Influence of demagnetizing field on thin-film GMI magnetic sensor elements with uniaxial magnetic anisotropy

Sensors and Actuators A 230 (2015) 142–149

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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna

Influence of demagnetizing field on thin-film GMI magnetic sensor elements with uniaxial magnetic anisotropy Hiroaki Kikuchi a,∗ , Shingo Kamata a , Tomoo Nakai b , Shuichiro Hashi c , Kazushi Ishiyama c a b c

Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka, Iwate 020-8551, Japan Industrial Technology Institute, Miyagi Prefectural Government, Sendai, Miyagi 981-3206, Japan Research Institute of Electrical Communication, Tohoku University, Sendai, Miyagi 980-8577, Japan

a r t i c l e

i n f o

Article history: Received 27 November 2014 Received in revised form 13 April 2015 Accepted 24 April 2015 Available online 9 May 2015 Keywords: Giant magnetoimpedance Demagnetizing field Uniaxial anisotropy Impedance change Sensitivity Discontinuous jump

a b s t r a c t We investigated the dependence of demagnetizing effect on the giant magnetoimpedance (GMI) properties of elements fabricated using a thin film with uniaxial magnetic anisotropy. Using photolithography techniques, we fabricated two types of sensor elements. One type has a typical GMI configuration, i.e., the easy axis is parallel to the width of the sensor element, whereas the other type has an inclined easy axis. In sensors with a typical GMI configuration, the impedance changes and sensitivity at the edges of the elements are reduced relative to the middle sections, whereas the discontinuous impedance jump is substantially reduced or modified in sensors with inclined easy-axis GMI elements. This divergence in behavior can be explained by the differences in the distribution of demagnetizing fields within the respective element types. Because the demagnetizing field has an increased gradient of growth at the edge of an element, rotation or movement of the magnetization moment becomes increasingly modified. We confirmed the changes in the distribution of the demagnetizing field within the element using magnetic-field analysis and confirmed by domain observation that nonuniform magnetic domain movement occurs at the edge of the element. The change in the direction-to-gain ratio associated with higher element sensitivity is also discussed, and a method to effectively utilize the discontinuous jump is introduced. Only the central part of the element should be used to eliminate the influence due to the distribution of the demagnetizing field. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Giant magnetoimpedance (GMI) elements are used in highly sensitive magnetic-field sensors [1]. Such sensors, which are composed of amorphous wires, are currently used as compasses in mobile phones [2], and research aimed at developing medical applications [3,4] and nondestructive testing methods [5] for GMI sensors continues to advance. On the other hand, many attempts have been made to investigate the development of materials, control anisotropy, sensor structures, and theoretical models to optimize GMI elements to achieve higher sensitivity, especially on wires and ribbons [6–12], and these works were reviewed in Ref. [6]. Recently, miniaturization of electronic devices and progress in fast signal processing have created a need for miniaturization of GMI elements. One prospective method to achieve this target is to use thin-film configurations because these are

∗ Corresponding author. Tel.: +81 19 621 6890; fax: +81 19 621 6890. E-mail address: [email protected] (H. Kikuchi). http://dx.doi.org/10.1016/j.sna.2015.04.027 0924-4247/© 2015 Elsevier B.V. All rights reserved.

compatible with integrated electronic devices. However, miniaturization will unavoidably decrease the sensitivity of thin-film GMI sensors because of the generation of demagnetizing fields. With regard to the demagnetizing effect, although the effect of shape anisotropy on the GMI properties was investigated in Ref. [13], the effects of the demagnetizing field must be more precisely ascertained to optimize design sensitivity in terms of sensor configuration. In the current study, we prepared sensor elements in which the GMI properties could be measured at different positions to assess the effect of the demagnetizing field at each point. The impedance was measured, and domain observations were experimentally performed for each of the prepared elements because the changes in the domain structures could provide us instructive information in interpreting the sensor behavior. We also calculated the impedance profiles by considering the demagnetizing effect using magnetic-field analysis. On the basis of our results, we discuss the influence of the demagnetizing field at various positions on an element and derive an indicative method to obtain higher sensitivity and to utilize the discontinuous impedance jumps.

H. Kikuchi et al. / Sensors and Actuators A 230 (2015) 142–149

2. Experimental procedure

3. Experimental results

Rectangular elements comprised of Co85 Nb12 Zr3 amorphous films were fabricated using photolithography and rf-sputtering processes. The elements were 2-␮m-thick each and were either 20-, 40-, or 80-␮m wide. The lengths varied from 1 to 5 mm. Each element was annealed in vacuum by applying a field of 3 kOe (240 kA/m) at 673 K to induce uniaxial magnetic anisotropy, with the anisotropy direction oriented at 0◦ or 60◦ relative to the width axis. The elements with an easy axis of 0◦ had typical GMI properties [6,12], whereas those with a 60◦ easy axis demonstrated hysteresis and discontinuous impedance jumps [14–18]. A Cu electrode was then fabricated to evaluate the impedance of different 1-mmlong sections of each element. Fig. 1 shows a photograph and the dimensions and structure of the 3-mm-long fabricated element. Starting from the right in Fig. 1(a), each element position is labeled in sequence as “0–1,” “1–2,” and “2–3”; for the other elements with different lengths, the positions are labeled in the same manner. The impedances along each 1-mm interval in the elements were measured using a network analyzer (HP8752A) by reflection method and a wafer probe (Picoprobe 40A-GSG-150-LP) by alternating the intensity of an applied DC external field. The applied current had a high-frequency of 100 MHz, and the incident power was −10 dBm. The network analyzer applied a high-frequency current along the length direction of the element (the current generated an exciting AC magnetic field in the transverse direction) and detected the reflected power, calculated the reflection coefficient  , and obtained the impedance of the elements using the following equation:

3.1. Impedance changes

1+ 1−

Figs. 2 and 3 show the impedance changes as a function of the external DC field for the 3-mm-long elements with easy axes of 0◦ and 60◦ , respectively, and with widths of 20, 40, and 80 ␮m. For each width, the 0◦ easy-axis results show that the impedance reaches a peak at approximately ±8 Oe (640 A/m), which is therefore the magnitude of the anisotropy field Hk of the film. The peak height decreases with increasing element width. By comparing the intensities at the edge positions of the elements (i.e., 0–1) with those in the middle section (1–2), we can see that the field intensity at maximum impedance becomes slightly stronger (an increase of within approximately 0.1 Oe), whereas the peak height decreases. For example, the impedance changes from 36 to 52  in the middle section (1–2), whereas it changes from 36 to 48  at the edge position of the elements (0–1) for the 20-␮m-wide element. No shift

55 Impedance Z (Ω)

edge middle

(1)

where Zc is the characteristic impedance of the transmission line; Zc was 50  in this study. The right side of Fig. 1(a) shows the setup used for impedance measurement in section “0–1” of the 3-mm element. “G” and “S” in the photograph indicate the ground and signal lines, respectively. Additionally, the domains of the respective elements were observed using a Kerr-effect microscope (NEOARK BH-68786IP) by applying a DC external field. The DC external field generated by a Helmholtz coil was applied to the elements along the longitudinal direction during the impedance measurements and domain observations. The applied DC external magnetic field was uniform within the area of the elements.

50 45 40 35 -16 -12 -8 -4 0 4 8 12 16 Magnetic field H (Oe) (a) 20 μm

30 28 Impedance Z (Ω)

Z = Zc

143

edge middle

26 24 22 20 18 16 -16 -12 -8 -4 0 4 8 12 16 Magnetic field H (Oe) (b) 40 μm

12 Impedance Z (Ω)

edge middle

11 10 9 8 -16 -12 -8 -4 0 4 8 12 16 Magnetic field H (Oe) (c) 80 μm

Fig. 1. Photograph, dimensions, and structure of the fabricated element.

Fig. 2. Field dependence of the impedance of the elements with an easy axis of 0◦ and with widths of 20, 40 and 80 ␮m.

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50 46 44 42

26

0-1 1-2 2-3 3-4

24 22 20

40

18

38

16 -16 -12 -8 -4 0 4 8 12 16 Magnetic field H (Oe)

36 -2

-1 0 1 Magnetic field H (Oe)

2

Impedance Z (Ω)

28 Impedance Z (Ω)

48 Impedance Z (Ω)

22

30 edge middle

(a) 0°

0-1 1-2 2-3 3-4

21 20 19 18

17 -4 -3 -2 -1 0 1 2 3 4 Magnetic field H (Oe) (b) 60°

Fig. 4. Field dependence of the impedance of the 40-␮m-wide and 4-mm-long elements with easy axes of 0◦ and 60◦ .

(a) 20 μm

Impedance Z (Ω)

22 21

edge middle

20 19 18 17 -2

-1 0 1 Magnetic field H (Oe)

2

(b) 40 μm

11 Impedance Z (Ω)

10.5 10 9.5 9

field strength at which impedance jump occurs drastically changes depending on the width of the element. For example, when the magnetic-field alignment changes from positive to negative, an impedance drop down is observed at −0.17 Oe (−14 A/m), 0.5 Oe (40 A/m), and 1.1 Oe (88 A/m) in the 20-, 40-, and 80-␮m-wide elements, respectively (these points are indicated by arrows in Fig. 3). In other words, the magnitude of the field jump increases with the element width, which is consistent with the results described in Ref. [19]. The jumping point depends on the magnitude of shape anisotropy Sa introduced by Matsuo in Ref. [20]. Sa is proportional to ky –kx , where kx and ky are the demagnetizing factors along the longitudinal and width directions of the element, respectively. The jumping point shifts to a higher applied field with the decrease in Sa , and Sa decreases with the increase in the element width. Fig. 4 shows the impedance profiles of the 40-␮m-wide 4mm-long elements with easy axes of (a) 0◦ and (b) 60◦ . The characteristics at positions “0–1” and “3–4” and at “1–2” and “2–3” are all similar to those at the corresponding positions in the 3-mmlong elements shown in Figs. 2(b) and 3(b), a trend that is further confirmed in the measurements of the 1-, 2-, and 5-mm-long elements. In each element, the 1-mm section around the element edge experiences impedance change-induced deterioration relative to the inner sections.

edge middle

8.5 -4 -3 -2 -1 0 1 2 3 4 Magnetic field H (Oe) (c) 80 μm Fig. 3. Field dependence of the impedance of the elements with an easy axis of 60◦ with widths of 20, 40, and 80 ␮m.

in the peak position is observed with increasing element width, although the peak width becomes broader as the element width increases. The results for each of the elements with a 60◦ easy axis show noticeable discontinuous jumps in the central region of the impedance profiles (1–2). The impedance is almost 40  at 2 Oe (160 A/m), and then it gradually increases followed by a drop to 38  at −0.17 Oe (−14 A/m) with the decrease in the applied field for the 20-␮m-wide element. Thereafter, the impedance maintains a relatively lower value, it jumps to 44  at −0.5 Oe (−40 A/m), and decreases to 40  at −2 Oe (−160 A/m). The same trend is observed in the middle parts of the elements with different widths. However, although the jump height obviously decreases at the edges (0–1) of the 20-␮m-wide element, the jump discontinuities are only barely observable at the edges of the 40- and 80-␮m-wide elements. The

3.2. Domain structure observations Figs. 5 and 6 show the domain observations at the edge and in the middle sections of the 40-␮m-wide 3-mm-long elements with easy axes of 0◦ and 60◦ , respectively, under various applied field strengths. The corresponding impedance changes (half-cycle) are also presented. In each element, decreasing the applied magnetic field in the positive quadrant causes a nucleation domain to appear in the initial single-domain structure at the end of the element [10 Oe (0.8 kA/m) for the 0◦ easy-axis element and 10.5 Oe (0.84 kA/m) for the 60◦ easy-axis element] and propagate toward the middle of the element (Figs. 5(a) and 6(a)). In addition, multiple domains suddenly appear and disappear in the wider middle parts of the 60◦ easy-axis elements (at 0.5 Oe (40 A/m) in Fig. 6 (b)). The field intensity in which a sudden domain structure change occurs is consistent with the field strength at which discontinuous jumps in the impedance occur (please see the blue line of the impedance changes shown in Fig. 6). The domains in the middle of the elements with an easy axis of 0◦ (Fig. 5(b)) do not show discontinuous changes, and they appear or disappear near the field position where the impedance peaks. Within the domains, the magnetization direction tends to gradually rotate toward a parallel orientation relative to the applied field.

H. Kikuchi et al. / Sensors and Actuators A 230 (2015) 142–149

145

Fig. 6. Domain structures at the edge and in the middle parts of the elements with an easy axis of 60◦ (width = 40 ␮m). (For interpretation of the references to color in the text, the reader is referred to the web version of this article.)

Fig. 5. Domain structures at the edge and in the middle parts of the elements with an easy axis of 0◦ (width = 40 ␮m).

Z

4. Discussion

dZ/dH

Cycle 1

Zm

Z

Cycle 2

4.1. Sensitivity of typical GMI sensor The 0◦ easy-axis elements show typical GMI properties and are utilized for higher sensitivity sensors. Because the quantitative changes in impedance and the slope of the impedance change against the field are important, they are discussed in this section. Fig. 7(a) shows the definition of impedance change Z and sensitivity dZ/dH. Fig. 8 shows the summaries of Z and dZ/dH measured for elements with an easy axis of 0◦ . dZ/dH is the maximum of the derivative of Z with respect to H, whereas Z is defined as Z = Zm − Z0 , where Zm is the peak value of the impedance and

ΔΖ Z0

ΔHm H (a)

Hu2 Hd1 0 Hd2 Hu1

H

(b)

Fig. 7. Sketch of the impedance profile for the (a) 0◦ and (b) 60◦ easy-axis elements. Definitions of Z, dZ/dH, and jumping fields Hu1 , Hd1 , Hd2 , Hu2 , and Hm .

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15 40 μm

10 80 μm

5

20 μm

Demagnetizing field Hd (Oe)

20 μm

Sensitivity dZ/dH (Ω/Oe)

Impedance change ΔZ (Ω)

1.2

20

20

15

10 40 μm 5 80 μm 0

0 Edge

Middle

Edge

Middle

Position

Position

(a) ΔZ

0.8 0.6 0.4 0.2 0 -1.5

(b) dZ/dH

Fig. 8. Z and dZ/dH for elements with an easy axis of 0◦ .

Z0 is the impedance at H = 0. The results indicated by the dots include all data measured from the 1-, 2-, 3-, 4-, and 5-mm-long elements. “Edge” means the parts that include the end of the elements, whereas “middle” means the parts that exclude the end of the elements. The lines show the tendency of the results and are obtained from the averaged measured values. Both averaged Z and averaged dZ/dH are larger in the middle sections than at the edges; the Z value decreases at the edges by 4.3, 4.2, and 2.2  relative to the middle section in the 20-, 40-, and 80-␮m-wide elements, respectively. The dZ/dH value decreases at the edges by 4.8, 4.9, and 1.1 /Oe in the same elements, respectively (3-mm-long elements were used. The data in the middle parts are the result of “1–2”, and the data at the edges are averaged values of “0–1” and “2–3”). The difference in the dZ/dH value in the 80-␮m-wide elements is smaller than those of the other elements with different widths, which is attributed to wider and broader demagnetizing field distribution, as discussed in Section 4.3. We can see a relatively large deviation in the sensitivity in the 20-␮m-wide elements, which is why we used a 25-mm square wafer and the thickness of the film has the deviation about 10% on the film, and the 20-␮m-wide elements have a relatively higher impedance. 4.2. Novel magnetic sensors utilizing discontinuous impedance jump

|Hd1 | + |Hd2 | 2

-1

-0.5 0 0.5 Position x (mm)

1

1.5

Fig. 9. Calculation results of the distribution of the demagnetizing field inside the elements.

Hu =

|Hu1 | + |Hu2 | 2

(3)

In addition, the largest impedance jumps or impedance changes similar to those defined in Section 4.1 are defined as Z, and the Z value is listed in Table 1. In this table, “NA” means that the element shows no discontinuous impedance jumps. The impedance change Z at the edge of the elements obviously decreases compared with that in the middle part. Although partial discontinuous impedance jumps appear at the edge part of the elements, almost edges show no impedance jump, i.e., “NA” in Table 1. This result indicates that control of the demagnetizing field distribution is quite important to utilize the discontinuous jump in developing a novel field sensor with switching and memory functions. The Hm and Hu values increase, and the Hd value decreases with the increase in the width of the elements in the middle parts. These results are consistent with the trend predicted by the simple domain structure model [18], which is explained using the magnitude of shape anisotropy Sa to be the same as the results presented in Section 3.1. 4.3. Effect of demagnetizing field

To develop a novel magnetic-field sensor that can be used as a switching element as well as for impedance jump-based detection of the threshold field, the process mentioned in Section 3.2 can be applied to the elements with an easy axis of 60◦ . The impedance profile for the 60◦ easy-axis elements is shown in Fig. 7(b). When the applied field H varies from the minimum to the maximum (Cycle 1), Z initially increases gradually and drops at Hd1 ; then, it stays at a relatively lower value and jumps up at Hu1 . By contrast, the impedance drops at Hd2 and jumps up at Hu2 when the applied field varies from the maximum to the minimum (Cycle 2). Here, the field range where the impedance shows a lower level is defined as Hm , which is equal to Hu1 –Hd1 or Hd2 –Hu2 . Table 1 lists the summary of the Hm , Hd , and Hu values, defined by the following equations for the edge and middle parts of the elements: Hd =

w=20 μm, l=3 mm w=80 μm, l=3 mm w=20 μm, l=1 mm

1

(2)

Fig. 9 shows the calculation results of the distribution of the demagnetizing field in the 1- and 3-mm-long elements with widths of 20 and 80 ␮m and thickness of 2 ␮m. The calculation was performed by the magnetic moment method (Qm, produced by Shift Lock Corporation). The magnetic moment method solves unknown magnetization of the material using integral equation method and then obtains the magnetic field by the magnetization and the field from other sources (applied current, magnet, etc.) [21]. In the calculations, the direction parallel to the longitudinal direction of the element is defined as the x-axis, and the center of the element is defined as the origin. The relative permeability of the element along the x direction is defined as r = 1000, and a uniform magnetic field of 1 Oe (79.6 A/m) is applied along the x direction of the element. We used the value of r which is close to the value obtained from Hk /0 Ms of the film used in this study, where Ms is the saturation of magnetization. The magnetic flux density B along the x direction inside material was calculated by the magnetic moment method

Table 1 Values of Hm , Hd , Hu , and Z at the edge and in the middle parts of a 60◦ easy-axis element. Width (␮m)

20 40 80

Z ()

Hm (Oe)

Hd (Oe)

Hu (Oe)

Edge

Middle

Edge

Middle

Edge

Middle

Edge

Middle

2.48 0.80 0.50

9.58 2.56 0.68

NA NA NA

0.20 1.12 2.22

NA NA NA

0.23 0.016 0.011

NA NA NA

0.44 0.76 1.25

H. Kikuchi et al. / Sensors and Actuators A 230 (2015) 142–149

0.006 Demagnetizing factor N

80 μm

Ms

0.004 middle

αHk 0

0.002 0.001 -1

-0.5 0 0.5 Position x (mm)

B 0 r

1

Fig. 11. Sketch of the magnetization curves using calculations for the impedance profile that take into account the distribution of the demagnetizing field.

1.5

(4)

where 0 is the permeability in vacuum. The demagnetizing field is given by the difference of the applied field (1 Oe here) and the effective magnetic field Heff . The demagnetizing field of the element has the following distribution properties: the field at the edge is larger than that in the middle section, whereas the field gradient is maximum at the edge and decreases inward until it becomes almost zero around the central region. As the element width increases, both the area over which the demagnetizing field is distributed and the field strength increase, whereas both the demagnetizing field strength and distribution decrease with increasing length. The demagnetizing field Hdem is expressed as follows: M 0

(5)

where N is the demagnetizing factor, M is the magnetization of the element. Since it is widely accepted the demagnetizing factor N depends on only configuration of element, we adopt the assumption in this discussion. By using the calculated magnetic flux density B (x) and the given uniform magnetic field H, the effective permeability of the element eff (x) (this is affected by demagnetizing effect) at the position x is expressed by the following equation: eff (x) =

B(x) 0 H

(6)

Using the given relative permeability (here, r = 1000) and the effective permeability by Eq. (6), the value of N(x) is obtained using the following equation [22]: r − eff (x) N(x) = eff (x)(r − 1)

(7)

Using Eqs. (6) and (7), we can calculate the distributions of N(x) and the results are shown in Fig. 10. Since the value of N is a function of position x, Hdem and the effective field in the element Heff are also a function of position x as follows: Heff (x) = Hex − Hdem (x) = Hex − N(x) M(x) =

Ms (Hex − ˛Hk ) Hs (x) + Hk

Hs (x) = N(x)

Ms 0

H

(1)

and then the effective magnetic field Heff was calculated using the following relation.

Hdem = N

Hk

(4)

Fig. 10. Dependence of the calculated demagnetizing factor on the position of the elements.

Heff =

(2)

(3)

edge

0.003

0 -1.5

Hs

M

20 μm

0.005

147

M(x) 0

(8) (9) (10)

where Hex is the applied uniform external field, Ms is the saturation magnetic flux density of the element, Hs (x) is the demagnetizing

field when the element at the position x is saturated, and ˛ is constant. The magnetization curves for the calculation of M(x) are shown in Fig. 11. For the element with an easy axis of 0◦ , because the external field is applied to the direction perpendicular to the easy axis, i.e., the hard axis of the elements, the magnetization curve that does not take into account the demagnetizing field is shown as the curve (1) in Fig. 11. It is linear against the applied field and saturates at anisotropy field Hk . When the demagnetizing effect is considered, additional field Hs (x), which is represented in Eq. (10), is required to magnetically saturate the material, and the magnetization curve becomes curve (2) in Fig. 11. Because the curve is proportional to the applied external field and has no hysteresis, ˛ = 0 in Eq. (9). When Hex is altered, magnetization M(x) at position x is obtained by Eq. (9), and thus, demagnetizing field Hdem (x) and effective field Heff (x) at position x are obtained by Eq. (8). For the element with an easy axis of 60◦ , the external field has an inclination of 30◦ from the easy axis, and the magnetization curve has remanence and coercivity. Therefore, the magnetization curve is represented by curve (3) in Fig. 11. It has a coercivity ˛Hk , and we assume ˛ = 0.55 here. The value of ˛ was determined as follows: the magnetization curves of a single magnetic moment can be calculated by the Stoner–Wohlfarth model [23]. When the magnetic field is applied parallel to 30◦ from the easy axis, the magnetization switches at nearly 0.55Hk [24]. The magnetization curve that considers the demagnetizing effect becomes curve (4), as shown in Fig. 11. Hdem (x) can be calculated using this curve. Because the impedance depends on the applied field and the effective applied field depends on position x owing to the distribution of the demagnetizing field, Z at position x is expressed as Z {Heff (x)}. Thus, the total impedance of the element (l1 and l2 are the positions at the ends of the elements, and l2 –l1 is the length of the elements) becomes Z=

1 l2 − l1



l2

Z{Heff (x)}dx.

(11)

l1

When the impedance profile without demagnetizing field is given as Z(H), the impedance profiles of the elements considering the effect of the demagnetizing field can be calculated using Eq. (11), and the calculated results are shown in Figs. 12 and 13. The parameters (l1 , l2 ) are (−0.5, 0.5) and (0.5, 1.5) for the middle and edge parts, respectively. The green solid line denotes the ideal impedance profile without the demagnetizing effect, and the dots show the calculation results. The experimental results for middle parts were used as the ideal impedance profiles. Because the distribution of the demagnetizing field is uniform and the demagnetizing field is small in the middle parts, the estimated results in those are expected to the same as the impedance profile without demagnetizing field. This is enough for the investigation to compare the effect of demagnetizing field distribution on the impedance profiles between the middle and the edge parts. In the result for the

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11.5 ideal edge middle

50

ideal edge middle

11 Impedance Z (Ω)

Impedance Z (Ω)

55

10.5

45

40

10 9.5 9

35

0

5 10 15 Magnetic field H (Oe)

8.5

20

(a) 20 μm

0

5 10 15 Magnetic field H (Oe) (b) 80 μm

20

Fig. 12. Calculated impedance profile that takes into account the distribution of the demagnetizing field elements with an easy axis of 0◦ . “ideal” means impedance profile without demagnetizing field given as Z(H) (the experimental results for middle parts were used as the ideal impedance profiles). Dots show the estimated value calculated by Eq. (11) and function Z(H).

20-␮m-wide element with 0◦ easy axis, the profile in the middle part is almost the same as the ideal impedance profile, i.e., it has a sharper peak at 8 Oe (640 A/m) except the slight deviation around 10–15 Oe, which is attributed to that the demagnetizing field is uniform and its intensity is close to zero in the central parts of the element (Note that the slight deviation implies the demagnetizing field distribution and intensity is not completely zero). On the contrary, the impedance change decreases in the result for the edge part. The reason is that the demagnetizing field has a wide distribution at the edge as shown in Fig. 9. In the result for the 80-␮m-wide element, the profile in the middle part is almost the same as the ideal impedance profile, but the peak position slightly deviates to a higher field (within 0.1 Oe) because the demagnetizing field is uniform but has a small intensity in the central parts of the element. On the other hand, the peak height decreases, and the peak position obviously deviates at the edge parts. The demagnetizing effect has a strong distribution at the edge part, as previously mentioned (Figs. 9 and 10). The demagnetizing field distribution causes a decrease in the impedance gradient, a shift in the peak position toward a higher field intensity, and an unclear impedance peak, demonstrating that the intensity in which the impedance peaks varies with respect to the position. In the elements with an easy axis of 60◦ , the discontinuous impedance jumps diverge, resulting in attenuation or an absence of discontinuous jumps at the edges of these elements (attenuation in the 20-␮m element and absence in the 80-␮m element), whereas those with a 60◦ easy axis in the middle parts demonstrate sudden 50

46

10.5 ideal edge middle

Impedance Z (Ω)

Impedance Z (Ω)

48

α = 0.55

impedance jumps. In the middle parts, all magnetic moments in the domains move or rotate together at the same field strength because the demagnetizing field is uniform. By comparing the calculation results with the experimental results, we can see that both results quantitatively and qualitatively agree well for the 0◦ easy-axis elements (see Figs. 3 and 12). In the 60◦ easy-axis elements, the calculation results are qualitatively consistent with the experimental results but have quantitatively slight deviations (see Figs. 4 and 13). The reason for the deviation is that the magnetization curves used in the calculation are different from those used in the experimental data. On the basis of the calculation of the demagnetizing field described above, when Hex = 10 Oe (0.8 kA/m) is applied to the 3-mm-long and 40-␮m-wide elements, the demagnetizing field becomes Hdem = 0.1 Oe (8 A/m), i.e., Heff = 9.9 Oe (0.79 kA/m) at the center part of the elements. Therefore, all magnetic moments are aligned to the direction parallel to the applied field, and no domain appears at Hex = 10 Oe (0.8 kA/m), as shown in Fig. 5. When Hex decreases, all moments move together because the demagnetizing field is uniform, and the changes in the domain shown in Fig. 5 are observed. On the other hand, the demagnetizing field becomes Hdem = 1 Oe (80 A/m) to 8.5 Oe (0.68 kA/m) and is distributed at the edges of the elements; hence, the element is partially saturated (Heff is from 1.5 to 9 Oe). Thus, the 180◦ domain structure remains at 10 Oe (0.8 kA/m). The propergative behavior in the domain structure can be explained by the distribution of the demagnetizing field.

44 42 40 38 36 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Magnetic field H (Oe)

(a) 20 μm

α = 0.55

10

9.5

9

ideal edge middle

8.5 -4 -3 -2 -1 0 1 2 3 Magnetic field H (Oe)

4

(b) 80 μm

Fig. 13. Calculated impedance profile that takes into account the distribution of the demagnetizing field elements with an easy axis of 60◦ . “ideal” means impedance profile without demagnetizing field given as Z(H) (the experimental results for middle parts were used as the ideal impedance profiles). Dots show the estimated value calculated by Eq. (11) and function Z(H).

H. Kikuchi et al. / Sensors and Actuators A 230 (2015) 142–149

Sections 4.1 and 4.2 mentioned that Z, dZ/dH, and the discontinuous jump at the edge parts for the 0◦ and 60◦ easy axes deteriorate compared with those in the middle parts . These results indicate that only the sensing elements that use a carrier current in the center of the element should be used because this will avoid the effects of the demagnetizing field distribution and thereby improve the sensitivity or utilize the abrupt impedance jump. Discontinuous impedance jump appears on the profiles of the elements with a 60◦ easy axis, which can be applied to a sensor that detects a threshold field. From the sketch shown in Fig. 7(b), when the applied magnetic field gradually increases from a zero magnetic field, the impedance jumps up at the intensity of Hu1 ; the field intensity of Hu1 becomes the detection threshold level. The impedance also maintains a relatively high impedance level after the discontinuous jump when the applied magnetic field decreases and stays under Hu1 (until the applied magnetic field decreases at Hd2 ). This result means that the element memorizes the applied magnetic-field overpass threshold level. If controlling the intensity of Hu1 and Hd2 is possible, a sensor element detection threshold with a memory function is realized. To precisely detect the threshold, the impedance must show an abrupt step at the threshold, which indicates that the element should be utilized while avoiding the demagnetizing effect. 5. Conclusions The GMI properties at different positions of a sensing element have been investigated to verify the effects of the distribution of the demagnetizing field on sensitivity. We show that the impedance gradient and therefore the sensitivity decreased at the edges of an element with a 0◦ easy axis. In addition, discontinuous impedance jumping was suppressed in elements with a 60◦ easy axis. To confirm the effect of the demagnetizing field on the obtained results, a brief estimation of the impedance profile that considered the distribution of the demagnetizing field was performed. The calculation results agreed well with the experimental results. Therefore, we conclude that the deterioration of the properties at the edge of the elements can be mainly attributed to the distribution of the demagnetizing field. The important point obtained from the results is that only the central regions of an element should be utilized for sensing applications to eliminate the adverse effect due to the distribution of demagnetizing field. Our results provide a guide for future works that will lead to the development of both a higher-sensitivity magnetic-field sensor and a sensor to detect the threshold fields with a memory function. Acknowledgments This work was supported in part by the Cooperative Research Project of the Research Institute of Electrical Communication, Tohoku University, and in part by the Grant-in-Aid for Challenging Exploratory Research, Grant No. 23656259, and for Scientific Research (B), Grant No. 25289119, from the Japan Society for the Promotion of Science. References [1] K. Mohri, K. Bushida, M. Noda, H. Yoshida, L.V. Panina, T. Uchiyama, Magnetoimpedance element, IEEE Trans. Magn. 31 (1995) 2455–2460. [2] C.M. Cai, M. Yamamoto, H. Aoyama, Y. Honkura, K. Mohri, in: Digests of the IEEE International Magnetics Conference, 3-Axis amorphous wire type giant magneto-impedance sensors (2005) 407–408. [3] S. Yabukami, K. Kato, Y. Ohtomo, T. Ozawa, K.I. Arai, A thin film magnetic field sensor of sub-pT resolution and magnetocardiogram (MCG) measurement at room temperature, J. Magn. Magn. Mater. 321 (2009) 675–678.

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Biographies Hiroaki Kikuchi received the B.E., M.E. and Ph.D. degrees from Tohoku University, Sendai, Japan, in 1995, 1997 and 2002, respectively. He is currently an Associate Professor in the Faculty of Engineering, Iwate University, Morioka, Japan. His research interests include magnetic field sensors using ferromagnetic thin film and development of electromagnetic nondestructive evaluation techniques. Shingo Kamata received the B.E. and M.E. degrees from Iwate University in 2013 and 2015. He is currently working at Ogikubo Tools & Dies Mfg. Co., Ltd., Japan. He developed highly sensitive magnetic field sensor using ferromagnetic thin films. Tomoo Nakai received the B.E. and Ph.D. degrees from Tohoku University in 1988 and 2005, respectively. He is currently working at the Industrial Technology Institute, Miyagi Prefectural Government, Sendai, Japan. His research interests include development of magnetic field sensors and its applications. Shuichiro Hashi received the B.E. and M.E. degrees from University of the Ryukyus, Nishihara-cho, Japan, in 1990, 1992 and received the Ph.D. degree from Tohoku University in 1998. He is currently an Associate Professor in the Research Institute of Electrical Communication, Tohoku University. His research interests include magnetic materials, magnetic sensors and motion capture systems. Kazushi Ishiyama received the B.E., M.E. and Ph.D. degrees from Tohoku University in 1986, 1988 and 1993, respectively. He is currently a Professor in the Research Institute of Electrical Communication, Tohoku University. His research interests include magnetic materials, magnetic sensors and actuators using magnetic materials.