alpha_{RT}$ and magnetostriction and from the absence of a comparable peak in permalloy; if the peak instead comes from interface strain, impurity relaxation, or another temperature-dependent loss channel, the central attribution collapses.

Editorial extensions

If this is right

FeGaB films with about 8–10% boron combine magnetostriction near 49 ppm with Gilbert damping near $6\times10^{-3}$, a combination useful for surface-acoustic-wave devices that need strong magnetoelastic coupling without excessive loss.
Coercivity drops from about 76 Oe to 3 Oe across the structural transition, so the amorphous films are magnetically softer while also being more magnetostrictive.
Because the damping at 5 K is below the room-temperature value for every boron concentration, cryogenic operation of FeGaB devices should not be penalized by extra damping.
The $\Delta\alpha/\alpha_{RT}$ metric gives a composition-sensitive measure of the 40 K damping feature and can be applied to other magnetostrictive alloy series.
The boron trend suggests that adding glass-forming elements is a general route to simultaneously improving magnetoelastic coupling and lowering damping in FeGa films.

Reading between the lines

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

If the 40 K peak is genuinely magnetoelastic, then its height under fixed composition should change when the film is placed on substrates with different thermal expansion or when an external stress is applied; such an experiment would test the causal link directly.
The room-temperature magnetostriction is extracted with a fixed elastic factor $E_f/(1+\nu_f)=50$ GPa, so the quantitative comparison between $\lambda$ and $\Delta\alpha/\alpha_{RT}$ assumes this factor stays representative at cryogenic temperatures; measuring the elastic moduli at low temperature would firm up the correlation.
The same glass-forming-dopant strategy could be tested in other high-magnetostriction systems, for example doping FeCo or FeGa with carbon or silicon, to see whether the simultaneous improvement of magnetostriction and damping is a general amorphous-phase effect.
A natural extension is to measure the 40 K damping peak as a function of film thickness; permalloy's peak is thickness-dependent, so a thickness scan on FeGaB would separate interface contributions from the bulk magnetoelastic one.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague — this paper deserves a serious referee. The genuinely new piece is the systematic boron-concentration sweep on Fe80Ga20 with FMR down to 2 K, plus the Δα/α_RT parameter, and the data support the main materials claim: around 8–10% B you get an amorphous film with 48.8 ppm magnetostriction, damping near 6e-3, and low coercivity. XRD, TEM, SQUID, and cantilever measurements are consistent, and the magnetostriction setup is benchmarked against known materials, which is more than many papers in this area do. The observation that damping at 5 K falls below the room-temperature value is a useful practical point for cryogenic magnon-phonon devices. The FMR analysis uses a standard Lorentzian fit and linear frequency dependence; the g-factor is fitted but its variation is shown to be negligible, so I do not see a circularity problem. Where I would want changes is the causal story. The paper attributes the boron-dependent height of the 40 K damping peak to magnetoelastic coupling because Δα/α_RT tracks room-temperature magnetostriction and because a non-magnetostrictive permalloy control shows no peak. The permalloy control is not matched in thickness or microstructure, and Ref. [36] reports a 40 K damping peak in permalloy films thinner than 10 nm, so an absent peak in a thicker control is a weak null. More importantly, the inhomogeneous linewidth ΔH0 also peaks at 8% B — exactly where Δα/α_RT is largest. That means the boron dependence is not a unique fingerprint of magnetoelastic damping; a defect or interface-strain channel tied to the same structural disorder would produce the same correlation. The authors are appropriately cautious in the discussion and explicitly call for further work, but the abstract and conclusion lean on the association more than the data support. Also, there are no error bars on the temperature-dependent damping or Δα/α_RT, so it is hard to judge how strongly the correlation actually holds. The assumption that room-temperature magnetostriction values stay representative at 40 K is addressed by a bulk FeGa reference showing weak temperature dependence, so I would call that a minor concern rather than a flaw. None of this undermines the material-optimization result. The 8–10% B window is well supported and practically relevant for SAW nonreciprocity and cryogenic devices. The citation pattern looks fair; the prior Lou/N. X. Sun work and Peria et al. on magnetoelastic damping are both cited. I would send this to peer review with a request for error bars, a better-matched control, and either a softened mechanistic claim or an additional experiment that separates inhomogeneous broadening from magnetoelastic damping.

Referee Report

4 major / 5 minor

Summary. The manuscript reports a systematic study of (Fe80Ga20)1−xBx thin films with boron contents x = 2–16%, combining structural characterization (XRD, HRTEM, SAED), static magnetic measurements (SQUID), cantilever magnetostriction, and temperature-dependent ferromagnetic resonance (FMR) from 5 to 300 K. The main experimental findings are a crystalline-to-amorphous structural transition near 8% B, a large reduction of coercivity from about 76 Oe to 3 Oe, a sixfold increase of saturation magnetostriction to 48.8 ± 0.9 ppm at 10% B, and a reduction of room-temperature Gilbert damping from about 1.6×10−2 to 5.7×10−3. The paper further defines a relative damping increase Δα/αRT at the 40 K peak, reports a maximum of 55.7% at 8% B, and argues that the boron dependence of this peak follows the magnetostriction trend, suggesting a magnetoelastic contribution to the damping. The authors acknowledge that the underlying mechanism requires further investigation.

Significance. If the reported trends are correct, the paper identifies a practical composition window — FeGaB with roughly 8–10% B — that simultaneously gives large magnetostriction and low Gilbert damping, which is directly relevant for SAW-driven magnon-phonon devices and cryogenic magnetoelastic applications. The study is valuable as a composition-series experiment with complementary structural and magnetic probes: XRD and TEM/SAED support the structural transition, the cantilever setup is calibrated against reference materials, and the FMR measurements cover a wide frequency and temperature range. The authors also include a permalloy control and explicitly flag open mechanistic questions. However, the central mechanistic interpretation — that the boron-dependent 40 K damping peak is caused by magnetoelastic coupling — rests on a correlation whose uniqueness is not fully established, and the key quantitative parameter Δα/αRT is presented without uncertainty estimates.

major comments (4)

[Section IV (Discussion) and Fig. 7] The attribution of the boron-dependent 40 K damping peak to magnetoelastic coupling is not uniquely supported by the data. In Fig. 7(d), the inhomogeneous linewidth broadening ΔH0 also reaches a maximum at 8% B, exactly where Δα/αRT is largest in Fig. 7(b). Because both λs and ΔH0 vary across the same mixed-phase structural transition, the correlation with λs alone does not exclude alternative mechanisms whose rates scale with structural inhomogeneity, such as two-magnon scattering, defect-mediated relaxation, or interface-strain effects. The observation that the ΔH0 peak occurs near 20 K while the α peak occurs near 40 K separates the temperature positions of the two features, but it does not identify the cause of the boron-dependent amplitude. In addition, the permalloy control is not matched in thickness or microstructure, and Ref. [36] reports a 40 K damping peak in permalloy films thinner than 10 nm, so the control is not a clean null experiment. The identification would be materially strengthened by measuring magnetostriction at cryogenic temperatures, by comparing samples with matched ΔH0 but different λs, or by quantifying two-magnon scattering through angle-dependent or oblique-field FMR.
[Section III.D and Fig. 7(a,b)] The key quantitative parameter Δα/αRT is presented without error bars or uncertainty propagation. The values depend on a single peak maximum at roughly 40 K and on the average of three room-temperature points, yet the manuscript does not report linewidth-fit uncertainties, field or frequency calibration uncertainties, or sample-to-sample reproducibility. Without these, the headline value of 55.7% at 8% B and the apparent boron-concentration trend in Fig. 7(b) are not quantitatively established, and the comparison between different doping levels could be consistent with scatter. Please provide an uncertainty estimate for α(T) and for Δα/αRT, or state explicitly if the plotted values are single-sample measurements without repeat statistics.
[Eq. (3) and Fig. S5] The extraction of Gilbert damping from the frequency-dependent linewidth relies on the gyromagnetic ratio obtained from a fitted electron g-factor of 2.11. The statement that the g-factor has negligible variation with boron concentration or temperature is not quantified in the main text. Since α is inversely proportional to γ, any temperature or composition dependence of g directly shifts α(T) and hence Δα/αRT. Please report the g-factor values and their uncertainties as functions of temperature and boron content, or provide an explicit error budget showing that g-factor variations do not affect the conclusions.
[Eq. (1) and Section IV] The magnetoelastic interpretation uses magnetostriction values measured at room temperature to explain a damping peak at 40 K. The only supporting evidence for weak temperature dependence is Ref. [34], which concerns bulk undoped FeGa alloys. For 100-nm boron-doped films, especially in the amorphous regime, the magnetostriction at cryogenic temperatures could differ substantially, for example because of substrate-induced strain or structural relaxation. A direct low-temperature magnetostriction measurement, or at least a stated quantitative estimate of the uncertainty introduced by using room-temperature values, is needed before Δλs ≈ 0 at 40 K can be assumed in the causal argument.

minor comments (5)

[Section II vs. Fig. 5 caption] The experimental section states that the magnetostriction films are 100 nm thick, while the caption of Fig. 5 says '80-nm (Fe80Ga20)1−xBx films'. Please reconcile this discrepancy.
[Section III.A] The sentence 'the spectra is shown' should read 'the spectra are shown'.
[Section V] In the conclusion, 'We conducted temperature dependent Gilbert damping study' should be lowercase 'we' and should read 'a temperature-dependent Gilbert damping study'.
[Fig. 7(d)] The axis label 'DH0' should be typeset as 'ΔH0' for consistency with Eq. (3).
[Supplementary material] The manuscript cites Figs. S1–S6, but these supplementary figures are not included with the submitted text; please ensure they are provided with sufficient captions and referenced accurately.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: magnetostriction, damping, and the relative damping peak are all independently measured observables.

full rationale

The paper's central claims rest on direct measurements rather than on fitted inputs or self-citation chains. Magnetostriction is obtained from cantilever deflection using Eq. 1 with stated elastic constants and is benchmarked against literature values; Gilbert damping is extracted from the slope of FMR linewidth versus frequency via Eq. 3, with the g-factor determined from the resonance condition and reported to be essentially independent of boron content and temperature. The relative damping increase Δα/αRT is defined directly from the measured temperature-dependent damping values as (α_max − α_RT)/α_RT, so it is not a fitted parameter renamed as a prediction. The correlation between Δα/αRT and the room-temperature magnetostriction is an empirical observation, and the attribution of the 40 K peak to magnetoelastic coupling is an interpretive step that the authors explicitly qualify as requiring further investigation. Although the paper cites prior work by overlapping authors, that citation is not load-bearing for the central measurements. No equation is shown to reduce to its own inputs, and no uniqueness theorem or ansatz is imported to force the conclusion. The potential alternative mechanisms noted for the 40 K peak concern causal interpretation, not circular derivation, and therefore do not raise the circularity score.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The central results are measured quantities, not derived from a model; the ledger captures the main external inputs and interpretation assumptions.

free parameters (1)

Electron g-factor = 2.11
Extracted from the frequency dependence of the FMR resonance field and used in Eq. 3 to convert linewidth-frequency slope into Gilbert damping. Assumed independent of temperature and boron content based on Fig. S5.

assumptions (6)

standard math Cantilever deflection model (Eq. 1 from Ref. [28]) accurately converts measured free-end displacement into film magnetostriction.
The extraction of all magnetostriction values depends on this mechanical model, which assumes elastic clamping and known film and substrate thicknesses.
domain assumption FeGaB film elastic constant Ef/(1+vf)=50 GPa from Ref. [30] is valid for all boron concentrations and temperatures used.
The absolute magnetostriction values in Fig. 5 scale with this assumed constant; the paper notes this is a convention rather than a measured value for each composition.
domain assumption FMR linewidth is dominated by Gilbert damping plus a frequency-independent inhomogeneous broadening (Eq. 3); two-magnon scattering is not separately modeled.
The linear Delta-H vs frequency fit assigns all frequency-dependent broadening to alpha and all offset to Delta-H0. Any substantial two-magnon contribution would be absorbed and could bias alpha.
domain assumption The room-temperature magnetostriction values are representative of the low-temperature magnetoelastic coupling, which is assumed to vary by at most about 15% down to 4 K based on bulk FeGa data (Ref. [34]).
Used to justify correlating delta_alpha/alpha_RT measured at low temperature with room-temperature saturation magnetostriction.
ad hoc to paper The 40 K damping peak in FeGaB is attributable to magnetoelastic coupling.
This is the interpretive assumption used to connect delta_alpha/alpha_RT with magnetostriction; the paper supports it with a correlation and a permalloy control, but does not derive it quantitatively from magnetoelastic parameters.
domain assumption Boron is uniformly distributed and the nominal composition from sputter power calibration reflects the actual film composition.
The paper uses linear growth-rate calibrations to set target powers; RBS is used only for Fe to Ga ratio, not for boron content, so the reported x values rely on sputter calibration accuracy.

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Pith. "Pith review of Magnetostriction and Temperature Dependent Gilbert Damping in Boron Doped Fe$_{80}$Ga$_{20}$ Thin Films." pith.science (2026). https://pith.science/paper/USK537ZS

@misc{pith2026250511472,
  author       = {Pith},
  title        = {Pith review of: Magnetostriction and Temperature Dependent Gilbert Damping in Boron Doped Fe$_80$Ga$_20$ Thin Films},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/USK537ZS}},
  note         = {Machine review of arXiv:2505.11472}
}

abstract

Magnetic thin films with strong magnetoelastic coupling and low Gilbert damping are key materials for many magnetoelectric devices. Here, we investigated the effects of boron doping concentration on magnetostriction and temperature dependent Gilbert damping in magnetron sputtered (Fe$_{80}$Ga$_{20}$)$_{1-x}$B$_{x}$ films. A crystalline to amorphous structural transition was observed for a boron content near 8% and coincided with a decrease in coercivity from 76 Oe to 3 Oe. A 10% doping concentration is optimal for achieving both large magnetostriction of 48.8 ppm and low Gilbert damping of $6 \times 10^{-3}$. The temperature dependence of the damping shows an increase at low temperatures with a peak around 40 K and we associate the relative increase $\Delta\alpha/\alpha_{RT}$ with magnetoelastic contributions to the damping, which has a maximum of 55.7% at 8% boron. An increase in the inhomogeneous linewidth broadening was observed in the structural transition regime at about 8% boron concentration. This study suggests that incorporation of glass forming elements, in this case boron, into Fe$_{80}$Ga$_{20}$ is a practical pathway for simultaneously achieving enhanced magnetoelastic coupling and reduced Gilbert damping.

Figures

Figures reproduced from arXiv: 2505.11472 by the authors.

**Figure 2.** FIG. 2. XRD spectra for undoped Fe [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** shows HRTEM images of (Fe80Ga20)100B0 and (Fe80Ga20)84B16. In the case of non-doped Fe80Ga20, clear lattice fringes can be seen with random orientation showing an overall nanocrystalline nature of the thin film. In contrast, no clear lattice fringes can be observed in Fe80Ga20 with 16% boron doping, indicating its overall amorphous structure. B. Static Magnetic Properties Static magnetic properties were investigated… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. (a) Magnetic hysteresis loops of undoped Fe [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: FIG. 5. (a) Magnetostriction constants as a function of applied in-plane field strength of 80- [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 6.** Figure 6: FIG. 6. (a) FMR spectrum at different excitation frequencies for 20-nm (Fe [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

**Figure 7.** Figure 7: FIG. 7. (a) Gilbert damping as a function of temperature for 20-nm (Fe [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

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