Scaled demagnetization models: susceptibility, resonant and relaxation frequency prediction compared to magnetic composite measurements

Rick L. Moore

REVIEW 4 major objections 6 minor 46 references

Scaled demagnetization models: susceptibility, resonant and relaxation frequency prediction compared to magnetic composite measurements

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A volume-scaled demagnetization correction fitted to a single ferrite composite transfers across chemistries and improves prediction of susceptibility, resonant frequency, and relaxation frequency over classical effective-medium models.

desk verdict New model forms for resonant and relaxation frequency prediction, but validation is mostly visual and the scaling function's transferability is untested beyond the one material it was fitted to. read the letter →

arxiv 1908.00603 v1 pith:CQSF3A56 submitted 2019-08-01 cond-mat.mtrl-sci

Rick L. Moore This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords scaledeffectivemediumtheorydemagnetizationscalingmagneticcompositessusceptibilitypredictionresonantfrequencyrelaxationSchlomannmodel

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 argues that the failure of classical effective-medium models for magnetic composites is largely a volume-fraction-dependent demagnetization effect. It extends a previously developed scaled effective medium theory (ScEMT) in which the usual demagnetization factor is replaced by a function of particle volume fraction, fitted once to one NiZnCu ferrite composite, and applies it to susceptibility, resonant frequency, and relaxation frequency. Treated this way, ScEMT matches measured susceptibility and resonance better than Maxwell-Garnett and coherent-model approximations for particles with large susceptibility, while ScEMT-modified Schlomann models give the best relaxation-frequency agreement. The payoff would be a predictive design tool for magnetic composites that reduces the usual formulation-measurement-formulation iteration.

What carries the argument

The central object is the volume-scaled demagnetization coefficient $A_p(P_p)$, which replaces the fixed demagnetization constant $d-1$ in the Bruggeman effective-medium equation. It is defined by $A_c = A_0\{1-A_1(1-P_p)^\gamma\}$ and $A_p = (1-A_c)/A_c$, with fitted values $A_0=0.975$, $A_1=0.923$, and $\gamma=1.210$; this function encodes percolation-like clustering and chaining of high-susceptibility particles. The same demagnetization scaling is reused in the Snoek-law-based resonant frequency formula, Equation 19, and in the modified Schlomann relaxation frequency formula, Equation 26, and that reuse is what carries the argument from static susceptibility to frequency-dependent composite properties.

What would settle it

Prepare composites from a high-susceptibility ferrite not used in the fit, for example with susceptibility near 4000, at volume fractions of 2, 5, 15, 30, 45, and 65 percent, and compare measured susceptibility, resonant frequency, and relaxation frequency against ScEMT and Equation 26 predictions using the fixed coefficients. If the coefficients must be refit for each chemistry, or if the predicted susceptibility increase near 10% volume fraction appears in carefully measured data, the transferability claim fails.

Watch

Extended reading notes

Core claim

The central claim is that a single nonlinear demagnetization scaling, $A_p(P_p) = (1-A_c)/A_c$ with $A_c = A_0\{1-A_1(1-P_p)^\gamma\}$, fitted once to a NiZnCu ferrite composite with $A_0=0.975$, $A_1=0.923$, and $\gamma=1.210$, transfers to a broad family of magnetic-particle composites. The paper applies this ScEMT scaling to predict DC susceptibility, resonant frequency via Snoek's law, and relaxation frequency by inserting the same scaling into Schlomann's 1969 model. Across a wide range of particulate chemistries, volume fractions, and susceptibilities, ScEMT predictions agree better with measurement than CMA and MGT for high-susceptibility particles, and ScEMT-modified Schlomann models show the best relaxation-frequency agreement. The paper also derives a low-volume-fraction correction for BEMT and ScEMT by comparing their small-fraction expansions to MGT, while noting that the correction has a sign-change artifact near 10% and that ScEMT remains best used at mid-to-high fractions.

Load-bearing premise

The paper's improvements rest on the assumption that a demagnetization scaling fitted to a single NiZnCu ferrite composite transfers unchanged to every other particulate chemistry, particle size, and volume fraction, and to the frequency-dependent models for resonance and relaxation.

Editorial extensions

If this is right

If the universal ScEMT scaling holds, composite susceptibility and resonant frequency can be predicted from bulk particulate susceptibility and resonance alone, without iterative formulation-measurement cycles.
ScEMT and its Schlomann modification become the preferred models for high-susceptibility particles, roughly above susceptibility 100, while CMA and MGT remain most accurate for modest susceptibility below about 100.
The low-volume-fraction corrections extend the usable range of BEMT slightly, though ScEMT's validity there is bounded by a sign-change artifact near 10% volume fraction.
Designers of EMI suppressors and antenna substrates could screen particulate chemistries and volume fractions computationally before committing to lab formulations.
Measured data sets show that formulation-measurement repetition can differ by 10-20%, so model-measurement agreement within that spread is the realistic target for any effective-medium prediction.

Reading between the lines

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

Inference: the same volume-scaled demagnetization idea could be tested on electric permittivity composites, where percolation and clustering analogies exist, but the paper reports no such test.
Inference: the sign-change artifact near 10% volume fraction could be used as a calibration handle, since measured deviations in that range would constrain $A_1$ and $\gamma$ independently of the high-fraction fit.
Inference: the paper's own proposed experiment with ferrites of susceptibility roughly 20, 800, and 4000, particle sizes 1, 10, and 40 microns, and volume fractions from 2% to 65% would directly test whether the fitted universal coefficients hold or need chemistry-dependent values.
Inference: the fitted exponent $\gamma = 1.210$ could be compared with cluster statistics from micromagnetic or Brownian-dynamics simulations to give the scaling function a mechanistic derivation rather than a purely empirical 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

What you should know: this paper extends the author's earlier ScEMT to resonant and relaxation frequencies, and it compiles a broad set of magnetic composite data. The new pieces are the Snoek-law resonant frequency relation (Eq. 19), the low-fraction corrections (Eqs. 10-12), and the ScEMT-scaled Schlomann relaxation model (Eq. 26). Those are genuinely new combinations, not just repackaged old results. The paper is also honest: it says where MGT and CMA are better (modest susceptibility) and where ScEMT wins (high susceptibility), and it explicitly tells the reader not to treat graph-derived data as absolutes. That honesty earns credit.

The soft spot is exactly where the stress-test note lands. The Ap(Pp) scaling function was fitted to one NiZnCu ferrite in the author's earlier work, and that same material appears in the evaluation figures for resonant and relaxation frequency. So a meaningful part of the agreement is in-sample, not predictive. For the relaxation model, A0 and A1 are set to 1.0, leaving only gamma=1.210 carried over from that single fit, and no evidence shows that exponent is universal across particle chemistry, size, or frequency. There are no error bars, no RMS errors, no confidence intervals. The paper claims visual improvement over MGT/CMA, and the figures do often look better for high-susceptibility particles, but the lack of quantitative metrics makes it hard to judge how much better, especially when duplicate measurements of the same nominal composite differ by 10-20%. The low-fraction correction also turns out to have a sign-change artifact and the paper concedes it doesn't fully fix the problem, so that section is more of a side note than a contribution.

That said, the central argument is not broken. The model extensions are plausible, the algebra is straightforward, and the data compilation is useful for anyone working on magnetic composites. The citation pattern is mostly self-cites plus standard EMT and ferrite literature, which fits an author extending his own line of work. My main concern is that the claimed universality of the scaling function is an assumption, not a demonstrated result.

This paper deserves a serious referee. I would want the referee to ask for a quantitative comparison table and an out-of-sample test, or at least an explicit discussion of which predictions are in-sample. The proposed controlled experiment in the conclusions is the right kind of follow-up. With that revision, it could be a useful reference for the composites community.

Bring it to reading group if you want a concrete example of how effective medium models are evaluated against messy literature data; otherwise it's not urgent.

Referee Report

4 major / 6 minor

Summary. The paper extends the author's earlier Scaled Effective Medium Theory (ScEMT) to predict the magnetic susceptibility, resonant frequency, and relaxation frequency of magnetic-particle composites over a wide range of particulate susceptibilities (about 5 to 4000) and volume fractions (1-100%). After reviewing the ScEMT equations, the paper derives a low-volume-fraction correction for BEMT and ScEMT, then presents a resonant-frequency model (Eq. 19) based on a Snoek-like scaling assumption (Eq. 18) and a relaxation-frequency model (Eq. 26) that uses ScEMT-type volumetric scales and Schlomann's linewidth broadening. The models are compared to literature data collated from many sources; the central claim is that ScEMT-based models improve agreement with measurement over MGT and CMA, particularly for large-susceptibility particulates, while MGT and CMA remain accurate for modest susceptibilities.

Significance. If the claims hold, the paper would provide a simple and useful engineering tool for predicting the high-frequency magnetic response of composites, which is relevant to EMI suppression and antenna substrate design. The paper's strengths are its transparent algebraic derivations, the breadth of the compiled experimental dataset (12 composites, multiple chemistries), and its explicit and honest acknowledgment of data limitations (graph-reading error, duplicate-data scatter, and the need for controlled validation). However, the central evidence is qualitative: no error bars, goodness-of-fit metrics, or uncertainty propagation are reported, and part of the ScEMT evaluation uses the same material whose susceptibility was used to fit the model parameters. The significance paragraph of the abstract overstates the results relative to the evidence presented.

major comments (4)

[Validation sections (after Table 1, Figures 2-13)] The central claim that ScEMT and ScEMT-modified Schlomann improve over MGT and CMA is supported only by visual comparison. The manuscript itself states, after Table 1, that 'the reader should assume that there is some level of author reading error' and 'A full validation of models must await a series of carefully controlled experiments.' No quantitative metric (e.g., relative error, R^2, RMSE, or confidence intervals) is provided for any model-measurement comparison, and the text notes that duplicate formulations differ by 10-20% (Figure 2b and the Fe data in Figure 4). With such scatter, the claimed improvement may be within the digitization and measurement uncertainty. The paper should provide a quantitative error analysis that separates the fitted material from truly out-of-sample predictions and that propagates the stated reading error into the model comparison.
[ScEMT Review, Eqs. (5)-(6), and Figures 5b and 11] The ScEMT parameters A0=0.975, A1=0.923, and gamma=1.210 were fitted in prior work to the susceptibility of NiZnCu ferrite composites (Refs. [3],[4]). The same material appears in the resonant-frequency evaluation (Figure 5b) and in the relaxation-frequency evaluation (Figure 11, the NiZnCu entries with susceptibilities 839 and 863). These agreement plots are therefore partly in-sample and do not independently validate the model. For the other composites the parameters are assumed transferable, but no quantitative out-of-sample statistics are given. A leave-one-material-out analysis, or at least separate error metrics for the fitting material versus all other materials, is needed to support the universality claim.
[Relaxation Frequency Model, Eq. (26)] The 'ScEMT modifications to Schlomann' used in Eq. (26) do not actually employ the ScEMT parameters fitted to susceptibility; the text sets A0=A1=1.0 and C=1, and the alternative 'Volume Ratio' scale sets x=1 while noting that simulations suggested x near 3/2. Thus the relaxation model contains at least two additional adjustable choices beyond the original ScEMT fit. With these adjustments, the 'overall best agreement' reported for the relaxation model is not a test of the fixed ScEMT theory. The paper should either use the same parameters as the susceptibility fit, or treat C and x as fitted parameters with a documented model-selection criterion and uncertainty estimates.
[Eqs. (17)-(19), resonant frequency model] The derivation of the composite resonant frequency assumes a Snoek-like relation, chi_c f_rc = gamma P_p (2/3) 4 pi M_s, for the composite. This proportionality is not justified for metallic particulates (Fe, NiFe), where Snoek's law in the form of Eq. (17) is in general not valid because of eddy currents and different resonance mechanisms. Equation (19) depends only on the ratio of the Snoek products, so the model can still be tested against data, but the paper should either verify that the bulk particulate properties satisfy Eq. (17) or restrict the resonance predictions to ferrites. The poor Fe comparison noted by the authors (Figure 7b) may be a symptom of this invalid assumption; the paper should discuss this possibility explicitly.

minor comments (6)

[Abstract] There is a missing period after 'composites are presented' in the abstract; the sentence should end before 'ScEMT predictions'.
[Figure 9 caption] The caption writes 'Coe~1.0' but the parameter is denoted C in the text; please correct the notation.
[Figure 11 caption] The caption is confusing: it describes two NiZnCu ferrites with a vertical line, then mentions a MnO-ZnO ferrite. Please clarify which symbols correspond to which material and which vertical line separates the two NiZnCu data sets.
[Equation (24)] The term 1.38/chi_p^2 in Eq. (24) has units of inverse susceptibility squared, which may be dimensionally confusing since chi_p is dimensionless in this paper; please rewrite the expression to make the cancellation of chi_p explicit (e.g., 1.38 f_r / chi_p).
[Section 'Small Volume Fraction Correction'] The paper derives a low-fraction correction for ScEMT, but then concludes that the correction is not sufficient and that ScEMT should not be applied at low volume fractions because of a sign-changing artifact. This negative result is presented honestly, but it is in tension with the abstract's claim that the paper 'modifies BEMT and ScEMT for volume fractions below about 10%;' please reconcile this in the introduction or conclusions.
[Terminology] The paper defines 'relaxation frequency' as the full width at half maximum of the imaginary part of susceptibility, which is more conventionally called a linewidth or bandwidth. Please state this definition whenever the term is used and ensure it is consistent with the Schlomann references cited.

Circularity Check

2 steps flagged · score 4.0 of 10

ScEMT scaling parameters are fit to one NiZnCu ferrite and then reused as predictions for that same material; out-of-sample comparisons give independent content but no quantitative cross-validation.

fitted input called prediction [ScEMT Review, Eqs. (5)-(6); Characteristic Composite Frequencies, Eq. (19); Figs. 3-5]
"The free parameters, A0, A1 and γ were determined by fitting the ScEMT Equation 5 to measurement of non-dispersive, low frequency (< 10 MHz) susceptibilities of composites made from 10 - 40 μm, multi-domain Ni0.31 Zn0.58 Cu0.08 F2.03 O4. Samples were made with ferrite volume concentrations of 18, 20, 21, 30, 32, 45, 57 and 64 %, [3] [4]."

Equation 6 defines Ap(A0,A1,γ) and Eq. 5 uses it to predict composite susceptibility. The three constants were obtained by fitting Eq. 5 to measured susceptibility of a NiZnCu ferrite composite. The same material's susceptibility and resonant-frequency data appear in the evaluation, e.g., Fig. 5b, and Eq. 19 predicts f_rc from the ScEMT chi_c. For that composite, the susceptibility input to the frequency prediction is the fitted quantity itself, so the displayed agreement is in-sample rather than a fresh prediction. Other chemistries are genuine out-of-sample tests, so the circularity is partial.
fitted input called prediction [Relaxation Frequency Model and Measurement, Eq. (26); Figs. 9-11]
"As noted in the previous ScEMT Review section, the values for the ScEMT scaling function parameters were determined from a fit to measured values of one ferrite-composite susceptibility. The same coefficients have been applied to all other composites. The derived parameter values are: A0 = 0.975, A1= 0.923 and γ = 1.210, when rounded to the nearest thousandth. In the following calculations the parameter values are equalized(A0 = A1 = 1.0) thus satisfying boundary conditions. In addition, the numeric constant C is set equal to unity."

Equation 26 uses Ap from Eq. 25 with γ=1.210, an exponent inherited from the single-ferrite susceptibility fit, and relaxation data for the same NiZnCu ferrite family are plotted in Fig. 11. Thus the displayed agreement for that material is not an independent test of the scaling function. The choices A0=A1=1 and C=1 are not fitted to relaxation data, and most large-susceptibility relaxation comparisons use other ferrites, so the central relaxation claim retains independent content; however, the nominally universal exponent is neither re-fit nor separately validated for the other chemistries.

full rationale

The paper's derivation chain is mostly not circular: Eqs. (1)-(3), (7)-(12), (13)-(19), and (20)-(26) are ordinary algebraic constructions from MGT, CMA, BEMT, Schlomann, and Snoek's law, and improvement over MGT/CMA is claimed against many independently published composite data sets in Table 1 and Figures 2-13. The principal partial-circularity issue is that the ScEMT scaling function Ap(Pp), Eq. (6), is not derived from first principles; it is parameterized by A0, A1, and γ obtained by fitting Eq. (5) to susceptibility measurements of one NiZnCu ferrite composite from the author's prior work [3],[4]. The paper then presents ScEMT susceptibility and frequency predictions for the same ferrite family as supporting agreement, which is in-sample for that material. For the relaxation model, Eq. (26) inherits γ=1.210 from that same fit while setting A0=A1=1 and C=1; the fitted exponent is assumed transferable to Fe, MnZn ferrite, BaCoZn ferrite, and other composites, and relaxation data for the original NiZnCu ferrite are included in the validation. This weakens the independence of those particular comparisons, and the paper itself warns that graph-derived data 'should not be taken as absolutes' and that 'a full validation of models must await a series of carefully controlled experiments.' No quantitative error metric or out-of-sample cross-validation is reported. Nevertheless, the core comparison against CMA and MGT is not definitionally forced: ScEMT's improvement on external datasets is an empirical claim that could fail, and the paper reports cases such as Fe composites and low-susceptibility particulates where ScEMT is less accurate. Thus the circularity is partial and localized, not a derivation equivalent to its inputs.

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

No new physical entities are introduced; Ap and D(Pp) are functional scaling factors, not new particles, fields, or conserved quantities. The model's free parameters are a small set, but they were fitted to one material and then transferred, which limits the independence of the validation.

free parameters (5)

A0 = 0.975
Fitted in prior work to susceptibility versus volume fraction for Ni0.31Zn0.58Cu0.08Fe2.03O4 composites; used in ScEMT Eqs 5-6 for all susceptibility, resonance, and relaxation predictions.
A1 = 0.923
Fitted together with A0 and gamma to the same NiZnCu ferrite susceptibility dataset.
gamma = 1.210
Fitted together with A0 and A1; controls the nonlinear volume-fraction dependence of demagnetization.
C = 1.0
Replaces Schlomann's numerical constant 1.5 in Eq 23 based on prior experimental papers by Pointon, Gurevich, and Krishnan; chosen, not fitted in this paper.
x (volume ratio exponent, optional model variant) = 1.0
The volume-ratio scaling {(1-Pp)/Pp}^x is used with x=1; prior micromagnetic simulations suggested x near 3/2, so x=1 is a hand choice for one model variant.

assumptions (5)

domain assumption Snoek's law for bulk ferrites: chi_p * f_rp = (2/3) gamma 4 pi Ms (Eq 17)
Used to rewrite anisotropy and magnetization contributions in the relaxation model and to derive the resonant frequency relation. Standard for bulk ferrites.
ad hoc to paper The composite obeys a Snoek-like relation chi_c * f_rc = gamma * Pp * (2/3) 4 pi Ms, i.e., magnetization scales linearly with particle volume fraction (Eq 18)
Introduced as 'we choose' without independent derivation. This assumption is the load-bearing step for the ScEMT resonant frequency model Eq 19.
ad hoc to paper The ScEMT demagnetization function Ap, fitted to one ferrite's susceptibility, is transferable to other particulate chemistries and to relaxation broadening D(Pp) (Eqs 6, 25-26)
Universal transferability is assumed but not derived; it is the core of the paper's claims about broad application.
domain assumption MGT is the correct baseline at low volume fractions because particulates are isolated (Section 'Small Volume Fraction Correction')
Used to derive the low-fraction correction terms by subtracting MGT expansions from BEMT and ScEMT.
domain assumption Schlomann's 1956/1969 equations describe relaxation broadening due to pores and voids and apply to magnetic particles in nonmagnetic matrices (Eqs 20-21)
The relaxation model modifies Schlomann's second term; its applicability to arbitrary particle volume fractions is assumed.

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Pith. "Pith review of Scaled demagnetization models: susceptibility, resonant and relaxation frequency prediction compared to magnetic composite measurements." pith.science (2026). https://pith.science/paper/CQSF3A56

@misc{pith2026190800603,
  author       = {Pith},
  title        = {Pith review of: Scaled demagnetization models: susceptibility, resonant and relaxation frequency prediction compared to magnetic composite measurements},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CQSF3A56}},
  note         = {Machine review of arXiv:1908.00603}
}

read the original abstract

Maxwell-Garnett Theory (MGT), Bruggeman Effective Medium Theory (BEMT), Coherent Model Approximation (CMA), Scaled Effective Medium Theory (ScEMT) and models of Schlomann (E. Schlomann, Phys. Rev. B, 182, 7, 632 (10 June 1969) and E. Schlomann, Conf. on Mag. and Mag. Materials, AIEE Spec. Publ. T-91, 600 (1956)) are applied to predict magnetic susceptibility, resonant and relaxation frequency in polymer-magnetic particle composites. Particulates had aspect ratios near unity; bulk low frequency susceptibilities ranging from approximately 5 to 4000 and particle volume fractions between 1 and 100%. Previous publications demonstrated that ScEMT improved the prediction of DC susceptibility as compared to classical models. This paper first modifies BEMT and ScEMT for volume fractions below about 10%. A ScEMT based model of composite resonant frequency is presented and compared to MGT, CMA models and measurement. Model and measurement comparisons of resonant frequency are followed by model-measurement comparisons of relaxation frequency. CMA, MGT, models of Schlomann, and volumetric scaled modifications of Schlomann are tested in the relaxation frequency study. The paper emphasizes the broad application of the models and therefore composite data for a wide range of particulate chemistries are presented ScEMT predictions of susceptibility and resonant frequency continue to show reasonable agreement with measurement and represent improvement over the CMA and MGT models. ScEMT modifications to Schlomann show overall best agreement with relaxation frequency measurement. CMA and MGT are most accurate for modest susceptibility (~ < 100) while ScEMT modified Schlomann models are most accurate for large susceptibility.

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Works this paper leans on

46 extracted references · 46 canonical work pages

[3]

Moore, AIP Advances 9, 3, (8 March 2019)

R. Moore, AIP Advances 9, 3, (8 March 2019)

work page 2019
[4]

Moore, J

R. Moore, J. Appl. Phys.,125, 8, 085101 (28 Feb 2019)

work page 2019
[1]

Bashar Issa, et.al., Int. J. Mol. Sci. 14, 21266, (2013)

work page 2013
[2]

Idris, et.al., J

Fadzidah Mohd. Idris, et.al., J. Mag. Mag. Mat., 405, 197, (2016)

work page 2016
[5]

Maxwell Garnett, Phil

J.C. Maxwell Garnett, Phil. Trans. Royal Soc., 203A, 385, (1904)

work page 1904
[6]

Visser, M.T

E.G. Visser, M.T. Johnson, J. Mag. Mag. Mat., 101, 143 (1991)

work page 1991
[7]

Schlomann, Conf

E. Schlomann, Conf. on Mag. and Mag. Materials, AIEE Spec. Publ. T-91, 600 (1956)

work page 1956
[8]

Schlomann, Phys

E. Schlomann, Phys. Rev. B, 182, 7, 632 (10 June 1969)

work page 1969

Show all 46 references

[9]

Tsutaoka, et.al., 2013 IEEE EMC International Symposium Digest,.545, IEEE-978-1-4799-0409-9/13

T. Tsutaoka, et.al., 2013 IEEE EMC International Symposium Digest,.545, IEEE-978-1-4799-0409-9/13

2013
[10]

B. Lax, K. J. Button, Microwave Ferrites and Ferrimagnetics, 474-477, McGraw Hill, (1962)

1962
[11]

Krishnan, IEEE

R. Krishnan, IEEE. Trans. Mag., MAG-7, 1, (March 1971)

1971
[12]

Bruggeman, Ann.Phys.24,636 (1935)

D.A.G. Bruggeman, Ann.Phys.24,636 (1935)

1935
[13]

Chevalier, M

A. Chevalier, M. Le Floc’h, J. Appl. Phys., 90, 7, 3462 (1 Oct. 2001)

2001
[14]

Anhalt, et.al., 18th Soft Magnetic Materials Conference, B-0011 (Sept

M. Anhalt, et.al., 18th Soft Magnetic Materials Conference, B-0011 (Sept. 2007)

2007
[15]

Alvarez, S

C. Alvarez, S. H. L. Klapp, Soft Mater, 8, 7480 (2012)

2012
[16]

Mattei, D

J.L. Mattei, D. Bariou, A. Chevalier, M. Le Floc’h, J. Appl. Phys., 87, p4975 (2000)

2000
[17]

Mattei, M

J.L. Mattei, M. Le Floc’h , J. Mag. Mag. Mat, v357 p335 (2003)

2003
[18]

Mattei, P

J.L. Mattei, P. Laurent, A. Chevalier, M. Le Floc’h J. Physique. IV France 7, C1-547 (1997)

1997
[19]

Clerc, G

J.P. Clerc, G. Giraud, J.M. Laugier, J.M. Luck, Advances in Physics, 39, 3, 191-309, (1990)

1990
[20]

Moore, Electromagnetic Composites Handbook: Models, Measurement and Characterization, Chapter 12, McGraw Hill ISBN: 978- 1-25-958504-3 2016T

Rick. Moore, Electromagnetic Composites Handbook: Models, Measurement and Characterization, Chapter 12, McGraw Hill ISBN: 978- 1-25-958504-3 2016T
[21]

Markel, J

V. Markel, J. Opt. Soc. America, 33, 7, 1244 (July 2016)

2016
[22]

Webman, J

I. Webman, J. Jortner, M. Cohen, Phys. Rev. B, 15, 12, 5712 (14 June 1977)

1977
[23]

Lewin, Radio Sci., 94, III,65 (1947) 21

L. Lewin, Radio Sci., 94, III,65 (1947) 21

1947
[24]

Kasagi, et.al., J

T. Kasagi, et.al., J. Mag. Soc. Of Japan, v 22, n S1 (1998)

1998
[25]

Rozanov, et.al., J.Appl.Phys., 97, 013905 (2005)

K.N. Rozanov, et.al., J.Appl.Phys., 97, 013905 (2005)

2005
[26]

Rozanov, M

K.N. Rozanov, M. Y. Koledintseva, J. Appl. Phys., 119, 073901 (2016)

2016
[27]

Snoek, Physica, 14, 207 (1948)

J.L. Snoek, Physica, 14, 207 (1948)

1948
[28]

Fiske, et.al

J .J. Fiske, et.al. J.Mat.Sci., 32, 5557 (1997)

1997
[29]

Tsutaoka, J

T. Tsutaoka, J. Appl. Phys., 93, 5 2789 (March 2003)

2003
[30]

Zheng Hong, et.al., Chin. Phys. Lett., 26, 1, 017501 (2009)

2009
[31]

A Multifunctional Approach to Development, Fabrication, and Characterization of Fe3O4 Composites

S. Liong, PhD Thesis, “A Multifunctional Approach to Development, Fabrication, and Characterization of Fe3O4 Composites” School of Material Science and Engineering, Georgia Institute of Technology, (2005)

2005
[32]

Initial Permeability Spectra of Ferrites and Garnets

J.E. Pippin and C.L. Logan, “Initial Permeability Spectra of Ferrites and Garnets”, Harvard University 1959

1959
[33]

Babayan, et.al., Applied Surface Science, 258, 7707 (2012)

V. Babayan, et.al., Applied Surface Science, 258, 7707 (2012)

2012
[34]

Z. W. Li, Y. B. Gan, Xu Xin, G. Q. Lin, J. Appl Phys. 103, 073901 (2008)

2008
[35]

Massango, T

H. Massango, T. Tsutaoka, T. Kasagi, Materials Research Express, 3, 095801 (2016)

2016
[36]

Medeiros Gama, et.al., J

A. Medeiros Gama, et.al., J. Aerospace Tech. and Management, n1, v2, 5a (1 Jan.-April 2010)

2010
[37]

Shimada, M

Y. Shimada, M. Yamaguchi, J. Appl. Phys., 101, 09M505 (2007)

2007
[38]

Ramprasad, P

P. Ramprasad, P. Zarcher, M. Petras, M. Millr, P. Renaud, J. Appl. Phys., 96, 1, 529 (1 July 2004)

2004
[39]

Modification of Frequency Spectra of Ferrite Composites

J. Slama, A. Gruskova, V. Jancarik, P. Siroky, M. Lehotsky., “Modification of Frequency Spectra of Ferrite Composites”, Sept. 10-12, 2007, Pilsen Czech Republic

2007
[40]

Chih-Wen Chen, Magnetism and Metallurgy of Soft Magnetic Materials, ISBN 13: 9780486649979
[41]

Nakamura, T

T. Nakamura, T. Tsutaoka, K. Hatakeyama, J. Mag. Mag. Mat., 138, 319 (1994)

1994
[42]

A. J. Pointon, J. M. Robertson, Phil. Mag., 12, 725-733 (1965)

1965
[43]

Gurevich, I

A.G. Gurevich, I. E. Gubleer, A. P. Safant Evskii, Sov. Phys. Solid State, 1, 1706-1708 (1960)

1960
[44]

Krishnan, IEEE Trans

R. Krishnan, IEEE Trans. Magnetics, Mag-7, 202 (1 March 1971)

1971
[45]

Jorge L. C. Domingos, F. M. Peeters and W. P. Ferreira, Phys. Rev. E 96, 012603 (2017)

2017
[46]

Jorge L. C. Domingos, F. M. Peeters and W. P. Ferreira, PloS One 13 (4), e0195552 (2018)

2018

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [3]

Moore, AIP Advances 9, 3, (8 March 2019)

R. Moore, AIP Advances 9, 3, (8 March 2019)

work page 2019

[2] [4]

Moore, J

R. Moore, J. Appl. Phys.,125, 8, 085101 (28 Feb 2019)

work page 2019

[3] [1]

Bashar Issa, et.al., Int. J. Mol. Sci. 14, 21266, (2013)

work page 2013

[4] [2]

Idris, et.al., J

Fadzidah Mohd. Idris, et.al., J. Mag. Mag. Mat., 405, 197, (2016)

work page 2016

[5] [5]

Maxwell Garnett, Phil

J.C. Maxwell Garnett, Phil. Trans. Royal Soc., 203A, 385, (1904)

work page 1904

[6] [6]

Visser, M.T

E.G. Visser, M.T. Johnson, J. Mag. Mag. Mat., 101, 143 (1991)

work page 1991

[7] [7]

Schlomann, Conf

E. Schlomann, Conf. on Mag. and Mag. Materials, AIEE Spec. Publ. T-91, 600 (1956)

work page 1956

[8] [8]

Schlomann, Phys

E. Schlomann, Phys. Rev. B, 182, 7, 632 (10 June 1969)

work page 1969