1 Introduction

The giant magnetoimpedance (GMI) effect is a change in the complex impedance at high frequency (usually >0.1 MHz) and arises from the magnetic field-induced change of the dynamic relative permeability μr of the magnetic material. The GMI-based magnetic sensors have several advantages (smaller size, high sensitivity, higher stability and lower power), so the GMI effect is extensively studied in soft amorphous ferromagnetic wires (Atalay et al. 2006; Li et al. 2003), thin film (Zhou et al. 2001; Makhnovskiy et al. 2004), and ribbons (Yang et al. 2014; Chen et al. 2009a, b) in order to produce high-performance and practical GMI-based sensors. In today’s word, the GMI-based magnetic sensors are widely used in electronic compass, magnetic ink reading, vehicle detection, non-destructive testing of metals, detection of biomarkers, and so on.

The GMI effect of the amorphous ribbon may be related to the high transverse permeability caused by the transversely oriented domain configuration (Panina et al. 1995). The amorphous ribbon has low magnetostriction and controlled magnetic anisotropy, so much work has been done on the GMI effect in soft magnetic Co-based amorphous wires and ribbons (Beach and Berkowitz 1994; Sommer and Chine 1996; Jang et al. 2000). Recent years, some biosensor prototypes based on GMI effect of the amorphous ribbon with single strip structure (Kurlyandskaya et al. 2003; Devkota et al. 2013; Yang et al. 2010) and tortuous shape (Chen et al. 2011; Yang et al. 2010) were introduced into biosensing field. So, it is very significant to observe the effect of size, magnetic field and frequency on the GMI ratio of the ribbons with single strip structure and tortuous shape. Chaturvedi et al. (2010) reported a systematic study of the influence of sample length on the GMI effect and its field sensitivity (%/Oe) in Co69Fe4.5Ni1.5Si10B15 amorphous ribbons with single stripe and a width of 1 mm in the frequency range of 0.1–10 MHz. The influence of varying width from 4 mm down to 300 μm on the GMI effect in soft ferromagnetic amorphous Co65Fe4Ni2Si15B14 ribbons with single stripe and a length of 1 cm was investigated by Devkota et al. (2014). The effect of length and width on the GMI effect in micro-patterned Co-based ribbons with a meander structure was investigated by Yang et al. (2014). Chen et al. (2009a, b) revealed that the maximum GMI ratio was got in the three-turns meander ribbon with 600 μm line width at a frequency of 20 MHz and a field of 10 Oe, however, the designed length of 10 mm was a little bit of large. In order to meet the requirements of biosensor using amorphous ribbon to detect the biomarker, a miniaturization technology of amorphous ribbon is needed, and MEMS technology is the best choice for the micro-sized GMI-based sensor. It is possible to use amorphous ribbons in more biosensing fields.

So, in this context, micro-patterned Co-based amorphous ribbons (Metglas® 2714A) with single strip structure and tortuous shape were fabricated by MEMS technology. The GMI ratio of the with single strip structure (length = 5 mm, width = 250 μm) and tortuous shape (length = 5 mm, width = 250 μm, and turn number = 6) at different magnetic fields (0–60 Oe) and frequencies (1–40 MHz) was discussed. The influence of different length (5 and 10 mm) and widths (250–2000 μm) on the GMI ratio of the ribbons with single strip structure was observed, and at the same width and length, the GMI ratio of the ribbon with single strip structure was compared with those in the ribbons with tortuous shape of varying turn numbers from two turns to six turns.

2 Experimental procedures

In this section, the micro-patterned GMI sensor elements were made of a Co-based commercials amorphous ribbon (Metglas® 2714A). The main physical and magnetic properties of the ribbons were listed in Table 1.

Table 1 The main physical and magnetic properties of commercials ribbon
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Before MEMS processing, some rectangular ribbons (20 μm thick, 5 cm wide and 8 cm long) were annealed with an applied magnetic field along the transverse direction of the sample to induce a transverse anisotropy. A transverse induced anisotropy was evident from the magnetization curve as shown in Fig. 1. The whole annealing processing was finished in a small vacuum chamber within which the ribbon was fixed firmly. A permanent magnet was placed at the center of chamber with 200 Oe field strength. It took 1.5 h to reach the annealing temperature of 250 °C (higher than the Curie point of Co-based ribbon). When the temperature reached to 250 °C, heating was kept on this temperature for 3 h and then it took 5 h to cool down to room temperature gradually.

Fig. 1
figure 1

Transverse hysteresis loop of the field-annealed ribbon

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The micro-patterned ribbons with single strip structures and tortuous shape (two-turn, four-turn, and six-turn structures) (as shown in Fig. 2a) were designed with width of 250 μm and length of 5 mm. In addition, the micro-patterned ribbons with single strip structures were designed with different widths (250, 500, 1,000, 1,500, 2,000 μm) and length of 10 mm. The intervals of tortuous shape were 30 μm. Each ‘n’ shape in the meander structures was called one turn. The ribbons with different structures were fabricated by photolithography and chemical etching methods. Firstly, the ribbon was bound on clean glass substrates using an epoxy adhesive, during binding we should try to ensure tight bonding and no air between the ribbon and the substrate. And then photoresist coating with thickness of 10 μm was spun on the surface of the ribbon and patterned by lithography. At last, the ribbon was etched in an acidic mixed solution (mixture of HNO3, HCl, H2O2 and H2O with a certain proportion) for 5 min. After removing photoresist layer, we got the micro-patterned Co-based ribbons with different structures as shown in Fig. 2b. The micro-patterned ribbons with single strip structures and the length of 10 mm were not shown here.

Fig. 2
figure 2

a Top view of the micro-patterned ribbon with different structure; b photograph of the samples after etching process

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The GMI effects in micro-patterned ribbon were measured by an impedance analyzer (HP4194A) in the frequency range of 1–40 MHz with the constant current amplitude of 10 mA. An external magnetic field (Hex) of 1–60 Oe was applied along the longitudinal direction of the sample. Magnetic field is got from a permanent, the magnitude of that was controlled through changing the distance between the permanent and micro-patterned ribbon. The permanent slowly closed to the ribbon along the central axis of ribbon. Magnetic fields at different locations were measured strictly by a magnetometer, so the different marked locations standed for different magnetic fields (Yang et al. 2014). Figure 2a shows the different structures of patterned ribbons and the direction of the AC current and external magnetic field. The GMI ratio is defined as: GMI ratio (100 %) = 100 % × [Z(H) − Z(H 0)]/Z(H 0), where Z(H) and Z(H 0) are the magnetoimpedance with and without magnetic field, respectively.

3 Results and discussion

Figure 3 shows field and frequency dependence of the GMI ratio for micro-patterned Co-based amorphous ribbons with single strip structures (l = 5 mm, w = 250 μm). In sample testing, an external magnetic field of 1-60 Oe is applied along the longitudinal direction of the meander ribbon and is perpendicular to the transverse anisotropy direction of the sample.

Fig. 3
figure 3

a Field and b frequency dependence of the GMI ratio of the ribbons with single strip structures (l = 5 mm, w = 250 μm)

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The maximum GMI ratio is 44 % and obtained at Hex = 10 Oe and frequency f = 40 MHz. On increasing the applied magnetic field Hex, the magnitude of the GMI ratio first reaches a sharp peak and then gradually decreases to zero and even negative values. This typical characteristic has been observed by Sommer and Chine (1996). Sommer indicates that a longitudinal GMI spectrum of soft magnetic materials with high transverse permeability has the typical characteristic. The GMI curves in Fig. 3a agree well with this typical characteristic, which can be explained by the magnetization rotation model (Kumar et al. 2007; Amalou and Gijs 2001) and it goes as follows: the rotational magnetic permeability related to the GMI ratio increases with the increase in Hex and reaches a maximum value as Hex = HK, where Hex is perpendicular to the transverse anisotropy direction of the sample and HK is the anisotropy field. Thereafter, the permeability decreases with Hex and the GMI ratio gradually drops. The anisotropy field HK of the ribbons with single strip structure is different at different frequency as can been seen in Fig. 3a. Besides, we can find the GMI curve at the frequency of 40 MHz is different from others. In the rage of 0–10 Oe, the GMI ratio changes drastically, and sometimes does not exceed to the value at low frequency.

It is observed that all the maximum values are obtained at 40 MHz (named as relaxation frequency), The relaxation frequency, where the peak GMI ratio is located, are the same under different magnetic fields and got in the measuring range of 1–40 MHz. However, it tends to move upward with the increase of measuring range of frequency, this is different from that mentioned in some work (Jang et al. 2000; Prida et al. 2003). The GMI ratios tend to move upward all the time when the magnetic field Hex = 10–30 Oe, and the GMI ratio first decreases and then increases to the peak GMI ratio when the magnetic field Hex = 40–60 Oe as can be seen in Fig. 3b. The curves have no intersection. The frequency dependence of the GMI ratio of the ribbon can be explained with two different magnetization mechanisms, called domain wall movement and magnetization rotation, which dominates in lower and higher frequency ranges, respectively. In the low frequency range (1 MHz to several MHz), the GMI effect originates mainly from the variation of the skin depth, due to a strong change in the effective permeability caused by the external field Hex (Phan and Peng 2008), in the high frequency range (several tens of MHz), reduction in the GMI ratio is related to the fact that the domain walls become strongly damped by the eddy current and only magnetization rotation contributes to GMI.

The micro-patterned ribbons with single strip structure were designed with different widths (250, 500, 1,000, 1,500, 2,000 μm) and length of 10 mm to observe the effect of size on GMI ratio (Fig. 4). It is obvious the maximum of GMI ratio (64 %) in the single strip- structured sample with 250 μm width and 10 mm length is large than that mentioned above (43 %). From the previous work (Yang et al. 2014), the increase of the length from 5 mm to 10 mm leaded to an increase of the GMI effect. In present work, we only observed two lengths of 5 and 10 mm on the effect of GMI ratio, and we think the GMI ratio increases with the increasing of length from 5 to 10 mm. This is different from the report made by Chaturvedi et al. (2010), Chaturvedi considers that there exists a critical length (∼8 mm) below which the maximum GMI decrease with decreasing sample length (L) and above which they increase with decreasing L. Different raw material composition and thermal treatment may be used to explain it. The increase of the length of the sample may result in an increase in magnetized uniformity and soft magnetic properties. The length of micro-patterned ribbons with single strip structures used in biosensing field was usually more than or equal to 10 mm (Kurlyandskaya et al. 2003; Devkota et al. 2013; Yang et al. 2010; Chen et al. 2011), so the sample with 10 mm length was designed. From the Fig. 4a, at the frequency of 40 MHz, we can find the maximum of the GMI ratio decrease from 64 % in the sample with 250 μm width to 24 % in the 2,000 μm sample. The HK of the different-width ribbon with single strip structure is 5–10 Oe. The frequency dependence of the GMI ratio for single strip-structured ribbons with different widths is shown in Fig. 4b, and the GMI ratios of different line-width samples are chose at the Hk. We can find the maximum of the GMI ratio are obtained at the frequency <40 MHz (22 MHz for 250 μm, 24 MHz for 500 μm, 15 MHz for 1,000 μm, 11 MHz for 1,500 μm and 5 MHz for 2,000 μm). The high frequency is not advisable in practical application. The experimental results show the ribbons (length ≥10 mm) with single strip may be used in biosensing field (Kurlyandskaya et al. 2003; Devkota et al. 2013; Yang et al. 2010; Chen et al. 2011). Compared with the research (Chaturvedi et al. 2010; Devkota et al. 2014), smaller size (width = 250 μm) and wider operational frequency of the ribbon are observed.

Fig. 4
figure 4

a Field and b frequency dependence of the GMI ratio of the single strip-structured ribbons with different widths (l = 10 mm)

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The field and frequency dependence of the GMI ratio of the tortuous-shaped ribbons with six turns (l = 5 mm, w = 250 μm) are shown in Fig. 5. The maximum GMI ratios of six turns structure is 82 %. The relaxation frequency is 40 MHz. According to the definition of HK mentioned above, the HK of the ribbon of tortuous shaped is 15–20 Oe. The field dependence of the GMI ratio of the tortuous-shaped ribbons (Fig. 5a) has the same variation trend compared with Fig. 3a, so the same explanation of the mechanism can be presented mentioned above. In Fig. 5a, the anisotropy field HK of patterned ribbons that the peak GMI ratio varies in the range of 15–20 Oe (15 Oe for 5–10 MHz and 20 Oe for 20–40 MHz).

Fig. 5
figure 5

a Field and b frequency dependence of the GMI ratio of the tortuous-shaped ribbons with six turns (l = 5 mm, w = 250 μm)

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On increasing the frequency, the GMI ratio of the ribbon with six turns urges intersection at different magnetic field (Fig. 5b), we consider the complex magnetic interaction between turns is the main result. With respect to impedance when an ac current with a high frequency is applied to a ferromagnetic material and the skin effect appears, the impedance Z can be expressed as follows: Z = R(ω, μ) − j X(ω, μ) = R(ω, μ) − j ω[Ls (ω, μ) + Lm(ω, μ)], where R is the resistance, X is the reactance, Ls is the self-inductance, Lm is the mutual inductance, inductance L = Ls + Lm, ω is the ac current frequency and μ is the permeability of the conductor, which changes with Hex and ω. For the tortuous-shaped ribbon, Lm is very complex and the main reason leading to the great change of the GMI effect, because several factors should be considered, such as distribution of the magnetic field in the conductor and exterior space, distribution of the ac current, magnetic interaction among each individual line segment, effect of the domain structure, and the magnetoelastic anisotropies on permeability and so on.

Figure 6 shows field and frequency dependence of the GMI ratio of the tortuous-shaped ribbons with different turns (l = 5 mm, w = 250 μm). And the GMI ratios of different samples in Fig. 6b are chose at the Hk and different frequencies. The results show that the GMI ratios of the ribbons with tortuous shape are lager that of the ribbon with single strip-structured ribbon. This result is identical with the previous research by Chen et al. (2009a, b). Compared with the research, we design small length and investigate the influence of more turns number on GMI ratio of the ribbon with tortuous shape. The maximum of the GMI ratio increases from 44 % for the single strip-structured sample to the 82 % for the sample with six turns. This is can be explained from the point of the view of inductance. When the ac current flows through the tortuous ribbon, just as for the flux in each longitudinal and transverse straight line in a plane inductance, the fluxes will correlate with each other by mutual inductance of the magnetic chains. This is higher than the self-inductance of a single strip structure and the more turns of the meander structure, the more intense the interaction becomes. As a result, these effects lead to the increase in Lm and Z. Although the maximum of the GMI ratio (82 %) is largest, the work frequency was a little high. So Co-based amorphous ribbon with tortuous shape should be further studied in biosensing field, the aim is to get high GMI ratio at lower frequency and smaller size.

Fig. 6
figure 6

a Field and b frequency dependence of the GMI ratio of the tortuous-shaped ribbons with different turns (l = 5 mm, w = 250 μm)

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4 Conclusion

In conclusion, the GMI ratio of micro-patterned Co-based amorphous ribbon with single strip structure increases with increasing in length and decreases with the increasing in width. The increase of the length of the sample may result in an increase in magnetized uniformity and soft magnetic properties. The ribbon (length = 10 mm) with single strip structure can get higher GMI ratio at lower frequency (<40 MHz). The GMI ratio of micro-patterned tortuous-shaped Co-based amorphous ribbon with six turns is biggest with 82 %, obtained at a frequency of 40 MHz and a field of 20 Oe, and the GMI ratio increases with the increasing of turn from two turn to six turns. All mechanisms (line width and tortuous shape) that influence the inductance and resistance will result in changes in the impedance and the GMI effect. The anisotropy field HK (15–20 Oe) of tortuous-shaped ribbon that the peak GMI ratio is larger than that (5–10 Oe) of the ribbon with single strip structure. The effect of the frequency on the GMI ratio of the ribbons with tortuous shape is more complex. This can be explanation by complex inductance of tortuous shape ribbon.