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7.1 Criteria for Selecting GMI Materials

To search for a GMI material for GMI sensor applications, two main requirements should be satisfied, namely a high GMI ratio (or a large GMI effect) and a high sensitivity to the applied field (or a high magnetic response). In view of the theoretical analyses and experimental results, it is concluded that a large GMI effect should exist in magnetic materials with the following desirable properties:

  • low resistivity, ρ;

  • high magnetic permeability, μ;

  • high saturation magnetisation, M s; and

  • small ferromagnetic relaxation parameter (or low damping parameter), α.

In this context, crystalline ferromagnetic materials have the advantage of lower resistivity (ρ), but amorphous ones have better soft magnetic behaviour (e.g. higher magnetic permeability, μ, and saturation magnetisation, M s) because they lack magnetocrystalline anisotropy. In particular, non-magnetostrictive materials can be expected to show the best GMI performance because the magnetoelastic contribution to magnetic anisotropy substantially weakens the soft magnetic behaviour. Improvement in the magnetic softness of an actual amorphous material by appropriate thermal treatment and/or the application of external parameters (mechanical stress, magnetic field, etc.) can lead to a simultaneous improvement in the GMI effect and its field sensitivity. The damping parameter (α) is often considered in the high frequency range where ferromagnetic resonance takes place, while it can be neglected in the intermediate frequency range (i.e. f = 0.1–10 MHz), where most GMI-based sensing applications have been identified (see Chap. 8). In addition, for practical sensor applications, the mass manufacturability and cost of materials are also important factors.

7.2 Evaluation of GMI Wires

In ferromagnetic materials, the highest value of the GMI effect experimentally observed is much smaller than the theoretically predicted value. Research in the field has been focused on special thermal treatments and on the development of new materials with properties appropriate for practical GMI sensor applications. In this section, all existing GMI wires will be reviewed and evaluated.

7.2.1 Co-Based Wires

Both conventional and glass-covered Co-based amorphous wires exhibit a GMI effect, owing to their high circular permeability. This is mainly due to the presence of circumferential anisotropy and an outer shell circular domain structure that results from coupling between negative magnetostriction and quenching compressive stress [1–5]. Among the Co-based amorphous alloys investigated, an alloy system with the nominal composition of Co–Fe–Si–B exhibits nearly zero and negative magnetostriction of λ s = −0.4 × 10−7. This alloy is often obtained by alloying Fe–Si–B that has a positive λ s of 25 × 10−6 with Co–Si–B that has a negative λ s of −3 × 10−6 [5, 6]. As a result, a record value of GMI ratio (1200 % at 14.2 MHz) has been achieved in the conventional amorphous Co68Fe4.35Si12.5B15 wire [7]. This value is much larger than that reported earlier (600 %) with the same composition [2, 5]. This larger value of GMI ratio is a result of minimising contact resistance and cancelling parasitic impedance [7]. However, a high field sensitivity of GMI (~500 %/Oe) was reported by Vazquez [2], while no information was found in the work by Garcia et al. [7].

In an attempt to develop magnetic wires for high-frequency sensor applications, Nie et al. [8] reported that a Co–Mn–Si–B amorphous glass-covered wire with nearly zero magnetostriction exhibited a GMI effect at high frequencies. For the amorphous Co68.2Mn7Si10B15 microwire, the GMI ratio and magnetic response reached the values of 153 and 65 %/Oe, respectively, at a frequency of 30 MHz. Vinai et al. [9] recently revealed that these microwires also exhibited a GMI effect at frequencies up to GHz. In the frequency range of 100 MHz–6 GHz, the GMI ratio reached a maximum value of ~100 % at a frequency of 2 GHz. As shown earlier in Chap. 6, for Co-based amorphous wires, the GMI effect can be further improved by appropriate field annealing [10], Joule current annealing [11–15], or the application of a tensile stress [16, 17].

In summary, the Co-based amorphous wires with nearly zero and negative magnetostriction are good candidates for GMI sensor applications. It should be noted that while the Co-based conventional and glass-covered amorphous wires are suitable for sensor applications in the low and intermediate frequency range (up to several MHz), the glass-covered amorphous microwires can be used for electrotechnical devices operating at much higher frequencies (up to several GHz). Due to their relatively high resistivity, the microwires retain their large GMI value at higher frequencies, when compared to ribbons and wires. In practice, depending upon the specific requirements of a sensor device (e.g. the operating-frequency range), either wires or microwires should be chosen accordingly.

7.2.2 Fe-Based Wires

Fe-based amorphous wires have relatively small or even no MI effects, owing to their relatively small effective permeability, which is due to the presence of an outer shell radial domain configuration that results from the coupling between the highly positive magnetostriction and the quenching compressive stress [4, 10, 18, 19]. A primary alloy of Fe–Si–B having a positive λ s of 25 × 10−6 was found to show poor magnetic softness and hence a small MI effect (~3 %), while a larger MI effect (~36 %) was obtained in the annealed wires [10, 19, 20]. It was the precipitation of an FeSi nanocrystalline phase that significantly decreased the bulk positive magnetostriction and hence gave rise to the MI effect of the annealed Fe–Si–B wires [20]. The crystallisation of Fe–Si–B-based amorphous alloys containing Nb and Cu causes the formation of a nanoscale bcc structure, and the bcc alloys exhibit excellent ultrasoft magnetic properties (i.e. high effective permeability and small coercivity) [6, 10]. In these alloys, the roles that Cu and Nb play are to maximise the density of crystal nuclei and to retard grain growth, respectively, leading to an ultrafine grain structure. Among these alloys, the nanocrystalline alloys with a nominal composition of Fe73.5Si13.5B9Nb3Cu1 were found to show the best magnetic softness. These materials are therefore expected to show large MI effects. Indeed, Knobel et al. [10] reported that conventional Fe73.5Si13.5B9Nb3Cu1 nanocrystalline wires (e.g. the amorphous wire samples annealed at 550–600 °C) exhibited a GMI effect. The largest value of GMI ratio was about 200 % at a frequency of 500 kHz for the wire sample annealed at 600 °C for 1 h. In another study, Li et al. [21] partially substituted Fe by Cr in Fe73.5Si13.5B9Nb3Cu1 nanocrystalline wires with the expectation of further reducing the magnetostriction of the primary alloy. They found that, although the GMI ratio and magnetic response were slightly smaller in Cr-doped samples, the addition of Cr improved the GMI response and significantly reduced the undesirable hysteretic effect in GMI curves with increasing and decreasing applied magnetic fields [21]. In addition, the presence of Cr significantly improved the corrosion resistance properties, which is desirable for sensing applications in a corrosive environment. The GMI effect was also observed in Fe-based nanocrystalline glass-coated wires and microwires [4, 18]. Interestingly, the Fe89B1Si3C3Mn4 nanocrystalline glass-covered microwires were found to show the GMI effect in the GHz frequency range [9]. At a frequency of 4 GHz, the GMI ratio reached a value as high as 70 % for the sample annealed at 350 °C. For this typical microwire, conventional furnace annealing proved more effective in improving the GMI effect compared with current annealing. Furthermore, it should be recalled that for both Fe-based amorphous and nanocrystalline glass-covered wires, the removal of the glass layer can significantly improve the GMI effect and magnetic response. However, the GMI ratios of Fe-based nanocrystalline wires are often smaller than those of Co-based amorphous wires [5].

7.2.3 Electrodeposited Wires

Besides rapidly quenched wires, electrodeposited wires, which comprise a highly conductive non-magnetic metal core (e.g. Cu, CuBe, and Ag) and a thin layer of soft magnetic metal (e.g. NiFe, NiFeRu, NiFeMo, CoP, and CoNiFe), have been found to show excellent GMI behaviours [22–42]. For electrodeposited wires, the magnetic layer has either a circular or a radial domain configuration, depending strongly upon the alloy composition and the sample processing conditions [40]. Wires having a circular domain structure are often expected to show a larger MI effect [38, 42].

In a pioneering work, Usov et al. [38] predicted that the GMI effect could be further improved in a composite amorphous wire when the electrical conductivity of the inner core is much higher than that of the shell region. Since this work, experimental efforts have been devoted to investigating the GMI effect in electrodeposited wires, such as CoP/Cu [22–26, 39], NiFe/Cu [28–30, 41], CoNiFe/Cu [31, 32, 40], NiFeRu/Cu [33], and NiFeMo/Cu [34]. Sinnecker et al. [22] reported that an electrodeposited CoP/Cu wire exhibited radial magnetic anisotropy (i.e. the radial domain structure) and the size of the closure domains increased with the magnetic layer thickness (CoP). It is interesting to note that, although magnetic wires with a radial magnetic anisotropy are not expected to show any GMI effect, a significant increase in GMI ratio with the magnetic layer thickness of the CoP/Cu composite wire was attained [22]. This indicated that the observed GMI effect was associated with the current distribution along the sample radius, with two well-defined regions having different transport and magnetic properties [23–26]. Recently, Phan et al. [39] optimised the processing conditions in order to achieve the largest GMI effect in a typical CoP/Cu electrodeposited wire. The largest GMI ratio was achieved with a deposition time of 6 min and an electrolytic current density of 639 mA/cm2. At the measured frequency of 10.7 MHz, the GMI ratio and magnetic response reached the highest values of 534 and 21 %/Oe, respectively. It was proposed that the changes of deposition time and electrolytic current density caused variations in the domain structure of the CoP magnetic layer and hence the GMI behaviour [39]. More interestingly, Kurlyandskaya et al. [40] found that the GMI ratio reached a value as high as 1200 % at a frequency of 4 MHz for FeNiCo/CuBe electroplated wire. This is the highest value reported until now, among existing electrodeposited wires. However, no information on the magnetic response of GMI was given [40]. In a comprehensive study investigating the influences of processing parameters (e.g. electrodeposition current density, duty cycle, electrolyte solution, pH value, applied magnetic field, magnetic layers, and post-annealing) on the GMI of electrodeposited NiFe/Cu wires, Li et al. [41] reported that the GMI ratio and magnetic response reached maximum values of 1110 and 218 %/Oe, respectively, at a frequency of 4 MHz for a dc Joule-annealed wire sample.

Recently, it has been revealed that the GMI effect can be further improved in electrodeposited wires by the inclusion of an insulating interlayer between the core and the magnetic shell (e.g. CuBe/insulator/NiFeB wires) [36, 37]. For instance, the GMI ratio reached a value of 250 % at f = 500kH–1 MHz for an electrodeposited CuBe/insulator/NiFeB wire, which is much larger than that of ~23 % at f = 1 MHz for the electrodeposited CuBe/NiFeB wire without the insulator layer [36]. This can arise from the differences in current distribution under the external magnetic field and from the electromagnetic interaction between the conductive core and the ferromagnetic layer of the composite wires with and without an insulator layer [36, 37]. In this context, Buznikov et al. [42] have recently developed a model for predicting the GMI effect in these typical wires. The model reveals that the field dependence of magnetic shell permeability significantly affects the eddy current distribution and therefore leads to the observed GMI effect. The inclusion of a thin insulator layer can lead to a further improvement in the GMI effect at sufficiently high frequencies, because it actually increases both the diagonal and off-diagonal impedance [42].

In general, electrodeposited composite wires are good candidate materials for producing high-performance magnetic sensors and sensing devices operating at low and intermediate frequencies (up to several MHz). Within this operating regime, electrodeposited composite wires may be even more promising than rapidly quenched wires and ribbons.

7.2.4 Multilayer Wires

Multilayer wire is a new family of magnetic microwires with multilayer bimagnetic characteristics [43, 44]. A typical biphase magnetic microwire consists of a ferromagnetic nucleus, an intermediate glass layer, and a ferromagnetic outer shell, as exemplified in Fig. 7.1. They were prepared by several complementary techniques including quenching and drawing for precursor glass-coated magnetic/metallic core microwire, sputtering for Au metallic intermediate nanolayer, and electroplating for magnetic external microtube. This combination of techniques enables the manipulation of different soft/hard magnetic characteristics at different layers and hence permits one to tune the properties of the biphase microwires. The peculiarity of the multilayer wires lie in the coupling between various layers. The presence of an external magnetic shell around a glass-coated microwire induces a longitudinal anisotropy in the nucleus of the latter, drastically modifying its magnetoinductive behaviour, making it very sensitive to the presence of an applied external stress and temperature [45, 46].

Fig. 7.1
figure 1

a Scheme of multilayer microwire. SEM images of FeSiB/CoNi multilayer microwires: b FeSiB nucleus and glass cover, c glass layer and CoNi outer shell, d CoNi outer shell, and e cross-sectional view of the multilayer microstructure (reprinted with the permission of Springer [48])

Full size image

The most notable magnetic characteristic is the step-like magnetisation process arising from the different magnetic phases and couplings [47]. These can be optimised by specific thermal treatment processing to grow a new structural phase with a hard magnetic character at the magnetic core via conventional thermal annealing, or by inducing suitable helical anisotropy at the magnetic shell via helical magnetic field annealing or torsion annealing. Different magnetic configurations have been explored thus far: soft (nucleus)/hard (outer shell), hard/soft, and soft/soft [48]. One can invariably make use of the magnetic interactions to manipulate the soft magnetic core behaviour. For instance, it can be modulated through the hard phase stray fields, or magnetic bistability can be modified through the magnetoelastic anisotropy induced by the external phase. In addition to the soft/hard magnetic nature of each magnetic phase, an effective tuning of average behaviour can be achieved by adapting the thickness of each layer.

These multilayer wires are of practical significance as sensing core elements in sensor devices. Subject to a delicate control in terms of the reversal magnetisation of the soft phase, this type of microwire has come to be an ideal candidate in a variety of sensor technologies from temperature/tensile stress and torsion/position sensors to coil-less orthogonal fluxgates. The versatility of their properties and the high degree of freedom for tailoring give these wires an outstanding edge in the competitive sensing technology field.

7.3 Nominated GMI Materials for Sensor Applications

A wide variety of GMI materials are currently available for practical GMI sensor applications. Table 7.1 summarises several materials that possess a high GMI ratio and magnetic response and are promising for making high-performance GMI sensors. Appropriate selection is dependent upon specific requirements, such as their field sensitivity, working frequency range, size, and thermal stability. The ultrahigh sensitivity of GMI to external dc magnetic field (down to 10−8 Oe) can be used for magnetic field sensors and other sensors based on the change of a local magnetic field. It should be emphasised that not only the GMI ratio (η) and the magnetic response (ξ), but also the particular shape of the η(H) curve are important for high-performance sensor applications. In this context, the longitudinal weak-field-annealed amorphous ribbons [64, 67–74] and amorphous wires subjected to dc bias current [75–84] are promising candidate materials for producing auto-biased linear field sensors.

Table 7.1 Candidate materials for GMI sensors
Full size table