Experimental evaluation of domain wall dynamics by Barkhausen noise analysis in Fe30Co70 magnetostrictive alloy wire

Accepted Manuscript Research articles Experimental evaluation of domain wall dynamics by Barkhausen noise analysis in Fe30Co70 magnetostrictive alloy wire Takahiro Yamazaki, Yasubumi Furuya, Wataru Nakao PII: DOI: Reference:

S0304-8853(18)31054-0 https://doi.org/10.1016/j.jmmm.2018.11.011 MAGMA 64570

To appear in:

Journal of Magnetism and Magnetic Materials

Received Date: Revised Date: Accepted Date:

10 April 2018 30 October 2018 2 November 2018

Please cite this article as: T. Yamazaki, Y. Furuya, W. Nakao, Experimental evaluation of domain wall dynamics by Barkhausen noise analysis in Fe30Co70 magnetostrictive alloy wire, Journal of Magnetism and Magnetic Materials (2018), doi: https://doi.org/10.1016/j.jmmm.2018.11.011

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Experimental evaluation of domain wall dynamics by Barkhausen noise analysis in Fe30Co70 magnetostrictive alloy wire Takahiro Yamazaki1, Yasubumi Furuya,2 and Wataru Nakao1 1

Department of Materials Science and Engineering, Yokohama National University, Yokohama 240-8501, Japan 2

Micro System Integration Center, Tohoku University, Sendai 980-0845, Japan E-mail: [email protected]

________________________________________________________________________________________

Abstract Magnetic Barkhausen noise (MBN) plays significant roles to describe the dynamic of domain walls (DWs), but an in-depth understanding of the correlation between Barkhausen effect and magnetostrictive effect during magnetization process is still limited. In this study, we investigated MBN signals and the frequency spectra in a high-magnetostrictive Fe30Co70 alloy wire (λs = 102 ppm) by evaluating the stress effects on MBN profiles at the stress range of 0-150 MPa using tensile test machine. The results from MBN profiles revealed that MBN in the high magnetic field region was responsible for the localized changes of magnetic flux density, dB/dt induced by magnetic distortion related to non-180o DWs or the magnetization rotation. In MBN spectra, the peak shift towards lower frequencies with the increase of stress indicates that the rough pulse-like MBN outbreaks increase, and it results mainly from the increase of DW jumping length which is caused by the pinning effect at grain boundaries where DW energy is relatively high. In addition, stress dependence of the root mean square (RMS) value of MBN showed a good sensitivity (0.038 mV/MPa). Overall, these findings indicate that new MBN measurement system utilizing magnetostrictive materials can be helpful for a wide range of applications such as mechanical stress sensors and energy harvester systems. Keywords: Magnetostrictive materials, Domain wall dynamics, Magnetic Barkhausen noise, Stress sensor, Frequency spectrum

1. Introduction Magnetostrictive materials, which is one of the smart materials utilizing energy conversion with external magnetic fields as a mechanical function, have attracted considerable recent interest as alternative methods to conventional energy supply systems to implement efficient Internet of Things (IoT). The use of inverse magnetostrictive effect (also known as the Villari effect) plays an increasingly key role in many applications, including actuators, damping devices, energy harvester systems, and stress sensors [1–4]. One of the typical magnetostrictive materials, Terfenol-D (Tb-Dy-Fe) exhibits huge magnetostriction with low magnetic anisotropy [5]. The large magnetostriction (λs = 800–1600 ppm) arises from structural phase transitions at the boundaries between TbCo2 and DyCo2 phases, originally implicated from a study of piezoelectricity enhancement at the morphotropic phase boundary of PbZrO3-PbTiO3 systems [6]. However, some problems related to the brittleness or the high eddy current losses for the materials are still unsolved. While large magnetostriction (λs ~ 400 ppm) and steel-like mechanical properties in Galfenol (Fe-Ga-Al) alloys under very low magnetic field were achieved by controlling of the precipitation phases, microstructures, and magnetic domain structures [7–10]. However, Galfenol has not yet been commercialized due to the inferior in the productivity and the workability. Moreover, Fe-Co alloys having high Co content (66 ≦ Co ≦ 75 mol%) with excellent workability, large magnetostriction, high strength, and low production cost have been developed [11–18]. Yamaura et al. prepared cold 1

rolled polycrystalline Fe1-xCox (x = 75-85 mol%) alloys (rolling rate ~ 97%) and exhibited large magnetostriction (λs = 128 ppm) along the rolling direction using as-rolled Fe25Co75 alloys [14]. More recently, we have developed the Fe30Co70 alloy film plate (thickness ~0.02 mm) [15] and the Fe30Co70 alloy wire (diameter ~0.02 mm) [16]. These materials having strongly textures of {110} <001> orientation exhibited a relatively high mechanical, magnetic and magnetostrictive properties. In particular, it was found that the output power characteristics due to the inverse magnetostrictive effect in the micro energy harvesting device have low correlation not only with magnetostriction but also with coercive force and residual magnetic flux density. This result implies that it is impossible to estimate the output power using only the magnetostrictive constant which is a static or semi-static parameter, and it is necessary to evaluate dynamic magnetization and magnetostriction characteristics. Narita [17] demonstrated that the output performance was increased as the applied stress rate increased by evaluating the influence of residual stress in Fe-Co fiber/ polymer composites. The trend is sufficiently similar between the calculation and measurement. However, the differences exist between theoretical and experimental results [18]. He inferred that the error of the output value did not consider domain wall (DW) dynamics, i.e., Barkhausen effect which is a microscopic phenomenon during the magnetization process. Magnetic Barkhausen noise (MBN), which is a minute change of magnetic flux density occurred by the discontinuous DW movement, has been investigated since H. Barkhausen found its phenomenon in 1919 [19]. MBN is generated by the pinning effect at microstructures such as grain boundaries [20,21], sub-grain boundaries [22,23], and dislocations [24,25]. In addition, the measurement conditions such as residual/ applied stress [26–30], magnetizing frequency and magnetizing/ pick-up coil system [31] are also important factors of Barkhausen effect. In particular, Durin and Zapperi [32–34] reported the stress effects on MBN parameters by investigating the MBN distributions, scaling exponents, and magnetic domain structures in FeCoB amorphous ribbon (λs = 46.5 ppm). Similarly, Bohn et al. [35] discussed the magnetization processes occurring in the low and high magnetic field region for non-oriented electrical steel sheet with {110} <100> texture in order to evaluate the relationship between MBN and magnetostriction in reference to 90o and 180o DWs movement, and the magnetic domain evolution like a nucleation, growth, and annihilation as shown in Fig. 1. However, there are few cases where the MBN behavior in magnetostrictive materials under changing stress has been evaluated, and the influence of metallographic structure on the microscopic MBN mechanism and its stress effect in magnetostrictive alloys have not been clarified. Therefore, we aim to evaluate the correlation between Barkhausen effect

and magnetostrictive effect

by

establishing a MBN detection and analysis system under changing tensile stress. Furthermore, we investigated the stress dependence of MBN profiles and the frequency Fig. 1 Schematic illustration of the pinning effect (magnetic Barkhausen noise) and Joule effect (magnetostriction) during the magnetization process.

spectrum in annealed FeCo alloy wire for the long-standing challenge in synthesizing new magnetostrictive materials. 2

Besides, the fabricated MBN stress sensor in this study was

designed for

engineering application,

especially for the first step toward the establishment of nondestructive

inspection

technology

of

stress/

accumulated damages assuming the embedded or fixed type mechanical sensor for structural health monitoring. 2. Experimental

2.1. Sample preparation Fig. 2 Microstructural images of the (a) longitudinal and (b) cross-sectional section of annealed Fe-Co magnetostrictive alloy wire obtained by laser scanning microscope.

Extruded wires of a high magnetostrictive (λs = 102 ppm) Fe30Co70 alloy having a diameter of 1 mm, which is produced by Tohoku Steel Co. (Japan) were prepared in this study. These samples were annealed at 420°C for 24 hours in a vacuum sealed quartz tube with Ar in order to remove the residual stress and internal strains. The obtained wires were subsequently cut to a length of 120 mm for MBN measurement. Figure 2 shows typical microstructural images of the longitudinal and crosssectional section of the sample obtained by a laser microscope (Keyence Co., VK-X250). Crystal grains were extended to the drawing direction with the average width, dg ≈ 13 µm and the aspect ratio, RD/TD ≈ 8.2. The annealed sample had a single bcc phase without any impurities or precipitation phases. Furthermore, a strong [110] <001> texture was

Fig. 3 MBN measurements system. (a) The dimension of the specimen and magnetizing/ pick-up coil. (b) Apparatus block diagram of measuring and analyzing MBN signal.

formed by wire drawing processing as a result of electron backscatter diffraction (EBSD) analysis using a field emission scanning electron microscope, FE-SEM (JEOL Ltd., JSM-7001F). Our previous experiments [16] have described that this annealed FeCo alloy wire shows a high strength (UTS ≈ 1100 MPa), low coercivity (Hc = 13.1 Oe) and a high saturation magnetization (Ms = 200.6 emu/g). 2.2. Magnetic Barkhausen noise measurement setup Figure 3 shows the block diagram of the experimental setup for measuring MBN under changing tensile stress. The specimen was magnetized by a triangular wave current transmitted from a function generator (3B Scientific Corp., FG-100) to a magnetizing coil (φin = 10 mm (φout = 20 mm) x 28 mm) with 2500 turns. Subsequently, the generated signals (magnetic flux density change, dB/dt) were detected using a small pick-up coil (φin = 3 mm (φout = 6.4 mm) x 12 mm) with 1750 turns.

3

The detected signals were amplified by the amplifier (40 dB) after passing through the high pass filter (300 Hz) and low pass filter (10 kHz). The signals were acquired and digitized by a data logger (Keyence Co., NR600-HA08) with the sampling rate of 50 kHz. The maximum applied voltage was set to 8 V (= 0.15 A), and the magnetic field was measured by Gauss Meter (Denshijiki Industry Co., Ltd., GM 5005). Here, the applied magnetic field (Hmax = 21.6 Oe) was calculated from the average field/ voltage ratios of 2.7 [Oe/V] at the position of the pick-up coil when the maximum voltage of 8.0 V was applied to the magnetizing coil. While the effective magnetic field (Heff) in the wire could be higher than that in the air out because the magnetostrictive material has a large relative magnetic permeability (µr ~ 500-1000 [36]). MBN measurements were carried out with an elastically tensile stress up to 150 MPa along the drawing direction [001] using a tensile test machine (AG-5 kN, Shimadzu Corp.). There was almost no effect of clamping both edges of the sample directly. On the other hand, it is assumed that a complementary MBN signal caused by the minute change in magnetic flux density due to magnetostriction itself when a magnetic field is applied to the sample is measured because the distortion of the sample is fixed by the clamp. 2.3. MBN data acquisition The pick-up coil was set about 5 mm apart from the edge of the magnetizing coil not only for reducing the noises induced by the mutual inductance but also for designing MBN detection sensor considering the engineering application as a stress sensor to the infrastructure in the future. Actually, the magnetizing coil generates the distribution of magnetic field strength in the length direction of the pick-up coil, so it is inevitable to be sensitive to discuss the magnetization process and the behavior of MBN generation. However, this point can be almost ignored by the following four arguments. (1) The magnetic field propagation induced by the magnetizing coil occurred only inside the FeCo wire because the magnetostrictive material has a large relative magnetic permeability. (2) Since the magnetostrictive material has a uniform wire shape, the magnetization process (generation, movement, and rotation of magnetic domain) and the behavior have homogeneous distribution at each point in the longitudinal direction. (3) Because the MBN generation behavior at each point in the longitudinal direction has always analogous waveform, it is possible to collect the averaged MBN output data over the longitudinal direction inside the pick-up coil even though there is the change depending on the magnetic field strength distribution from the magnetization coil. As a result, the acquired data can be regarded as a representative value of MBN change in the center portion of the pick-up coil. (4) The experimental data demonstrated that the change of MBN profiles (signals strength, the shape changes of the RMS envelope and frequency spectra) is almost the same as in case of using two magnetizing coils (See Appendix). As described above, from (1) to (4), it can be considered that the MBN mechanism can be sufficiently discussed even in setting the one side pick-up coil with the FeCo wire in this experiment. Furthermore, it was experimentally confirmed that there is almost little or no influence of electromagnetic or mechanical noise which may be generated due to a tensile test machine. Finally, the magnetizing frequency was set to 0.25 Hz in order to suppress the eddy

4

H (Oe)

------ MBN signals ------ RMS envelope 30 20 10 0 -10 -20 -30

σ=56

VP2

σ=0

σ=75

σ=19

σ=113

1.0 0.5 0.0 -0.5

I

MBN (V)

VP1

σ=38

-1.0 0.0

0.5

1.0

1.5

σ=150

2.0

Time (s)

Fig. 4 Input and output signals at a stress of 56 MPa. Fig. 5 MBN signals and the root mean square (RMS) Each profile shows (a) exciting voltage; (b) magnetic envelopes (gray line) of MBN for annealed Fe-Co alloy flux density change, dB/dt, (c) magnetic flux density, B, wire under the stress of 0-150 MPa. and (d) MBN (black line) and the root mean square (RMS) envelopes (gray line); where µmax shows the maximum magnetic permeability and the VP1 and VP2 are the first peak in the low filed (LF) region and the second peak in the high field (HF) region, respectively. current caused by the skin effect. Due to skin depth considerations, MBN is primarily a surface technique, with

the detected MBN signal originating from depths less than ~0.2 mm below the surface [25, 37, 38]. 2.4. Data analysis After acquiring MBN signals at the different stress levels, fast Fourier transform (FFT) and Wavelet Transform (WT) analysis carried out using OriginPro (OriginLab Corp.), which is a data analysis and graphing software in order to identify the MBN occurrence factors. In addition, the root mean square (RMS) value, VRMS of the MBN spectra is calculated from the MBN profiles, X(f) using the following equation,
 

| | ∆

,

(1)

    

(2)

where 

   

and x(t) indicates MBN profiles as a function of time. In each FFT analysis result, 10-time series are acquired along the half hysteresis loop, and the effective VRMS of the MBN is the average value of the VRMS of 10 acquisitions. 3. Results and discussion

3.1. MBN profiles in low and high magnetic field region

5

Table 1 Results of MBN profiles for FeCo alloy wire at different tensile stress levels.

No.

Stress (MPa)

1

1st peak of RMS envelope, Vp1(σ)

2nd peak of RMS envelope, Vp2(σ)

Applied magnetic field (Oe)

Peak voltage (mV)

Applied magnetic field (Oe)

Peak voltage (mV)

0

3.09

22.8

15.8

19.2

2

19

3.41

28.1

14.9

22.1

3

38

3.13

40.8

12.7

30.1

4

56

3.05

45.1

9.61

38.1

5

75

2.72

43.9

7.67

67.9

6

113

2.70

58.1

5.79

77.7

7

150

2.57

75.0

4.06

115

Vp1(150)/Vp1(0) = 3.29

Vp2(150)/Vp2(0) = 5.99

Figure 3 shows the exciting voltage having a triangular waveform and the output signals detected by the pick-up coil as a function of time at 56 MPa stress. The effective B(t) induced in the pick-up coil as shown in Fig. 4c was calculated using the dB/dt by Faraday's law,  ＝･ ･ $ ＝

!" 

%  &･'

!

d ,

,

(3) (4)

where v(t) is the voltage generated in the pick-up coil expressed as a function of time, N is the number of turns of the pick-up coil, A is the area of the pick-up coil, and B(t) is the average magnetic flux density at the center of pick-up coil. Here, B(t) shows a slightly smaller value than its actual value because the high-frequency components of the v(t) were cut off by the low pass filter (10 kHz) or by the skin effect on the surface of the specimen. Nevertheless, B(t) is approaching the saturation where the maximum magnetic permeability µmax of the FeCo wire is exceeded as compared the profiles as shown in Fig. 4(b) and Fig. 4(c). Also, Fig. 4(d) shows a time series of MBN obtained by passing through the high pass filter (300 Hz) in order to remove an induced B(t) generated by the magnetizing coil. Making a connection with the induction B－H curves, the same regions along a half cycle of the curve as shown in Fig. 4d. It can be seen that these curves are separated in the following region; the low magnetic field (LF) region and high magnetic field (HF) region, where each magnetic induction region is associated to a particular dominant magnetization process. In the LF region, the MBN signals greatly increased to the first peak voltage (called VP1) where the magnetic flux density became around B(H) = B (µmax). And then, decreased slightly; whereas in the HF region, the MBN signals increased again to the second peak voltage (VP2), and eventually dropping to almost zero before the input field reached the maximum magnetic field. Next, the stress effects on the MBN signals were investigated. It is shown that the MBN profiles and the RMS envelope measured when the tensile stress of 0, 19, 38, 56, 75, 113, 150 MPa is applied to FeCo alloy wire in the longitudinal direction as shown in Fig. 5. Furthermore, Table 1 shows the peak voltages (Vp1, Vp2) and the applied magnetic field at each time as MBN measurement parameters from these MBN profiles and the RMS envelopes. Focusing on the peak values of the RMS envelope, the both Vp1 and Vp2 were increased. In each region, the output ratios showed VP1 (150) / VP1 (0) = 3.29 and VP2 (150) / VP2 (0) = 5.99, respectively. These results revealed that the 6

MBN generated in the HF region shows the larger change with the increase of stress than that in the LF region. For the VP1, it is suggested that the increase of MBN signal can be caused by the increase in the magnetic permeability [31] as the applied stress increased. For the VP2, on the other hand, MBN signals showing the Vp2 was due to non-180o DW motion or the magnetization rotation in the HF region since it occurs after the Vp1 is generated. In particular, it is considered that the second peak of MBN envelope is due to the inverse magnetostrictive effect in the HF region because the displacement of the total length was constant when the sample was clamped by the tensile testing machine. The distortion of the wire in the longitudinal direction induce the relatively large dB/dt in the specimen. 3.2. Frequency spectra In order to further understand the Barkhausen effect in

Fig. 6 Frequency spectra at a stress of 56 MPa. (a) A single MBN profile, (b) Wavelet transform (WT) analysis result and (c) fast Fourier transform (FFT) analysis results in the LF region (above) and in the HF region (below).

FeCo magnetostrictive alloy wire, the frequency spectra of

Pinning interval, lp/vw (ms)

analysis as shown in Fig. 6. Here, we performed the WT

7

σ = 150

6

σ = 75

5

σ=0

analysis for a specimen under a stress of 56 MPa. From the intensity distributions showing the color gradient, it was revealed that the MBN signal having relatively high frequencies in the LF region shifted to lower frequencies in the HF region as the applied magnetic field increased. Since the frequency axis and the time axis of MBN occurring

in

the

magnetization

process

of

the

magnetostrictive wire are displayed in the same graph, the frequency analysis of MBN shows internal stress

LSD (mV/Hz)

MBN signals were investigated by performing frequency

10 8

1

0.1

4 3 2 1 0 100

1000

Frequency (Hz)

10000

Fig. 7 Linear spectrum density (LSD) of MBN signals after performing FFT analysis at 0, 75, and 150 MPa stress.

distribution [39] and microstructure morphology [40], jumping phenomenon [41], etc., which provide very important information for the discussion on the MBN mechanism. Furthermore, FFT analysis was conducted in order to quantitatively investigate the changes in frequency spectra. The FFT analysis results in the LF region and in the HF region are shown in Fig. 6c. As a result, in the LF region, the frequency spectrum had relatively high-frequency components with the peak frequency of 520 Hz, while, in the HF region, the frequency spectrum had a relatively low-frequency component with the peak frequency of 340 Hz comparing the normalized RMS envelope of MBN spectra.

7

These results show that the generation factor of MBN

18

VRMS (mV)

15

V RMS

was changed from the 180o DWs movement to the 180o

Fitting

DWs movement or the magnetization rotation, referring to

12

the magnetization process of the ferromagnetic material

9

[42]. Assuming there are no transverse strains, the

VRMS = 0.038 σ + 9.5

6

magnetoelastic energy Eσ due to stress is )*  − 3.2 /0123 4, where λ is the magnetostriction and φ is the angle between the direction of magnetization and the

3 0

0

30

60

90

120

150

direction of applied stress [43]. Therefore, it is considered

Tensile stress (MPa)

Fig. 8 Stress dependence of the RMS value of MBN (VRMS) and the linear fitting.

that the B in FeCo wire increased by the stress-induced magnetic field Hσ (= 1/µ0

*

δEσ/δM). So, the λ in the

dynamic magnetization process is also affected by the magnetostrictive susceptibility, d m. These results can be said that shifting the MBN signals to the lower frequencies shows an important result to explain the dynamic behavior in the magnetization process. Next, FFT analysis under each stress was carried out. Fig. 7 shows a linear spectral density (LSD) at the stress of 0, 75, 150 MPa. The shift of frequency peaks toward lower frequencies with the increase of stress indicated that the jumping interval (lp/vw, where vw is DW velocity, and lp is pinning site length), which were calculated from the reciprocal of the MBN spectra. Therefore, it is considered that the peak frequency of MBN spectra shifted to lower frequencies with increased stress since the DW mobility increased and the interval of Barkhausen jump was widened. Finally, we investigated the stress dependence of the root mean square (RMS) value of MBN, VRMS in Fe30 Co70 magnetostrictive alloy wire as shown in Fig. 8. It is shown that VRMS has a linear relationship with applied stress with a slope of 0.038 mV per MPa. The quantitative fitting formula can be expressed as:
567  0.038 × σ + 9.5 .

(5)

The stress dependence in this sample shows a good sensitivity (0.038 mV / MPa). It is considered that the intercept of the fitted line depends on the magnetic permeability, µ (the Vp1 in the LF region), and the slope of the fitted line depends on the magnetostriction, λS (the Vp2 in the HF region) of the sample. These sensor characteristics for magnetoelastic stress for Fe-Co alloy wires can be equivalent to that of the other stress sensors utilizing the phenomena such as magnetic anisotropy [44, 45, 46], magneto-impedance (MI) [47], magnetic acoustic emission (MAE) [48], and magnetic switching using amorphous microwires [49], etc. This inclination or the change of VRMS might be a physical constant related to the Barkhausen effect contributing to a correction factor for estimating the power generation performance utilizing the inverse magnetostrictive effect in magnetostrictive materials. 3.3. Barkhausen jumps We discuss the DW dynamics based on metallography considering the stress effects on the MBN profiles and the frequency spectra in the magnetostrictive alloy. Fig. 9(a) shows image quality (IQ) map and inverse pole figure (IPF) map obtained by SEM-EBSD analysis of annealed FeCo alloy wire. From the crystal orientation distribution of this material, it can be seen that many fine sub-crystal grains (about several hundred nm to several micrometers) are

8

Fig. 9 Domain wall (DW) dynamics driven by a magnetic field along FeCo wire. (b) Image quality (IQ) map and inverse pole figure (IPF) map of the microstructure from the angle of ND. (a)Schematic of Barkhausen jump induced by the change of DW velocity due to the pinning effect, which is associating with the microstructures such as grain boundary (GB) or sub-grains. (c) Example of MBN signals and the enlarged wave profile at 56 MPa stress.

formed in a crystal grain. Moreover, there is a plurality of signals which the pulse signals with large output voltage are generated at wide intervals, while the pulse signals with small output voltage are generated at short intervals as shown in Fig. 9(c). This DW dynamics accompanied by the Barkhausen jump is resulting from the increase in the DW velocity, vw and the decrease in microstructural factors such as DW jump length lp according to the study by Hauser [50]. The microscopic magnetic flux change can be given as: @" @

∝ BC DE

%F GH

,

(6)

where α is a constant related to magnetostrictive susceptibility and the number of jumping walls, Ms the saturation magnetization, and µ0 is the magnetic permeability of free space. At this time, since the magnetic permeability in the material varies with the stress application, Barkhausen effect can be influenced sensitively by the DW dynamics in the magnetostrictive materials. Furthermore, the dynamic behavior of Barkhausen jump caused by the pinning effect can be explained by the pinning model [51] using DW energy. As shown in Fig. 9(b), the DW energy depending not only on the thickness of DW but also on the microstructures. Also, the vw can be expressed by the following equation using the DW energy per unit area, γw (x) with respect to the position x of the DW, I  −

@JF K @K

.

(7) 9

Fig. 9(b) shows the schematic illustration of DW dynamics influenced by the pinning effect at different stress. As a result, the MBN signals in the LF region show the length of the pinning site is small because the movement of 180° DWs include relatively small Barkhausen jumps. On the other hand, the MBN signals in the HF region indicate the length of the pinning site is large since the non-180° DW motion includes relatively large Barkhausen jumps. From these findings indicate that MBN features in a high-magnetostrictive Fe-Co alloy wire were utilized by taking into consideration the peculiar feature of MBN in the magnetostrictive alloy, that is, the magnetic distortion due to the magnetostrictive effect, which related to the non-180o DW motion or magnetization rotation in the HF region. 4. Conclusions We investigated magnetic Barkhausen noise (MBN) profiles and the frequency spectra in a high-magnetostrictive FeCo alloy (λs = 102 ppm) at the stress range of 0-150 MPa using the tensile testing machine for evaluating the correlation between Barkhausen effect and the magnetostrictive effect. As a result, the followings were revealed. (1) MBN profiles and the frequency analysis at the different tensile stress levels indicated that the peaks position shift towards lower frequencies with the increase of stress is caused by the increase of DW jumping length. (2) The stress dependence of the RMS value of MBN shows a good sensitivity (0.038 mV/MPa). This inclination is considered to be a physical constant related to the Barkhausen effect contributing to the estimation of power generation performance of magnetostrictive materials. (3) It is suggested that the DW dynamics accompanying Barkhausen jumps over the pinning obstacles with a small energy gap, but larger MBN signals occur at a large interval such as a grain boundary. In summary, these findings indicate that new MBN measurement system utilizing magnetostrictive materials can be helpful for the understanding Barkhausen effect from the point of view of metallography and for a wide range of applications such as mechanical stress sensors and energy harvester systems. Acknowledgments This work was supported by the Inter-University Cooperative Research Program of the Institute for Materials Research, Tohoku University (17K0076), and Grant-in-Aid for Scientific Research (B) (17H03140).

Fig. A1 Three type of MBN measurement system: (a) pile-up type and (b) Helmholtz-type.

10

Appendix Here, the details of the MBN experimental verification in the case of using two magnetizing coils or one magnetizing coil to pick-up coil are presented. We investigated MBN profiles using the following two types of MBN measurement system as shown in Fig. A1. One is the pile-up type system that the pick-up coil is set 5 mm apart from the edge point of magnetizing coil. The other is a Helmholtz type system that the pick-up coil is set between the two same magnetizing coils. The performance of the magnetizing coil was measured and calculated as following Eq. (A1) and the results are shown in Fig. A2, H (t) =

nI(t) b (l⁄2)-x r2 dydr,   2l(b-a) a (-l⁄2 )-x (r2 +y2 )3 ⁄2

(A1)

where n is the number of turns per unit length, I is the current, l is the length of the magnetizing coil, a and b are inside and outside diameter of the coil, respectively. The results of MBN measurement using two types of coil system in each case were shown in Fig. A3 and Fig. A4. These MBN profiles show the difference between when using (a) pile-up type and (b) Helmholtz-type coil system. As the results of our experimental data analysis, the tendencies of MBN data profiles (signals strength, the shape changes of the RMS envelope and frequency spectra) is almost similar between two types of the detecting system. In a comparison of these two types of MBN signals and frequency spectra as shown in Fig. A3(a)(b), the induced voltage of the pick-up coil in case of (b), becomes rather weaker than that of a case of (a). Moreover, the BMN signals of a case of (b) contain the irregular electromagnetic noise as shown the many peaks of spectra in the case of (b), which would result from the mutual inductance from both sides of magnetizing coils. From these reasons, it can be said that the influence of the spatial magnetic field gradients on the detected signals is considered to be very small to a negligible degree in this experiment as we described in Section 2.3.

Fig. A2 Magnetizing coil and the generated magnetic field distribution used in this study. Black plots indicate measure data and the red line shows theoretical data calculated from Eq. (A1).

11

(a) pile-up type (σ=56 MPa)

(b) Helmholtz type (σ= 50 MPa)

H (Oe) dB/dt (V)

dB/dt (V)

H (Oe)

30 20 10 0 -10 -20 -30 8 4 0 -4

3 0 -3 -6 0.6

1.6

MBN (V)

MBN (V)

-8

30 20 10 0 -10 -20 -30 6

0.8 0.0 -0.8 -1.6

0.3 0.0 -0.3 -0.6

0

1

2

3

4

5

0

1

Time (s)

3

4

5

0.003

0.010

Harmonic wave noise LSD (V/Hz)

Harmonic wave noise LSD (V/Hz)

2

Time (s)

0.005

0.002

0.001

0.000

0.000 0

2000

4000

6000

8000

0

10000

Frequency (Hz)

2000

4000

6000

8000

10000

Frequency (Hz)

Fig. A3 MBN profiles and the frequency spectra measured by using (a) pile-up type coil system and (b) Helmholtz type coil system.

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Highlights •

Domain wall dynamics in a high magnetostrictive Fe-Co alloy wire (λs = 102 ppm) was evaluated by magnetic Barkhausen noise (MBN) technique.

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Stress effect on MBN profiles and the frequency analysis were investigated by using a tensile test machine.

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The peaks of MBN spectra were shifted toward lower frequencies with the increase of tensile stress.

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The stress dependence of the root mean square (RMS) of the MBN signals shows a good sensitivity (0.038 mV/MPa).

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