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REVIEW 3 major objections 6 minor 87 references

Magnetoimpedance properties of CoNbZr, multilayer CoNbZr/Au and multilayer NiFe/Au thin films

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Gold interlayers enhance the giant magnetoimpedance of CoNbZr thin films by about 50 percent and halve their ferromagnetic-resonance frequency, with a 20 µm × 5000 µm CoNbZr/Au strip reaching a GMI ratio of (300 ± 1) percent at 1.8 GHz…

desk verdict Solid empirical GMI study with new CoNbZr/Au data, but the headline FMR frequencies are inferred from GMI curves, not measured, so the 50% FMR reduction claim is unproven. read the letter →

arxiv 2505.24659 v1 pith:FC4BHC23 submitted 2025-05-30 cond-mat.mtrl-sci physics.app-ph

Indujan Sivanesarajah , Leon Abelmann , Uwe Hartmann This is my paper
classification cond-mat.mtrl-sciphysics.app-ph
keywords giantmagnetoimpedanceCoNbZrthinfilmsAuinterlayersNiFe/AumultilayersferromagneticresonanceGMIsensorsdemagnetisingfactor
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

This paper sets out to show that inserting non-magnetic gold layers between amorphous CoNbZr magnetic layers improves the giant magnetoimpedance (GMI) response enough to make CoNbZr/Au a practical sensor material. Against single-layer CoNbZr, the gold interlayers are reported to raise the GMI ratio by about 50 percent and lower the onset of ferromagnetic resonance from about 1.4 GHz to about 0.7 GHz. Against the established NiFe/Au multilayer, CoNbZr/Au reaches a similar or higher GMI ratio while needing a lower applied field (2 mT versus 4 mT) for its peak response. The best measured element, a 20 µm × 5000 µm CoNbZr/Au strip, reaches (300 ± 1) percent at 1.8 GHz. If these numbers hold, CoNbZr/Au becomes a viable alternative for sensitive low-field magnetic sensing, especially in miniaturised high-frequency geometries.

What carries the argument

The central object is the transverse permeability $\mu_t$ of a thin ferromagnetic film, which controls how much the skin depth $\delta = \sqrt{2\rho/(\omega\mu)}$ and the impedance $Z = R_{\mathrm{dc}} i k t \coth(i k t)$ change with an applied magnetic field. The GMI ratio is $\eta = (|Z(B)| - |Z(B_{\mathrm{ref}})|)/|Z(B_{\mathrm{ref}})|$, and the paper extracts $|\mu_t|$ from measured impedance by a nonlinear least-squares fit to the thin-film impedance formula. The Au interlayers are the design variable: they reduce $\delta$, raise $|\mu_t|$ at low frequencies, and shift the field-dependent peak structure in the GMI curves, whose broadening the paper takes as the signature of ferromagnetic resonance. Geometry enters through in-plane demagnetising factors, which set the shape anisotropy and hence the field position of the GMI peaks.

What would settle it

Measure the frequency-dependent impedance of the same 0.1 mm × 1 mm stripes and the 20 µm × 5000 µm strip in a direct FMR apparatus over 0.1–3 GHz and compare the resonance fields with those predicted from the measured Ms (1.01, 0.85 and 0.68 MA/m) and in-plane anisotropy. If no resonance appears near 1.4 GHz, 0.7 GHz and 0.5 GHz for the three systems, or if the predicted values disagree, the paper's central comparison between the materials would not be supported.

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Extended reading notes

Core claim

The paper claims that a multilayer of ten 104 nm CoNbZr layers separated by nine 10 nm Au layers outperforms a single 1040 nm CoNbZr film of the same magnetic thickness: the GMI ratio increases by about 50 percent and the ferromagnetic-resonance onset falls from about 1.4 GHz to about 0.7 GHz. The explanation offered is that the Au interlayers shorten the skin depth and raise the transverse permeability at low frequencies while the amorphous CoNbZr layers keep the total resistivity high; because impedance at fixed frequency scales with the product of resistivity and transverse permeability, CoNbZr/Au can match or exceed NiFe/Au despite having roughly half the transverse permeability. The measured record is (300 ± 1) percent at 1.8 GHz under 2 mT for a 20 µm × 5000 µm CoNbZr/Au element, compared with (280 ± 1) percent at 4 mT for NiFe/Au. The paper links the differing peak fields to saturation magnetisation and in-plane demagnetising factors, with the highest ratios appearing for long, narrow elements.

Load-bearing premise

The paper's FMR frequencies are inferred from the onset of broadening in the GMI curves, not from a direct resonance measurement, and they are not checked against the standard resonance formula using the measured saturation magnetisation and anisotropy.

Editorial extensions

If this is right

  • If the 50 percent enhancement is reproducible, CoNbZr/Au multilayers can replace single-layer CoNbZr in high-frequency GMI sensors without adding a complex process step beyond the already standard multilayer deposition.
  • Because the peak GMI of CoNbZr/Au occurs at 2 mT rather than 4 mT, a CoNbZr/Au sensor can operate with smaller biasing coils and lower power in the same geometry.
  • The strong length dependence (a 7.5-fold GMI increase from 0.5 mm to 5 mm at fixed 20 µm width) means that practical sensor elements should be made as long, narrow strips, with widths in the 10–20 µm range.
  • The 199 %/mT sensitivity reported for the best CoNbZr/Au strip is the paper's most direct quantitative argument that the material belongs in low-field measurement applications.

Reading between the lines

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

  • Beyond the paper, a clean way to test the proposed mechanism is to vary the Au layer thickness (fixed here at 10 nm) and check whether the GMI gain and resonance shift scale monotonically; if they do not, interface anisotropy rather than conductivity might be the dominant effect.
  • The paper's EDX result that the Co/Nb ratio changes from 7.1 in the target to 13 in the film implies that nominally identical CoNbZr films made in different sputter systems may differ substantially, so composition verification should accompany any comparison across laboratories.
  • The suggestion to add one thicker conductive non-magnetic layer implies a testable design principle: in the skin-effect regime, redistributing the drive current through a low-resistivity layer may raise the GMI ratio more than adding magnetic volume, a hypothesis that a series of asymmetric multilayer stacks could settle.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper reports a comparative experimental study of the electric, magnetic, and giant magnetoimpedance (GMI) properties of single-layer amorphous CoNbZr, multilayer CoNbZr/Au, and multilayer NiFe/Au thin films. The authors find that Au interlayers increase the GMI ratio by about 50% relative to single-layer CoNbZr and claim that they reduce the ferromagnetic resonance (FMR) frequency by 50% (from 1.4 GHz to 0.7 GHz). The highest GMI ratio of 300% is reported for a 20 µm × 5000 µm CoNbZr/Au strip at 1.8 GHz under 2 mT, with NiFe/Au reaching 280% at 4 mT. The paper includes detailed fabrication, structural characterization (TEM/EDX), magnetic characterization (VSM, MOKE), and systematic GMI measurements as a function of frequency, annealing current, and lateral aspect ratio, together with model-based extraction of transverse permeability and skin depth.

Significance. If the results hold, the paper provides a useful comparative dataset for GMI sensor materials, showing that CoNbZr/Au multilayers can outperform the commonly used NiFe/Au system in GMI ratio at moderate fields. The experimental methods are well described, including probe deembedding, TOSM calibration, and systematic control of sample geometry. The direct measurement of the GMI enhancement (50% increase, 300% maximum) appears robust and is the main empirical contribution. The paper also gives careful microstructural evidence for the amorphous CoNbZr layers and crystalline Au/NiFe layers. However, the claimed FMR frequencies and the associated claim of a 50% reduction in FMR frequency are inferred from qualitative GMI curve features rather than measured directly, and the Kittel equation is not used to cross-check them; this weakens a headline result of the abstract and conclusion.

major comments (3)
  1. [4.4.1, Abstract, Conclusion] The FMR frequencies (1.4 GHz for CoNbZr, 0.7 GHz for CoNbZr/Au, 0.5 GHz for NiFe/Au) are not measured by a direct ferromagnetic resonance method; they are inferred from qualitative GMI curve changes, and the operational criterion is inconsistent across samples. For CoNbZr, the onset is identified from broadening at 1.4 GHz, for CoNbZr/Au from broadening at 0.7 GHz, and for NiFe/Au from double-peak splitting at 0.5 GHz. The Kittel equation (Eq. 7) is never used to check these frequencies against the measured Ms (Table 6), the demagnetizing factors (Table 1), or the double-peak positions at 1.8 GHz (2, 3, and 4 mT). Since the abstract and conclusion present the 50% FMR-frequency reduction as a headline result, this claim is not yet substantiated.
  2. [4.4.1] The sentence 'The reduced FMR frequency for CoNbZr/Au is related to its smaller skin depth' is physically unjustified. FMR frequency is determined by magnetic parameters such as saturation magnetization, anisotropy, and demagnetizing fields, not by the skin depth. The skin depth argument may explain differences in the GMI magnitude or the frequency dependence of impedance, but it does not explain a shift in the resonance frequency. This causal statement should be removed or replaced with a mechanism consistent with the Kittel equation.
  3. [4.4.1, Tables 7-8] The transverse permeability μt is extracted by fitting the same impedance data that defines the GMI ratio (via Eq. 2 with a Levenberg-Marquardt fit) and is then used to explain the observed GMI differences, e.g., 'the enhanced transverse permeability of CoNbZr/Au plays a crucial role in achieving an improved GMI ratio'. This is partly self-referential: the model-based permeability and the measured GMI ratio are not independent. The authors should either validate μt with an independent measurement (e.g., permeability spectroscopy or FMR-derived permeability) or explicitly state that the explanation is model-based and not an independent confirmation.
minor comments (6)
  1. [Table 5] The header 'Out-of-plane (Width)' is misleading because the measurements are in-plane hysteresis loops along the width direction. This should read 'In-plane (Width)' to be consistent with Section 3.3.
  2. [4.4.1] The identification of 'FMR frequency' from the onset of GMI curve broadening should be explicitly defined as an operational definition; the term 'FMR frequency' in the abstract and conclusion implies a direct resonance measurement, which is not the case.
  3. [4.4.1] The statement 'With CoNbZr approaching a skin depth of (101 ± 1) nm at 1.4 GHz and CoNbZr/Au reaching (102 ± 1) nm at 0.7 GHz, both systems approach the FMR regime' is not supported by an explicit relation between skin depth and FMR onset; the skin depth changes are a consequence of the permeability changes, not a cause of resonance.
  4. [Tables 7-9] The reported uncertainties (e.g., ±1 nm for skin depth, ±0.1×10^3 for permeability, ±1 % for GMI ratios) appear unrealistically small given the multi-step deembedding, calibration, and Levenberg-Marquardt fitting chain. Please report full error propagation including systematic contributions, or provide reproducibility statistics from repeated measurements.
  5. [2.3.2 and 4.3] The dilution model prediction given by Eq. 12 is a thickness-weighted average of measured quantities; its 'agreement' with the data (e.g., Table 6) is a consistency check rather than an independent validation. The text should avoid calling this an independent prediction.
  6. [4.4.1] The attribution of minor double peaks in CoNbZr above 0.3 GHz to 'experimental misalignments' is speculative; no misalignment quantification is provided. Consider removing or substantiating this claim.

Circularity Check

2 steps flagged · score 3.0 of 10

The directly measured GMI ratios are independent, but the explanatory layer is partially self-referential: permeability fitted from the impedance data is used to explain the impedance, and the reduced FMR frequency is 'explained' by a skin depth computed from the same GMI curves, while the FMR frequencies themselves are inferred rather than measured.

  1. self definitional [Section 2.1 and Section 4.4.1 (Eqs. 2-3, Table 8)]
    "By measuring |Z| and its phase, R and X can be determined. Then, the real, imaginary and absolute values of k, δ and µt can be estimated numerically using the Levenberg-Marquardt (L-M) method to solve Eq. 2. ... According to Eq.3, at a fixed frequency, the impedance is determined by the product of resistivity and transverse permeability. The superior GMI ratio of CoNbZr/Au can be attributed primarily to its significantly higher resistivity..."

    The paper first solves Eq. 2 for the transverse permeability µt by fitting it to the measured impedance Z, then uses Eq. 3 to express Z as (1+i)√(π f ρ µt) and attributes the measured GMI differences to the fitted µt and the measured resistivity. Because µt was chosen to reproduce the same Z that defines the GMI ratio, this attribution is a re-description of the fit rather than an independent explanation. The product √(π f ρ µt) is consistent with the impedance input by construction, so the 'explanation' adds no independent evidence.

  2. self definitional [Section 4.4.1 (Fig. 11, Table 7)]
    "Beyond 1.4 GHz, the broadening of the GMI curves and the shift of the double peaks to higher fields mark the onset of the FMR regime. ... The reduced FMR frequency for CoNbZr/Au is related to its smaller skin depth. At 0.7 GHz, the skin depth of CoNbZr/Au is (102 ± 1) nm, significantly smaller than the (145 ± 1) nm observed for single-layer CoNbZr. ... With CoNbZr approaching a skin depth of (101 ± 1) nm at 1.4 GHz and CoNbZr/Au reaching (102 ± 1) nm at 0.7 GHz, both systems approach the FMR regime."

    The FMR onset is identified from the GMI curves, and the skin depth used to 'explain' it is computed from Eq. 1 using the permeability fitted from those same GMI curves via Eq. 2. The paper further notes that CoNbZr at 1.4 GHz and CoNbZr/Au at 0.7 GHz both reach δ ≈ 100 nm, so the FMR onset in both systems is the point where the impedance-derived skin depth crosses the same value. Saying the lower FMR frequency is 'related to its smaller skin depth' therefore restates the impedance criterion used to identify the FMR regime; it is not an independent magnetic explanation and is never checked against the Kittel equation (Eq. 7).

full rationale

The paper's central quantitative results — the 300% GMI ratio for the 20 µm × 5000 µm CoNbZr/Au strip and the 50% enhancement relative to single-layer CoNbZr — come from VNA impedance measurements after TOSM calibration and open/short de-embedding (Secs. 3.4 and 4.4.3). Those numbers are not derived from the fitted permeability and are therefore not circular. The dilution-model comparisons (Eqs. 11 and 12) are thickness-weighted averages of measured single-layer and multilayer values; they are consistency checks rather than independent predictions, but they do not feed back into the GMI claim. The partial circularity is elsewhere. First, the transverse permeability is obtained by numerically inverting the measured impedance via Eq. 2, and is then cited — through Eq. 3 — as the reason for the measured GMI ranking. That is an algebraic re-description of the same data: the fitted µt reproduces Z by construction, so attributing the GMI differences to µt and ρ adds no independent evidence. Second, the FMR frequencies in the abstract (1.4/0.7/0.5 GHz) are inferred from GMI-curve broadening and double-peak structure in Sec. 4.4.1, not from a direct FMR experiment or from Kittel Eq. 7. The paper then says the lower FMR frequency of CoNbZr/Au is 'related to its smaller skin depth,' where the skin depth is computed using the permeability fitted from those same GMI curves. Because the text also states that CoNbZr at 1.4 GHz and CoNbZr/Au at 0.7 GHz both reach δ ≈ 100 nm, this explanation restates the impedance criterion used to identify the FMR onset rather than providing a magnetic mechanism. These issues weaken the explanatory and comparative FMR claims, but the main GMI-enhancement result is an independent measurement. No load-bearing self-citation was found; the only author self-citation (Betzholz et al., Ref. [39]) is a contextual theoretical-maximum statement in the introduction.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claims rest on standard electromagnetic results and on a qualitative FMR identification that is not independently verified. The fitted permeability values are outputs of the model, not free parameters used to force agreement with an external benchmark. No new entities are postulated.

free parameters (2)
  • VSM diamagnetic background slope = 0.1 µAm²/T
    Subtracted linearly from VSM hysteresis loops in Sec. 3.3; affects reported Ms values slightly.
  • Levenberg-Marquardt fitted k, δ, µt values = not reported (varies with field/frequency)
    Extracted from impedance data using Eq. 2 in Sec. 2.1 and 4.4; these fitted permeability values are used to explain GMI differences.
assumptions (5)
  • standard math Skin effect impedance formula for a thin film, Z = Rdc ikt coth(ikt), Eq. 2
    Taken from Chen and Munoz [61] and Phan and Peng [62]; standard result for a film with lateral dimensions much larger than thickness.
  • domain assumption Dilution model: non-magnetic layers contribute negligibly to resistivity and saturation magnetization, Eqs. 11 and 12
    Invoked in Sec. 2.3.1 and 2.3.2 to compute effective resistivity and magnetization of multilayers.
  • ad hoc to paper FMR onset identified with broadening of GMI curves
    Sec. 4.4.1: 'Beyond 1.4 GHz, the broadening of the GMI curves... mark the onset of the FMR regime.' This assumption underpins the reported FMR frequencies.
  • standard math Demagnetizing factors from Aharoni [68] used to compute Hd in Table 1
    Used to calculate shape anisotropy and demagnetizing fields for the strip geometries.
  • domain assumption MOKE contrast interpreted as single-domain vs multidomain states in top magnetic layer
    Sec. 3.3 and Fig. 10; authors acknowledge MOKE only probes near-surface magnetization.

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Cite this review

Pith. "Pith review of Magnetoimpedance properties of CoNbZr, multilayer CoNbZr/Au and multilayer NiFe/Au thin films." pith.science (2026). https://pith.science/paper/FC4BHC23

@misc{pith2026250524659,
  author       = {Pith},
  title        = {Pith review of: Magnetoimpedance properties of CoNbZr, multilayer CoNbZr/Au and multilayer NiFe/Au thin films},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FC4BHC23}},
  note         = {Machine review of arXiv:2505.24659}
}
abstract

Thin-film magnetic sensors using the giant magnetoimpedance (GMI) effect show great promise for sensitive low-field magnetic measurements. Optimising sensor performance requires a thorough understanding of the properties of various soft magnetic materials. This study examines the electric, magnetic, and GMI properties of sputtered single-layer amorphous CoNbZr, multilayer amorphous CoNbZr/Au, and crystalline NiFe/Au thin films. GMI measurements reveal distinct ferromagnetic resonance (FMR) frequencies: 1.4 GHz for CoNbZr, 0.7 GHz for CoNbZr/Au, and 0.5 GHz for NiFe/Au. Au interlayers improve the GMI response, increasing the GMI ratio by 50% and reducing FMR frequency compared to single-layer CoNbZr. The highest GMI ratio of 300% occurs in a 20 $\mu$m x 5000 $\mu$m CoNbZr/Au strip at 1.8 GHz under 2 mT, while NiFe/Au exhibits 280% at 4 mT. These differences are linked to variations in in-plane demagnetising factors and saturation magnetisations, emphasising the role of material and geometry in GMI sensor performance.

Figures

Figures reproduced from arXiv: 2505.24659 by the authors.

Figure 1
Figure 1. Schematic representation of the GMI cure as a function of the external field [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Schematic representation of the sample preparation process. The steps include [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Schematic representation of the layer systems in cross-section: (a) a single-layer [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Images of the patterns used for (a) resistance and (b) magnetoimpedance measure [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: Schematic setup used for (a) resistance and (b) magnetoimpedance measurements. [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Deembedding structures used for magnetoimpedance measurements containing (a) [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Schematic setup used for annealing the GMI structures. [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: Cross-sectional TEM images and SAED patterns of (a-c) single-layer CoNbZr, (d-f) [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]
Figure 9
Figure 9. Figure 9: In-plane hysteresis loops of the magnetisation [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: MOKE images of (a) single-layer CoNbZr, (b) multilayer CoNbZr/Au, and (c) [PITH_FULL_IMAGE:figures/full_fig_p023_10.png]
Figure 11
Figure 11. Figure 11: GMI curves of 0.1 mm × 1 mm elements for (a) single-layer CoNbZr, (b) multilayer CoNbZr/Au, and (c) multilayer NiFe/Au, with a magnetic field sweep of B = ±10 mT. The GMI ratio η increases with frequency in all systems due to the rising impedance Z (see Eq. 3). For si…
Figure 12
Figure 12. Figure 12: Calculated absolute value of the transverse permeability [PITH_FULL_IMAGE:figures/full_fig_p026_12.png]
Figure 13
Figure 13. Figure 13: GMI curves for 0.1 mm × 1 mm structures measured over a magnetic field range of B = ± 10 mT as a function of annealing current at 0.7 GHz. The samples were annealed at currents of 0 mA, 500 mA, 750 mA, and 850 mA for the following systems: (a) single-layer CoNbZr, (b)…
Figure 14
Figure 14. Figure 14: MOKE images of 0.1 mm × 1 mm single-layer CoNbZr structures at (a) 0 mA, (b) 500 mA, (c) 750 mA, and (d) 850 mA. At 0 mA, the magnetic domains are aligned along the length of the structure, as indicated by the bipolar contrast and the white arrows. At 500 mA, the doma…
Figure 15
Figure 15. Figure 15: GMI curves measured as a function of aspect ratio over a magnetic field sweep [PITH_FULL_IMAGE:figures/full_fig_p032_15.png]

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Reference graph

Works this paper leans on

87 extracted references · 76 canonical work pages

  1. [1]

    G. Lin, D. Makarov, and O. G. Schmidt, Lab on a Chip 17, 1884 (2017)

    2017

  2. [2]

    Murzin, D

    D. Murzin, D. J. Mapps, K. Levada, V. Belyaev, A. Omelyanchik, L. Panina, and V. Rodionova, Sensors (Switzerland)20, 10.3390/s20061569 (2020)

    doi:10.3390/s20061569 2020

  3. [3]

    Elzenheimer, C

    E. Elzenheimer, C. Bald, E. Engelhardt, J. Hoffmann, P. Hayes, J. Ar- bustini, A. Bahr, E. Quandt, M. H¨ oft, and G. Schmidt, Sensors 22, 1 (2022). 40

    2022

  4. [4]

    Zhang, L

    H. Zhang, L. Liao, R. Zhao, J. Zhou, M. Yang, and R. Xia, Sensors (Switzer- land) 16, 10.3390/s16091439 (2016)

    work page doi:10.3390/s16091439 2016

  5. [5]

    Nakai, Sensors 21, 10.3390/s21124063 (2021)

    T. Nakai, Sensors 21, 10.3390/s21124063 (2021)

    work page doi:10.3390/s21124063 2021

  6. [6]

    A. D. Eslamlou, A. Ghaderiaram, E. Schlangen, and M. Fotouhi, Construc- tion and Building Materials 397, 132460 (2023)

    2023

  7. [7]

    M. J. Caruso, SAE Technical Papers 10.4271/970602 (1997)

    work page doi:10.4271/970602 1997

  8. [8]

    El-Sheimy and A

    N. El-Sheimy and A. Youssef, Satellite Navigation 1, 1 (2020)

    2020

Show all 87 references
  1. [9]

    Saltus, P

    R. Saltus, P. Alken, A. Balmes, N. Boneh, S. Califf, A. Chulliat, B. Meyer, and M. Nair, 2023 IEEE/ION Position, Location and Navigation Sym- posium, PLANS 2023 , 805 (2023)

    2023

  2. [10]

    C. A. Grimes, K. Ong, K. Loiselle, P. G. Stoyanov, D. Kouzoudis, Y. Liu, C. Tong, and F. Tefiku, Smart Materials and Structures 8, 639 (1999)

    1999

  3. [11]

    Hojjati-Najafabadi, M

    A. Hojjati-Najafabadi, M. Mansoorianfar, T. Liang, K. Shahin, and H. Karimi-Maleh, Science of the Total Environment 824, 10.1016/j.scitotenv.2022.153844 (2022)

    2022

  4. [12]

    ˇCulik, V

    K. ˇCulik, V. ˇStefancov´ a, and K. Hrudkay, Sensors23, 5740 (2023)

    2023

  5. [13]

    C. P. O. Treutler, Sensors and Actuators, A: Physical 91, 2 (2001)

    2001

  6. [14]

    Granig, S

    W. Granig, S. Hartmann, and B. K¨ oppl, SAE Technical Papers 2007, 776 (2007)

    2007

  7. [15]

    Nonomura, IEEJ Transactions on Electrical and Electronic Engineering 15, 984 (2020)

    Y. Nonomura, IEEJ Transactions on Electrical and Electronic Engineering 15, 984 (2020)

    2020

  8. [16]

    E. Boto, R. Bowtell, P. Kr¨ uger, T. M. Fromhold, P. G. Morris, S. S. Meyer, G. R. Barnes, and M. J. Brookes, PLoS ONE 11, 1 (2016)

    2016

  9. [17]

    Kanno, N

    A. Kanno, N. Nakasato, M. Oogane, K. Fujiwara, T. Nakano, T. Arimoto, H. Matsuzaki, and Y. Ando, Scientific Reports 12, 1 (2022). 41

    2022

  10. [18]

    M. J. Brookes, J. Leggett, M. Rea, R. M. Hill, N. Holmes, E. Boto, and R. Bowtell, Trends in Neurosciences 45, 621 (2022)

    2022

  11. [19]

    D. A. Robinson, A. Binley, N. Crook, F. D. Day-Lewis, T. P. A. Ferr´ e, V. J. S. Grauch, R. Knight, M. Knoll, V. Lakshmi, R. Miller, J. Nyquist, L. Pellerin, K. Singha, and L. Slater, Hydrological Processes 22, 3604 (2008)

    2008

  12. [20]

    Dentith and S

    M. Dentith and S. Mudge, Geophysics for the mineral exploration geoscient- ist (Cambridge University Press, 2014)

    2014

  13. [21]

    Stolz, M

    R. Stolz, M. Schiffler, M. Becken, A. Thiede, M. Schneider, G. Chubak, P. Marsden, A. B. Bergshjorth, M. Schaefer, and O. Terblanche, Mineral Economics 35, 467 (2022)

    2022

  14. [22]

    Aschenbrenner and G

    H. Aschenbrenner and G. Goubau, Hochfrequenztechnik und Elektroak- ustik 47, 177 (1936)

    1936

  15. [23]

    B. D. Josephson, Physics Letters 1, 251 (1962)

    1962

  16. [24]

    P. W. Anderson and J. M. Rowell, Physical Review Letters 10, 230 (1963)

    1963

  17. [25]

    R. C. Jaklevic, J. Lambe, A. H. Silver, and J. E. Mercereau, Physical Review Letters 12, 159 (1964)

    1964

  18. [26]

    E. H. Hall, American Journal of Mathematics 2, 287 (1879)

  19. [27]

    B. Uzlu, Z. Wang, S. Lukas, M. Otto, M. C. Lemme, and D. Neumaier, Scientific Reports 9, 10.1038/s41598-019-54489-0 (2019)

    2019 doi

  20. [28]

    Thomson, Proceedings of the Royal Society of London 8, 546 (1857)

    W. Thomson, Proceedings of the Royal Society of London 8, 546 (1857)

  21. [29]

    M. N. Baibich, J. M. Broto, A. Fert, F. N. V. Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Physical Review Letters 61, 2472 (1988)

    1988

  22. [30]

    Binasch, P

    G. Binasch, P. Gr¨ unberg, F. Saurenbach, and W. Zinn, Physical Review B 39, 4828 (1989). 42

    1989

  23. [31]

    Julliere, Physics Letters A 54, 225 (1975)

    M. Julliere, Physics Letters A 54, 225 (1975)

    1975

  24. [32]

    J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cap- pellaro, L. Jiang, M. V. Dutt, E. Togan, A. S. Zibrov, A. Yacoby, R. L. Walsworth, and M. D. Lukin, Nature 455, 644 (2008)

    2008

  25. [33]

    Balasubramanian, I

    G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud, J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hemmer, A. Krueger, T. Hanke, A. Leitenstorfer, R. Bratschitsch, F. Jelezko, and J. Wrachtrup, Nature 455, 648 (2008)

    2008

  26. [34]

    J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hem- mer, A. Yacoby, R. Walsworth, and M. D. Lukin, Nature Physics 4, 810 (2008)

    2008

  27. [35]

    L. V. Panina and K. Mohri, Applied Physics Letters 65, 1189 (1994)

    1994

  28. [36]

    R. S. Beach and A. E. Berkowitz, Applied Physics Letters 64, 3652 (1994)

    1994

  29. [37]

    Mohri, T

    K. Mohri, T. Uchiyama, L. V. Panina, M. Yamamoto, and K. Bushida, Journal of Sensors 2015, 1 (2015)

    2015

  30. [38]

    M. A. Khan, J. Sun, B. Li, A. Przybysz, and J. Kosel, Engineering Research Express 3, 022005 (2021)

    2021

  31. [39]

    Betzholz, H

    R. Betzholz, H. Gao, Z. Zhao, and U. Hartmann, Europhysics Letters 101, 10.1209/0295-5075/101/17005 (2013)

    2013 doi

  32. [40]

    S. q. Xiao, Y. h. Liu, S. h. Yan, Y. y. Dai, L. Zhang, and L. m. Mei, Physical Review B - Condensed Matter and Materials Physics 61, 5734 (2000)

    2000

  33. [41]

    Garc ´ ıa-Arribas, E

    A. Garc ´ ıa-Arribas, E. Fern´ andez, A. Svalov, G. Kurlyandskaya, and J. Barandiar´ an, Journal of Magnetism and Magnetic Materials 400, 321 (2016)

    2016

  34. [42]

    Morikawa, Y

    T. Morikawa, Y. Nishibe, H. Yamadera, Y. Nonomura, M. Takeuchi, J. Sakata, and Y. Taga, IEEE Transactions on Magnetics 32, 4965 (1996). 43

    1996

  35. [43]

    J. Yu, Y. Zhou, B. Cai, and D. Xu, Journal of Magnetism and Magnetic Materials 213, 32 (2000)

    2000

  36. [44]

    Yokoyama, K

    H. Yokoyama, K. Kusunoki, Y. Hayashi, S. Hashi, and K. Ishiyama, Journal of Magnetism and Magnetic Materials 478, 38 (2019)

    2019

  37. [45]

    Garc ´ ıa-Arribas, E

    A. Garc ´ ıa-Arribas, E. Fern´ andez, and D. de Cos,Magnetic Sensors - De- velopment Trends and Applications (InTech, 2017) pp. 39–62

    2017

  38. [46]

    Saito, H

    N. Saito, H. Fujiwara, and Y. Sugita, Journal of the Physical Society of Japan 19, 1116 (1964)

    1964

  39. [47]

    E. F. Silva, M. A. Corrˆ ea, R. D. D. Pace, C. C. P. Cid, P. R. Kern, M. Carara, C. Chesman, O. A. Santos, R. L. Rodr ´ ıguez-Su´ arez, A. Azevedo, S. M. Rezende, and F. Bohn, Journal of Physics D: Applied Physics 50, 0 (2017)

    2017

  40. [48]

    de Cos, V

    D. de Cos, V. N. Lepalovskij, G. V. Kurlyandskaya, A. Garc ´ ıa-Arribas, and J. M. Barandiar´ an, Journal of Magnetism and Magnetic Materials320, 954 (2008)

    2008

  41. [50]

    G. V. Kurlyandskaya, A. V. Svalov, E. Fern´ andez, A. Garc ´ ıa-Arribas, and J. M. Barandiar´ an, Journal of Applied Physics 107, 10.1063/1.3355473 (2010)

    2010 doi

  42. [51]

    A. V. Svalov, E. Fern´ andez, A. Garc ´ ıa-Arribas, J. Alonso, M. L. Fdez- Gubieda, and G. V. Kurlyandskaya, Applied Physics Letters 100, 1 (2012)

    2012

  43. [52]

    V. O. Vas’kovskii, P. A. Savin, S. O. Volchkov, V. N. Lepalovskii, D. A. Bukreev, and A. A. Buchkevich, Technical Physics 58, 105 (2013)

    2013

  44. [53]

    Kikuchi, Y

    H. Kikuchi, Y. Takahashi, K. Takahashi, T. Nakai, S. Hashi, and K. Ishiyama, Journal of Applied Physics 115, 14 (2014). 44

    2014

  45. [54]

    Kikuchi, S

    H. Kikuchi, S. Kamata, S. Oe, T. Nakai, S. Hashi, and K. Ishiyama, IEEE Transactions on Magnetics 51, 18 (2015)

    2015

  46. [55]

    Kikuchi, S

    H. Kikuchi, S. Kamata, Y. Takahashi, T. Nakai, S. Hashi, and K. Ishiyama, IEEE Transactions on Magnetics 51, 10.1109/TMAG.2014.2358221 (2015)

    2015

  47. [56]

    Kikuchi, M

    H. Kikuchi, M. Tanii, and T. Umezaki, AIP Advances 10, 10.1063/1.5130410 (2020)

    2020 doi

  48. [57]

    Kikuchi, A

    H. Kikuchi, A. Ueno, and M. Tanii, IEEE Transactions on Magnetics 58, 10.1109/TMAG.2022.3151985 (2022)

    2022

  49. [58]

    Kikuchi, A

    H. Kikuchi, A. Ueno, and M. Tanii, IEEE Transactions on Magnetics 59, 1 (2023)

    2023

  50. [59]

    M. A. Corrˆ ea, A. D. C. Viegas, R. B. da Silva, A. M. H. de Andrade, and R. L. Sommer, Journal of Applied Physics 101, 10.1063/1.2512867 (2007)

    2007 doi

  51. [60]

    M. A. Corrˆ ea, F. Bohn, A. D. C. Viegas, A. M. de Andrade, L. F. Schelp, and R. L. Sommer, Journal of Physics D: Applied Physics41, 10.1088/0022- 3727/41/17/175003 (2008)

    2008 doi

  52. [61]

    D. X. Chen and J. L. Munoz, IEEE Transactions on Magnetics 35, 1906 (1999)

    1999

  53. [62]

    Phan and H

    M. Phan and H. Peng, Progress in Materials Science 53, 323 (2008)

    2008

  54. [63]

    Buschow, Handbook of magnetic materials , 1st ed., Vol

    K. Buschow, Handbook of magnetic materials , 1st ed., Vol. 15 (Elsevier B.V., 2003)

    2003

  55. [64]

    Levenberg, Quarterly of Applied Mathematics 2, 164 (1944)

    K. Levenberg, Quarterly of Applied Mathematics 2, 164 (1944)

    1944

  56. [65]

    D. W. Marquardt, Journal of the Society for Industrial and Applied Math- ematics 11, 431 (1963)

    1963

  57. [66]

    Kittel, Physical Review 73, 155 (1948)

    C. Kittel, Physical Review 73, 155 (1948)

    1948

  58. [67]

    J. A. Osborn, Demagnetizing factors of the general ellipsoid (1945). 45

    1945

  59. [68]

    Aharoni, Journal of Applied Physics 83, 3432 (1998)

    A. Aharoni, Journal of Applied Physics 83, 3432 (1998)

    1998

  60. [69]

    Cullity and C

    B. Cullity and C. D. Graham, Introduction to magnetic materials (Wiley, 2009)

    2009

  61. [70]

    Tomus and H

    D. Tomus and H. P. Ng, Micron 44, 115 (2013)

    2013

  62. [71]

    A. J. Manuel and J. M. P. S. Quinton, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 273, 412 (1963)

    1963

  63. [72]

    T. E. Kolding, IEEE Transactions on Electron Devices 47, 734 (2000)

    2000

  64. [73]

    Kikuchi, Y

    H. Kikuchi, Y. Urakawa, and M. Tanii, Journal of Magnetism and Magnetic Materials 539, 168356 (2021)

    2021

  65. [74]

    N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, 1976)

    1976

  66. [75]

    R. J. Wakelin and E. L. Yates, Proceedings of the Physical Society. Section B 66, 221 (1953)

    1953

  67. [76]

    Yamaguchi, S

    M. Yamaguchi, S. Tanaka, Y. Endo, S. Muroga, and M. Nagata, 2015 Asia-Pacific International Symposium on Electromagnetic Compatibility (APEMC) , 536 (2015)

    2015

  68. [77]

    Klokholm and J

    E. Klokholm and J. A. Aboaf, Journal of Applied Physics 52, 2474 (1981)

    1981

  69. [78]

    Neidhardt, S

    J. Neidhardt, S. Mr´ az, J. M. Schneider, E. Strub, W. Bohne, B. Liedke, W. M¨ oller, and C. Mitterer, Journal of Applied Physics 104, 10.1063/1.2978211 (2008)

    2008 doi

  70. [79]

    Gall, Journal of Applied Physics 119, 1 (2016)

    D. Gall, Journal of Applied Physics 119, 1 (2016)

    2016

  71. [80]

    Nahrwold, J

    G. Nahrwold, J. M. Scholtyssek, S. Motl-Ziegler, O. Albrecht, U. Merkt, and G. Meier, Journal of Applied Physics 108, 10.1063/1.3431384 (2010)

    2010 doi

  72. [81]

    Hubert and R

    A. Hubert and R. Sch¨ afer,Magnetic Domains (Springer Berlin Heidelberg, 2009). 46

    2009

  73. [82]

    Y. Endo, T. Ito, T. Miyazaki, Y. Shimada, and M. Yamaguchi, Journal of Applied Physics 117, 1 (2015)

    2015

  74. [83]

    Br¨ omer and H

    H. Br¨ omer and H. Huber, Journal of Magnetism and Magnetic Materials 8, 61 (1978)

    1978

  75. [84]

    J. M. Barandiar´ an, A. Garc ´ ıa-Arribas, and D. de Cos, Journal of Applied Physics 99, 4 (2006)

    2006

  76. [85]

    Mohri, T

    K. Mohri, T. Kohzawa, K. Kawashima, H. Yoshida, and L. V. Panina, IEEE Transactions on Magnetics 28 (1992)

    1992

  77. [86]

    K. Hika, L. V. Panina, and K. Mohri, IEEE Transactions on Magnetics 32, 4594 (1996)

    1996

  78. [87]

    Morikawa, Y

    T. Morikawa, Y. Nishibe, H. Yamadera, Y. Nonomura, M. Takeuchi, and Y. Taga, IEEE Transactions on Magnetics 33, 4367 (1997)

    1997

  79. [88]

    Garc ´ ıa-Arribas, J

    A. Garc ´ ıa-Arribas, J. M. Barandiar´ an, and D. de Cos, Journal of Magnetism and Magnetic Materials 320, 5 (2008). 47

    2008

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