Large Linear Giant Magneto-Impedance Response of Microwire Annealed under Liquid Medium for Potential Sensor Applications

Abstract

Herein, we have presented the giant magneto-impedance (GMI) effect, microstructure and surface domain structure of the Co-Fe-based amorphous microwires after liquid medium—anhydrous ethanol Joule annealing (AJA). The AJA technique can effectively release the radial stress and induce large a circumferential magnetic field by changing the Joule heat transfer and the circumferential domain, to further tune the GMI performance of microwire. The linear response fields (0~3.5 Oe), the high sensitivity of 124.1%/Oe and the high GMI ratio make the microwire as promising materials for the miniaturized GMI sensors. The GMI ratios of [ΔZ/Z₀]_max(%) and [ΔZ/Z_max]_max(%) increase the near-linearly to 201.9% and 200.5%, respectively, for the 250 mA anhydrous ethanol Joule annealed wires. Moreover, a linear response to H_ex (ranging from 3.5 to 25 Oe, or more) is observed, which bears the potential in fabricating bi-sensors.

1. Introduction

Amorphous microwires exhibit excellently soft magnetic properties and mechanical properties, which possesses promising applications [1,2,3,4,5,6]. In particular, the superior giant magnetic impedance (GMI) effect [7,8,9,10] of the Co-Fe-based wire makes it as a unique material for high-sensitivity magnetic sensors [11,12]. The GMI performance is mainly reflected for the high impedance ratio, fast response sensitivity and large magnetic field response range under the magnetic field [13,14,15]. However, as-cast magnetic microwire is often unable to be applied directly, due to the inner stress during the fabrication and requires the necessary subsequent modulation [16,17,18,19]. Generally, the modulation methods of the microwire are mainly joule annealing (JA), magnetic field annealing, stress annealing, pulse current annealing and so on [20,21,22,23]. Among them, the Joule annealing method has been widely used, owing to its easy-operation and significantly improved impedance effect [24]. A proper Joule heat annealing current amplitude can effectively release residual internal stress, induce the magnetic anisotropy field, and improve the soft magnetic properties of the microwires [14,15,25]. It is reported that the optimized current amplitude for the conventional JA modulation of the melt-extraction amorphous microwires with a diameter of 30 μm is 70~90 mA [26,27]. Theoretically, the larger current amplitude of the JA modulation is, the larger circumferential field will be induced, which is conducive to the improvement of the impedance ratio and field response sensitivity [25]. In fact, a large amount of Joule heat generated by large current amplitude annealing will tend to the crystallization of the microwires [25]. In order to further increase the current amplitude, the microwire can be modulated by Joule heat in a liquid medium which could rapidly cool for avoiding crystallization, thus realizing the effect of the high-current modulation of the microwire and generating a larger linear response field [15,25].

The microwire still shows a high impedance ratio after the JA with the current amplitude of 250~300 mA in a liquid medium (such as liquid nitrogen, liquid oil, etc.), and the linear response magnetic field ranged from 2.5 to 6 Oe [15,25]. However, it is also found that there is no linear response of the impedance ratio in the range of 0~2.5 Oe, which is unfit to the application of the magnetic sensor in weak field detection. In impedance ratio analysis, the ΔZ/Z₀(%) and ΔZ/Z_max(%) curves are usually very different, which results in the GMI sensor development in the different field detection can be only one way to define the impedance effect and adopt different modulation treatments. Therefore, a large linear response field range and a weak external field response sensitivity are the keys for realizing the application of the microwires in the GMI sensor detection at different magnetic fields, which remains to be further studied.

In the present work, a unique liquid medium—anhydrous ethanol Joule annealing method, is employed to improve the GMI performances of the as-cast wires. The analysis and discussion of the relationship among the microstructure, surface domain structure and GMI for microwires with the DC current amplitudes (0~600 mA) were performed. Particular attention is paid to the characteristic 250 mA current amplitude, corresponding with the discussion of the modulation mechanism.

2. Experimental

The alloy with the nominal composition of Co_68.15Fe_4.35Si_12.25B_11.25Nb₂Cu_2, is prepared in an argon atmosphere, by arc melting and then sucked into a copper mould with a diameter of 8 mm. The continuous amorphous microwires are fabricated by a home-built high-precision melt extraction technology, using a copper wheel with a diameter of 160 mm and a 60° knife-edge [28,29,30]. During the melt extraction process, the circumferential velocity of the copper wheel is 35 m/s, and the feed rate of the molten is fixed at 90 μm/s. The temperature of the molten alloy is controlled by a Raytek integrated ratio infrared thermometer (MR1SB, Raytek, Santa Cruz, CA, USA) to be 50 K higher than the melting temperature. The AJA treatments are carried out in a self-assembly equipment, as shown in Figure 1. The microwire is connected to the circuit and immersed in the liquid medium—absolute ethanol, which is encapsulated in an adiabatic cavity. The thermal insulation material is used to avoid the influence of the external temperature difference. With the Joule heat produced by the microwire, the absolute ethanol evaporates and constantly transfers heat to cool the microwire. The numerical controlled constant-current source adjusts the output current amplitudes, which are taken from 50 to 600 mA and every current for 180 s, corresponding to the current density: 1.768 × 10⁵~8.488 × 10⁶ A/dm².

The structure information of the as-cast wires is performed on a XRD (D/max-rB, Rigaku, Japan), collected with CuKa radiation (Rigaku D/max-gB) and a transmission electron microscope (TEM, FEI, NY, USA)). The macroscopic feature of the wire is observed on a SEM (Helios Nanolab600i, FEI, Hillsboro, OR, USA)). The impedance measurements are carried out at the intermediate frequency range (100 kHz~20 MHz) by using an Agilent 4294A precision impedance analyser (Gamry Instruments, Warminster, PA, USA). The samples with a length of 18 mm, are tested with a driving current amplitude of 10 mA under an axial applied magnetic field H_ex, generated by a Helmholtz coils system with a maximum value of 95 Oe. The axial direction of the microwire was kept perpendicular to the geomagnetic field, to avoid its interference. The GMI ratio is usually defined, respectively, by two methods, as follows [1]:

$$\frac{\Delta Z}{Z_0}\left(\%\right)=\left[\frac{Z\left(H_{\mathrm{ex}}\right)-Z\left(H_0\right)}{Z\left(H_0\right)}\right]\times 100\%$$

(1)

$$\frac{\Delta Z}{Z_{\max }}\left(\%\right)=\left[\frac{Z\left(H_{\mathrm{ex}}\right)-Z\left(H_{\max }\right)}{Z\left(H_{\max }\right)}\right]\times 100\%$$

(2)

and the field response sensitivity is defined by:

$${\xi =(\Delta Z/Z}_0\%)/\Delta H\times 100\%$$

(3)

The observation of the surface domain structure of the microwire is taken by a Nanoscope III multimode atomic force microscope (AFM, Bruker AFM Probes, Camarillo, CA, USA) from Digital Instruments [25]. A Veeco micro-etched silicon probe tip (Veeco Instruments Inc, Plainview, NY, USA) is applied to collect the related information by using a combination of tapping and lift mode. The selected lift height range is 100 nm.

3. Results

In order to develop the GMI sensors suitable for different applications simultaneously, the GMI profiles of ΔZ/Z₀% and ΔZ/Z_max% ratios are discussed, respectively. The modulation of the GMI effect and its correlation with the microstructure and surface domain structure of Co-Fe-based microwires after a unique AJA are presented. Figure 2 displays the X-ray diffraction pattern and the SEM image of the as-cast Co-Fe-based microwire. The XRD pattern contains a broad halo pattern with only one broad diffuse peak observed and there are no visible crystalline peaks, which suggests its typically amorphous structural characteristics. The wires show an average diameter of ~40 μm and a length of 200 mm. As observed by the SEM, the microwire shows a high quality with a smooth surface and a uniform diameter of ~30 μm.

The field dependence of the GMI profiles (ΔZ/Z₀%) for the AJA microwires with current amplitudes of 0~600 mA at the selected frequency f = 20 MHz, is illustrated in Figure 3a. For the as-cast state, the GMI ratio of [ΔZ/Z₀]_max(%) is around 31.5%. It shows that the GMI response peak displays a low value (50~100 mA AJA) and increases after 200 mA AJA. The GMI ratio increases significantly and reaches the maximum of 201.9% for 250 mA (corresponding to 3.537 × 10⁶ A/dm²) with a monotonically increasing field response range of 0~3.5 Oe. Further to increasing the current amplitude to 300 mA, even to 600 mA, the ratio decreased sharply instead, which was due to the crystallization of the wires. For comparison, the inset plot clearly shows the corresponding external field H = 0~6.5 Oe of ΔZ/Z₀ for 0~600 mA AJA. Notably, the unique of ΔZ/Z₀% profile for 250 mA annealing current wires means the AJA approach can achieve a well-defined microstructure and magnetic domain structure. During the annealing process, the ethanol medium around the wire shows nucleate boiling first at a low current amplitude, and then turned into film boiling with the current increasing to 600 mA, resulting in the decrease of thermal conductivity. Figure 3b shows the field dependence of ΔZ/Z₀% ratios for 250 mA AJA microwire at the frequency f = 0.1~20 MHz. As the excitation frequency increases, the impedance ratio (ΔZ/Z₀%) displays a nearly linear increase in the external field H_ex < 3 Oe, which means the field response sensitivity ξ is obvious when H_ex is small. Meanwhile, the skin effect is dominant, especially in the intermediate frequency stage of 1 < f < 10 MHz. In addition, it can be inferred from the relationship between Z and ω, i.e., Z ∝ (ω∗φ)^1/2, the change of the impedance curve is more substantial. At the frequency f > 11 MHz, the impedance ratio curves show a similar tendency, due to the static circumferential permeability μ_φ retaining its value, the relaxation from the rotational magnetization and domain wall motion, are rapidly achieved. The impedance ratio reaches its maximum value at f = 20 MHz and H = 3.5 Oe. When 3.5 < H < 20 Oe, the GMI curves display obviously a linear decrease at f > 10 MHz. Therefore, the 250 mA AJA microwire has the characteristics of the near-linear response in the double magnetic field interval (i.e., H < 3.5 Oe and 3.5 < H < 20 Oe), which shows a promising application in the development of the dual-range GMI sensors.

Figure 3c illustrates the anisotropy field H_k and the impedance ratio [ΔZ/Z₀]_max(%) of the 250 mA AJA microwire dependence of the excitation frequency. Both the [ΔZ/Z₀]_max(%) and the anisotropy field H_k simultaneously increase dramatically with the frequency and reach to the maximum values at f = 20 MHz. The impedance ratio is nonlinear fitted and shows an exponential function. The H_k identified by the intense coupling between the circumferential field H_φ and the radial stress field, finally corresponds to the peak position of the GMI response to the DC external field H_ex [31,32]. In general, the H_k is taken as the critical transition field of circumferential anisotropy [33]. The large current through the microwire induces a large the circumferential field of H_φ ≈ I/2πr [34], which greatly modifies the distribution of circumferential domain as well. The induced circumferential field H_φ by the 250 mA current amplitude is carried out theoretically at about 33.3 Oe. The anisotropy field H_k = 3.5 Oe is far less than the value of the circumferential field H_φ. The energy loss (Hk < H_φ) is due to the cooling effect of the anhydrous ethanol gas volatilization for it takes most of the Joule heat away and inhibits the crystal growth at the same time. Comparison with the as-cast state [15], the corresponding anisotropy field H_k for the 250 mA AJA microwire increases more pronounced with frequency, which is the result from the excess Joule heat helping to improve the circumferential surface domain of the microwire. According to the changes of the H_k curve, the anisotropic field H_k is relatively stable for the frequency of 7~11 MHz and 13~19 MHz. Figure 3d presents the field dependence of the magnetic field sensitivity ξ (%/Oe) for the 250 mA AJA sample at f = 0.1~20 MHz. The monotonically increasing field response sensitivity ξ corresponds to the external field H_ex up to 1.1 Oe with a linear range of 0.5 Oe. The maximum field sensitivity ξ_max reaches 124.1%/Oe at f = 10 MHz. When the H_ex is less than 3.5 Oe, the field response sensitivity ξ of the microwire is relatively obvious for the frequency f > 1 MHz.

In order to develop GMI sensors suitable for different applications, simultaneously, it is very necessary to consider the other expression of the GMI ratio ΔZ/Z_max(%), as listed in Formula 2. The DC external fields dependence of the impedance ratios ΔZ/Z_max(%), for 0~600 mA AJA at different frequencies are shown in Figure 3e. In this case, the ΔZ/Z_max(%) is around 194.5% for H_ex = 0.6 Oe for the as-cast wire. This ratio is slightly enhanced with the annealing current amplitude from 200 mA to 250 mA and from 400 mA to 600 mA, respectively. The maximum ratio [ΔZ/Z_max]_max(%) reaches 246.7% at H_ex = 0.25 Oe with the annealing current amplitude I = 550 mA and then decreases rapidly with the increase of the DC external field. From the enlarged inset, the peak becomes pronounced at H_ex = 2.75 Oe and reaches 200.5% for the 250 mA AJA, for which the field response sensitivity ξ is 73%/Oe. Figure 3f shows the field dependence of the GMI ratio (ΔZ/Z_max%) of the 250 mA AJA microwire at the selected frequencies. All curves present a linear increasing trend for the excitation frequency f > 1 MHz and appear with the obviously rising peaks with the DC external field H_ex < 3.5 Oe. With the increase of the frequency, the ratio [ΔZ/Z_max]_max(%) increases obviously at first (f < 8 MHz) and then decreases gradually. More significantly, the anisotropic field H_k increases to 3.5 Oe at f = 20 MHz. For f > 7 MHz, the curves decrease linearly.

Overall, the AJA method yields a significantly optimized GMI response of the microwires in a large-range linear magnetic field H_ex ≈ 3.5 Oe for the 250 mA AJA. Therefore, it can be considered as an effective annealing technique.

In order to analyze the influence of the AJA with different current amplitudes on the impedance of the microwires, the impedance Z, resistance R and reactance X are listed, respectively, in Figure 4. The impedance vector consists of a real part (resistance, R) and an imaginary part (reactance, X), which can be expressed simply as R + jX. In the respective curves of Z, R and X, the maximum value was obtained at 250 mA AJA, together with the minimum value obtained near the zero field. The GMI ratios of the two expressions for the 250 mA AJA state present obvious advantages. As can be seen from the Z and R similar variation trends with similar values in Figure 4a,b, it indicates that the resistive term becomes greater and contributes to the total impedance Z. Meanwhile, the microwire modulated at 200 mA AJA exhibits an obvious rising peak, which was consistent with the curve changes in Figure 3a. The Z/R/X ratios for the 550 mA AJA wire are relatively high which verifies the ΔZ/Z_max(%) ratio showing largest value in Figure 3e. All of the X curves of the 0~250 mA AJA-ed wires present rising peaks, as shown in Figure 4c. When the current amplitude I > 250 mA, the rising peaks still exist but not significantly. It can be seen from the enlarged illustration that the X values of all annealing states at the external field of 3.5~25 Oe show a linear decrease. The changes in the reactance X of the samples upon application of the applied field (H_ex), mainly results from the contribution of inductance L (L = 0.175 μ₀l < μ_φ > /2π), which is proportional to the circumferential permeability μ_φ. The impedance values of the different annealing states show it is nearly-increasing with the frequency range of 0.1 < f < 10 MHz for H_ex = 3.5 Oe, as shown in Figure 4d. In this instance, the circumferential permeability μ_φ is the magnetic field independent. Moreover, the maximum impedance values Z_max for the different current annealing states at f = 15 MHz (Figure 4d) also verifies that the GMI ratios of the 250 mA and 550 mA AJA wires are optimal.

As well known, the impedance test is a dynamic magnetization process with the domain walls movement, magnetization rotation and the circumferential permeability changing. In fact, the GMI effect of the AJA microwire can be reflected by observing the magnetic domain structure on the microwire surface. In this way, the relationship between the GMI effect and the AJA modulation is established from the perspective of the magnetic domain structure, to further analyze the mechanism of the GMI effect.

Figure 5 exhibits the surface domain structures of the as-cast, 200 mA, 250 mA and 550 mA AJA samples, observed by MFM. For the as-cast state, the circumferential domain with an uneven width and indistinct domain wall is obtained, due to the residual stress generated during preparation process (Figure 5a). The average width of the domain is ~0.85 μm. Following the 200 mA AJA, the average width of the domain is ~0.82 μm (as shown in Figure 5b). However, the order degree of the magnetic domain is improved with the clear circumferential domain. This behaviour is consistent with the improved GMI ratios (Figure 3a), which conforms to the enhancement of the rising peaks in Figure 4. Obviously, the circumferential domain is improved with a clear domain wall of a width of ~0.86 μm for the 250 mA AJA microwire, as seen in Figure 5c. This state corresponds to the large GMI ratio with a relatively higher circumferential permeability μ_φ and response sensitivity ξ. For the sample with a larger annealing current 550 mA in Figure 5d, the surface domain structure deforms and becomes interlaced. This leads to the order degree of the circumferential domain decreasing with the average width at about 0.89 μm. In this case, the domain deformation may be resulted from the competitive effect amongst the atoms. The forming of the circumferential domain ordering distribution is induced by the large current amplitude and fast heat dissipation of the anhydrous ethanol around the microwire.

Figure 6 illustrates the high-resolution transmission electron microscopy (HRTEM) images of the wire’s surfaces at the as-cast state (a) and after the 250 mA AJA (b). In Figure 6a, a HRTEM image of the wire’s as-cast state is shown along with the selected area autocorrelation function (ACF) patterns of the amorphous wire. The isotropic maze pattern observed in the HRTEM image is of typical amorphous characteristics. No indication of fine crystallites has been observed through HRTEM observation. Comparing with the amorphous structure of the as-cast state in Figure 6a, the microstructure of the 250 mA AJA microwire shows an inconspicuous or partial crystallization. A large number of nanocrystals are verified by spots in the diffraction ring and described as embedded in the amorphous matrix (b) and (c). The crystalline phase of more than a dozen nanometers is due to the sufficient Joule heat prompting the local area atoms to full diffusion and structural relaxation, which are shown by the autocorrelation function (ACF) patterns (c) and fast Fourier transform and inverse fast Fourier transform (FFT-IFFT) patterns (d), respectively. Small-sized nanocrystals are reported as good for improving the soft magnetic properties of the materials [35].

From the microstructural evolution perspective, the Joule heat during the annealing process causes the atoms to transition to a more stable crystalline state. Atomic diffusion behavior can be described by the Stokes Einstein formula with the relationship between the atomic diffusion coefficient D and the state temperature T, based on the theory of microscale dynamics: D ∝ m^(−1/2)Tⁿ (n = 2). The atoms in the microregion can be fully relaxed and arranged in an orderly manner, in range of a few to a dozen nanometers. Consequently, the appearance of a large number of nanocrystals reduces the atomic diffusion coefficient D and leads to the orderly arrangement of the atoms, which is beneficial for the improvement of the magneto-crystalline anisotropy and promotes the increase of the equivalent anisotropy field H_k (shown in Figure 3e). Additionally, the circumferential magnetic field H_φ, induced by a large current makes the atomic magnetic moment in a more orderly-circumferential distribution, which realizes the domain structure modulation and thus improves significantly the GMI performance.

Based on the above-mentioned aspects, the systematic investigation of the AJA effect on the Co-Fe-based amorphous microwires was conducted. The GMI performance of the microwire changed appropriately at the current amplitude of 250 mA. In terms of the atomic structure, a large number of disordered and small-sized nanocrystals are precipitated inside the microwire, which not only help to reduce the its resistivity, but also improve the order degree of the atomic structure to a certain extent. In terms of the domain structure, the circumferential field, induced by the annealing current effectively changed the domain structure, improved the order degree of the circumferential domain of the “shell” on the wire-surface, the circumferential permeability, and achieved a significant improvement of the GMI performance of the microwire. From the perspective of application, the impedance ratio of the microwire, the field response sensitivity and the linear response range of the GMI properties are improved obviously after the AJA modulation, which is beneficial to the GMI sensor applications.

4. Conclusions

In summary, AJA is proved as an effective and superior method to optimize the GMI effect, which push the limitations of the sensing range constrained by the trade-off between the microstructure and the domain structure evolution with the usual tailoring techniques.

• The 250 mA AJA microwire has the characteristics of a near-linear response in the double magnetic field interval (i.e., H < 3.5 Oe and 3.5 < H < 20 Oe), which shows a promising application in the development of dual-range GMI sensors.
• The GMI effect has been improved with the ratio ΔZ/Z₀(%) of 201.9% and ΔZ/Z_max(%) of 200.5% for the 250 mA AJA, simultaneously.
• The microstructure of the 250 mA AJA wires with a large number of disordered and small-sized nanocrystals embedded in an amorphous structure are good for improving the soft magnetic properties.
• The surface domains of the microwire are modified and formed a well-defined circumferential domain, which its behaviour is consistent with the improved GMI ratios for the 250 mA AJA.