The magnetic properties and overall shape of hysteresis loops of amorphous microwires depend on composition of the metallic nucleus as well as on thickness of the glass coating. It should be mentioned that even the composition of the glass coating affects the magnetic properties of glass-coated microwires [37]. The effect of metallic nucleus composition on magnetic properties and hysteresis loop shape is illustrated by Figure 3, where the hysteresis loops of three main groups of amorphous microwires (Fe-rich, Co-rich and Co-Fe-rich with positive, negative and vanishing magnetostriction constant, λ_s, respectively) are shown.

The shape of the hysteresis loops changes from the rectangular one typical of amorphous Fe-rich compositions to the inclined one typical of Co-rich compositions. Microwires with vanishing λ_s exhibit quite soft magnetic properties.

If the composition of the metallic nucleus is the same, the thickness of glass coating also affects magnetic properties. Thus, Figure 4 shows hysteresis loops of amorphous microwires with the same composition (Co₆₇Fe_3.85Ni_1.45B_11.5Si_14.5Mo_1.7 with vanishing λ_s) but with different ρ-ratio defined as d/D (where d = metallic nucleus diameter, D = total microwire diameter). In the case of nearly-zero magnetostrictive Co₆₇Fe_3.85Ni_1.45B_11.5Si_14.5Mo_1.7 microwires, all samples exhibited inclined M(H) loops with extremely low coercivities (up to 4 A/m) but small magnetic anisotropy fields, H_k. The magnetic anisotropy field, H_k, increases with increasing the ρ-ratio (Figure 4).

Such a strong dependence of the hysteresis loops and magnetic anisotropy field on these parameters should be attributed to the magnetoelastic energy given by: (3) K m e ≈ 3 2 λ s σ i ,where σ_i is the internal stress. The magnetostriction constant depends mostly on the chemical composition and vanishes in amorphous Fe-Co based alloys with Co/Fe ≈ 70/5 [2]. On the other hand, the estimated values of the internal stresses in these glass coated microwires arising from the difference in the thermal expansion coefficients of metallic nucleus and glass coating are of the order of 100–1,000 MPa, increasing with the increase of the glass coating thickness [2-4,6]. Such large internal stresses give rise to a drastic change of the magnetoelastic energy, K_me, even for small changes of the glass-coating thickness at fixed metallic core diameter. Additionally, such a change of the ρ-ratio should be related to the change of the magnetostriction constant with applied stress [2,4,34]: (4) λ s = μ 0 M s 3 d H k d σ ,where μ₀M_s is the saturation magnetization, H_k- magnetic anisotropy field.

The main interest has been directed towards studies of Fe-rich compositions with positive λ_s exhibiting perfectly rectangular hysteresis loop (so-called magnetic bistability) and Co-rich compositions with nearly-zero λ_s with good magnetic softness. This is because soft magnetic microwires, exhibiting high magnetic permeability and also GMI effect are quite useful for applications in magnetic field sensors [2-5,34]. On the other hand microwires with rectangular hysteresis loops can be used for magnetic sensors for magnetic surveillance and for magnetic tags [2,5,34].

One of the main technological interest for utilization of amorphous microwires is related with the Large and single Barkhausen Jump (LBJ) [2,33,34,38]. It is worth mentioning that appearance of LBJ takes place under magnetic field above some critical value (called the switching field) and also if the sample length is above some critical value also known as the critical length. The switching field depends on the magnetoelastic energy K_me [2-4,33,34]. Regarding the critical length, detailed studies of the ferromagnetic wire diameter on magnetization profile and size of the edge closure domains have been performed in [2,33,34,38]. Particularly, critical length, L_cr, for magnetic bistability in conventional Fe-rich samples (120 μm in diameter) is about 7 cm. This critical length depends on saturation magnetization, magnetoelastic energy, domain structure, magnetostatic energy [2,33,34,38].

Enhanced critical length, L_cr, (of the order of few cm) observed in conventional amorphous wires has limited sensor applications. Reduction of the metallic nucleus diameter in the case of glass-coated microwires (almost one order lower) results in drastic reduction of the critical length, making them quite attractive for micro-sensor applications. Thus, magnetic bistability for the sample length L = 2 mm has been observed for Fe-rich microwire with metallic nucleus diameter, d, about 10 μm [33].

Recently great attention has been paid to studies of domain wall (DW) propagation in thin wires with sub-micrometric and micrometric diameter [30,31]. Growing interest in DW propagation is related to proposals for prospective logic and memory devices [39-41]. The speed at which a DW can travel in a wire has an impact on the viability of many proposed technological applications in sensing, storage, and logic operation. Special effort has been performed on nanowires to enhance the DW speed. Thus, application of transverse magnetic field proposed in [42] allowed one to slightly improve the DW speed, v, to about 600 m/s.

Similarly, we observed DW propagation in ferromagnetic microwires with rectangular hysteresis loops [5,32,43]. We studied the DW dynamics by classical Sixtus-Tonks experiments [44], as described recently elsewhere [5,32,43]. The dependence of v on applied magnetic field, H, measured for the Fe₆₉Si₁₀B₁₅C₆ microwire with the diameter of metallic nucleus 14 μm at different temperatures, T, is shown in Figure 6a.

Quite high DW velocity, v, and essentially non-linear magnetic field dependence, v(H) is observed. Even higher DW propagation has been observed in Co₆₈Mn₇Si₁₀B₁₅ (with the diameter of the metallic core being 8 μm and total diameter being 20 μm) which is characterized by the lowest possible magnetoelastic anisotropy (due to its low magnetostriction λ_s) among the microwires with single domain axial structure (see Figure 6b).

Observed non-linearity of v(H) dependences at low field related with change of the regime from the lower field with smaller DW velocity to the higher field with enhanced velocity at some critical field, H_cr, can be attributed to the change of the structure of the DW as well as to the adiabatic domain wall propagation at magnetic field slightly above critical field, attributed to the interaction of the DW with the local defects [45].

Regarding the change of the DW domain wall velocity due to the change of the DW structure, it was shown previously by micromagnetic simulations for the case of nanowires that the vortex-type domain wall is faster than the transversal one and the vortex domain wall is more stable for the case of thicker magnetic wires [5].

On the other hand, an abrupt increase of DW velocity is observed at high field region (see Figure 7) and can be explained by nucleation of additional DWs on local defects existing inside the microwire [46,47]. Such local defects have been found using short magnetizing coils placed far from the wire ends [46]. In this case, nucleation of new DW far from the wire end can be realized. Consequently much higher magnetic field is needed for such nucleation as-compared with the depining of the DW from the wire ends (Figure 7b). Moving the magnetizing coil along the wire we observed spontaneous fluctuations of local nucleation field H_n which is very sensitive to the presence of the local defects. The overall minimum H_N = min(H_n1, H_n2,…) correlated very well with the field of abrupt increasing of v (Figure 7a). Consequently, the defects existing in microwires play a role of the nucleation centers for new DWs. When the applied magnetic field exceeds H_N, new reverse domains can be nucleated, which results in s significant decrease of the magnetization switching time and acceleration of magnetization switching in magnetically bistable microwires. This mechanism of ultrafast magnetization switching through additional nucleation centers created artificially can be applied in spintronic devices for enhancing their performance.

Usually the GMI effect is characterized by the magnetoimpedance ratio, ΔZ/Z, has been defined as: (5) Δ Z Z = Z ( H ) − Z ( H max ) Z ( H max )where H_max is the maximum DC longitudinal magnetic field of the order of few kA/m, usually supplied by a long solenoid and/or Helmholtz coils. The appearance of the GMI effect and magnetic field dependence of impedance are intrinsically related with the magnetostriction constant, domain structure and above-mentioned outstanding magnetic softness of magnetic materials. As has been observed, hysteresis loops are quite sensible to the chemical composition and sample geometry (see Figures 3 and 4). Until now, the best soft magnetic properties and highest GMI effect have been observed in Co₆₇Fe_3.85Ni_1.45B_11.5Si_14.5Mo_1.7microwires [3]. Hysteresis loops presented in Figure 3c exhibit inclined almost unhysteretic M(H) loops with extremely low coercivities (up to 4 A/m). Magnetic anisotropy field, H_k, increases with increasing ρ-ratio (Figure 4). As expected we observe (see Figure 8) that the sample geometry strongly affects the DC axial magnetic field dependence of the real part of GMI, Z of Co₆₇Fe_3.85Ni_1.45B_11.5Si_14.5Mo_1.7 microwires.

Since it is known that the strength of the internal stresses is determined by the ρ-ratio, the relaxation of such internal stresses by means of thermal treatment should drastically change both soft magnetic behaviour and ΔZ/Z(H) dependence.

Figure 9 shows this dependence measured for as-prepared and annealed Co₆₇Fe_3.85Ni_1.45B_11.5 Si_14.5Mo_1.7 samples. Both ΔZ/Z and the DC-field, H_m, corresponding to the maximum of the GMI ratio, can be modified by annealing.

The development of miniaturized sensors requires microwires with thinner diameter but keeping their good soft magnetic properties and GMI effect. Consequently, enhanced soft magnetic properties (coercivity below 10 A/m) and considerable GMI effect observed in thin microwires with metallic nucleus diameter, d, below 10 μm should be considered as a significant achievement in development of materials for micro-sensor applications.

Recently it was found that off-diagonal compo­nents possess asymmetrical dependence on the magnetic field, the necessary condition for determination the magnetic field direction [3]. For practical sensors the pulsed excitation is preferred over a sinusoidal one because of the simple elec­tronic design and low power consumption. The practical circuit design [48] consists of a pulse generator, sensor element and output stage. The sharp pulses are produced by passing squared wave pulses through the differential circuit. When the pulse flows through the magnetic wire the magnetic field dependent signal, V_out, appears in the pickup coil as shown in Figure 10.

Figure 11 shows field dependence of the off-diagonal voltage response, V_out, measured as described elsewhere [3,34,48] in Co₆₇Fe_3.85Ni_1.45B_11.5Si_14.5Mo_1.7 (λs ≈ 3 × 10⁻⁷) microwire. The V_out(H) curves have asymmetrical shape exhibiting close to linear growth within the field range from −H_m to H_m (Figure 11). The H_m limits the working range of MI sensor to 240 A/m and should be associated with the anisotropy field.

The influence of Joule heating on off-diagonal field characteristic of nearly zero magne­tostriction Co₆₇Fe_3.85Ni_1.45B_11.5Si_14.5Mo_1.7 microwire with diameters 9.4/17.0 μm is shown in Figure 11. One can see that the thermal annealing with 50 mA DC current reduces the H_m from 480 A/m in as-cast state to 240 A/m after 5 min annealing.

One of the main features that can affect the magnetic field sensor's resolution is related with the MI hysteresis, as can be seen in Figures 9 and 12. The origin of this hysteresis is related to the deviation of the anisotropy easy axis from the circular direction in the wire's outer shell. To suppress the hysteresis a circular bias field H_B produced by the DC current can be used. Although this effect can be turn out to be very interesting for certain applications. For example, the hysteresis can be used for data storing.

The storage and erasing of the information can be performed simply by passing the current pulse through the wire while the stored data is retrieved by measurement of the wire's impedance in the presence of the constant magnetic field. The principle is shown in Figure 12. Independently of the initial state, after applying the constant current pulse I_B in one direction (from right to left in Figure 12a), the spins will orient along the easy axis in up direction (Figure 12b) which corresponds to the store logical ‘1’ state. Then, under applied external magnetic field makes spins rotate towards close to circumferential direction which characterized by low impedance (Figure 12c) that can be easily detected. To write logical '0' one need to pass current pulse I_B in the opposite direction (left to right in Figure 12d) that makes the spins aligned along the easy axis in down direction (Figure 12e). In this case, under application of the external magnetic field the spins rotate towards close to longitudinal direction characterized by high impedance as shown in Figure 12f. The change of impedance between the Low-Z and High-Z states about 50% or even higher might be observed. The main advantage of the proposed method for data storage is the absence of moving components such as the recording and writing heads that found in hard disk drives.

The phenomenon of magnetic bistability is characterized by the sharp voltage peaks induced in the pick-up coil wound around the sample. The induced emf is caused by an abrupt change of the magnetic flux during the large Barkhausen jump. This effect can be used in magnetic sensors. The first sensors based on magnetic bistability (MB) were introduced in the 1970s, when Wiegand wires [49] with rectangular hysteresis loops inducing sharp 20–30 μs pulses in the secondary coil mounted on the sample subjected to the AC magnetic field were developed. Such sensors were widely applicable in the automobile industry for the detection of the motions and positions [2,34]. However, such Wiegand wires need relatively large excitation fields (about 4 kA/m) to produce sharp voltage peaks and special processing. Therefore, amorphous Fe-rich (Fe₈₀B₂₀ or Fe₈₁B₁₇Si₂) magnetostrictive ribbons subjected by the special stress annealing were introduced at the beginning of the 1980s [50]. Stress annealing was performed in the samples of toroidal shape in order to induce tensile-stressed and compressive-stressed layers in the ribbon. Sharp voltage pulses with 20–50 μs duration at field amplitude of around 100 A/m at frequency of 0.1–6 Hz were found in these amorphous ribbons. Such magnetic bistability was initially used for the magnetometer and rotation speed sensors [50]. Later, the Matteucci effect, appearing in the twisted amorphous ribbon was also employed for the modified rotation speed sensor [51]. Like in the case of sensors based on magnetic bistability, sharp voltage pulses appears between the sample ends when it is submitted to magnetic field that was used for sensor design [51]. In this case the secondary coil was not necessary.

Throughout the 80s and later, an increasing interest has been focused on amorphous materials with a cylindrical shape. The in-rotating-water fabrication technique was widely employed for the production of around 120 μm amorphous wires. It was found that either as-cast or die-drawn then annealed magnetostrictive amorphous wires exhibit the re-entrant flux reversal characterized by large and single Barkhausen jump [2,34]. Consequently, a number of magnetic sensors based on magnetic bistability and/or Matteucci effect of amorphous wires were developed [2,19-21,34]. As it was expected, sharp voltage peaks appearing in the secondary coil or between the sample ends are commonly used for the distance sensor, revolution counter and position sensor [2,19-21]. On the other hand, such peculiar remagnetization process with large Barkhausen discontinuity exhibiting by amorphous wires has been used for design of magnetic markers and tags [52,53]. In these applications a consequence of voltage peaks appearing under the application of the external magnetic field is used. General problem of such applications is the limited number of combination for the good identification due to the similarity of the switching field values. In order to extend the switching field range, a coating by the hard magnetic materials is recently used [54].

Later it was found that thinner glass-coated amorphous microwires can also exhibit magnetic bistability effect even for samples with a length of a few millimeters and for nearly zero-magnetostrictive alloys [2-4,33,34], while the negative magnetostriction compositions do not exhibit magnetic bistability. It is important to outline that even Fe-rich glass coated microwires exhibit a wide range of switching fields. Besides such wide range of the switching field can be extended by the thermal treatments [2,17,34,38,55].

Magnetic bistability with extended switching field range and high stress sensitivity of magnetic parameters (switching, field) give rise to various technological applications of tiny magnetic wires coated by glass [2,34,38,55]. One of the applications is based on the wide range of coercivity, which can be obtained in microwires owing to its strong dependence on geometric dimensions and heat treatment. It was realized in the method of magnetic codification using magnetic tags [2,34,38,55]. The tag contains several microwires with well-defined coercivities, all of them characterized by a rectangular hysteresis loop. Once the magnetic tag submitted to the AC magnetic field, each particular microwire is remagnetized at different magnetic field giving rise to an electrical signal on a detecting system (see Figure 13). The extended range of switching fields obtained in Fe-rich microwires gives a possibility to use a big number of combinations for magnetic codification [2,34,38].

A magnetoelastic sensor of the level of a liquid can be designed using the stress dependence of the coercivity in nearly-zero magnetostriction CoMnSiB microwires. Such a sensor essentially consists of a piece of the wire surrounded by primary and secondary coils (Figure 14) [2,34,38,56]. The sample is loaded with approximately 10 grams and therefore exhibits a flat hysteresis loop. The weight is attached to the bottom of the sample. When a liquid arrives to cover the weight as a consequence of the actual stress, affecting the sample, decreases giving rise to the appearance of the rectangular hysteresis loop.

The principle of the sensor's work is based on the change of the voltage of the secondary coil, which increases drastically when the hysteresis loop of the wire became rectangular after the stress essentially decreases. A simple circuit including the amplification of the signal and alarm set was used to detect changes of voltage in the secondary coil under the change of tensile stresses owing the floating effect of the weight on the liquid.

The observed magnetic response on the external variable stresses can be used in many applications to detect different temporal changes of stresses, vibrations etc. As an example we introduce a “magnetoelastic pen” which can be used for identification of signatures [2,34,38,55,57]. It is known that the signature of each person can be represented by a typical series of stresses. The sequence and strength of those stresses are a characteristic feature of any personal signature, so temporal changes of the stresses while signing can be used for the identification of signature itself. We have used this behavior and designed a set-up consisting of a ferromagnetic bistable amorphous wire with positive magnetostriction, a miniaturized secondary coil and a simple mechanical system inside the pen containing a spring, which transfers the applied stresses to the ferromagnetic wire (see Figure 15). The resulting temporal dependence of the stresses, corresponding to a signature is reproducible for each individual person. The main characteristics of this dependence are time of signature, sign and sequence of the detected peaks. Examples of two magnetoelastic signatures corresponding to the same person are shown in the Figure 15.

Since the discovery of the magneto-impedance effect in 1994 [23,24], a number of studies and developments on this topic have been widely performed by different groups [2-4,34,55]. As a result, GMI and stress-impedance (SI) sensors with CMOC IC circuitry with advantageous features compared with conventional magnetic sensors have been developed [58,59]. Among the industrial applications, MI element using amorphous wire, electronics compass using MI element incorporated into mobile phones and accelerometers using MI sensor and 6 axis type of motion sensor which combine 3 axis magnetic sensors with 3 axis accelerometers have been reported by Aichi Steel Co. [58,59]. The sensor's circuitry, performance and comparative characteristics with the traditional sensors are presented in [58,59]. Similarly, the other sensors based on stress sensitivity of the GMI effect for the domestic use have been developed in Spanish groups [60].

As an example the air flux sensor is described below. This sensor is based on the stress sensitivity of GMI effect exhibited by magnetically soft Co_68.5Mn_6.5Si₁₀B₁₅ microwire. In the unstressed state GMI ratio, ΔZ/Z, of Co_68.5Mn_6.5Si₁₀B₁₅ microwire exhibits a maximum on magnetic field, H, dependence, ΔZ/Z(H) at around H = 120 A/m of axial applied field. This maximum displaces towards larger applied fields when external stress, σ, is applied.

This high sensitivity of the GMI ratio to applied stress makes this stress sensitive GMI effect to be very interesting for practical purposes. Figure 16 shows a sensitive magnetoelastic device based on GMI exhibited by this microwire with the following working principle: the microwire has rather high DC electrical resistance per length owing to its tiny dimensions. Therefore, large changes of the magnetoimpedance could induce rather large changes of the AC voltage under mechanical loading. Indeed, under the effect of tensile stresses, the GMI ratio at fixed applied field, H, decreases giving rise to a significant change of the AC voltage between the sample's ends.

A DC magnetic field corresponding to the maximum ratio (ΔZ/Z)_m without stresses has been applied by means of a small solenoid. The change of AC voltage (peak to peak) between the ends of the sample is of around 3.5 V for small mechanical loads attached at the bottom of the microwire (see calibration curve in the Figure 16c). This huge change presented at the output permits one to conceive the successful use of this kind of sensor in different technological applications related with the detection of alternative mechanical stress.

Among recent applications, temperature dependence of the GMI effect and magnetic susceptibility in microwires with low Curie temperature, T_C, can be mentioned [34]. Particularly, the functioning of the temperature sensor based on GMI effect is based on the drastic drop of the GMI effect after achieving the Curie temperature (see Figure 17). In this case the GMI effect of microwire disappears above the Curie temperature, which is detected by the proposed circuitry. On the other hand the schematic picture showing the principle of the sensor based on the change of the inductance of the coil with the microwire inside is shown in Figure 18. In this case, the inductance of the coil with ferromagnetic wire inside drastically changes above Curie temperature of the microwire, allowing detection of the temperature.

On the other hand, as mentioned above, new types of magnetic field-tuneable, stress-tuneable and temperature-tuneable composite materials based on thin ferromagnetic wires with the effective microwave permittivity depending on an external DC magnetic field, applied stress or temperature recently have been introduced [34-36]. Such composites consist of arrays of continuous or short-cut (Figure 19) pieces of conductive ferromagnetic wires embedded into a dielectric matrix. Using magnetic microwires makes it possible to engineer low density materials with relatively high values of the effective magnetic permeability originated from natural magnetic properties of the wires with a circumferential magnetic anisotropy. The magnetic field in the incident wave along the wire will generate substantial magnetic activity as it will be in the orthogonal position with respect to a static magnetization.

The possibility to control or monitor the electromagnetic parameters (and therefore scattering and absorption) of the composites is of great interest for large-scale applications such as remote non-destructive testing, structural health monitoring, tunable coatings and absorbers. A number of applications have been proposed (as, for example, shown in Figure 19), including stress-sensitive media for remote non-destructive health monitoring of different structures, temperature-dependent media and selective microwave coatings with field-dependent reflection/transmission coefficients [34-36]. The important advantage of such applications is that the soldering problems are avoided because of the non-contact detection of the signals. It is worth mentioning that thin wires with stress sensitive magnetic anisotropy exhibiting stress sensitive GMI effect and SI effect are quite necessary for designing such composites.

On the other hand magnetic domain wall propagation has become a hot research topic because of the possibility of applications in magnetic devices, such as Magnetic Random Access Memory, Integrated Circuits, Hard Disks, Domain-wall Logics, etc. [30,31]. The high velocity of domain wall propagation observed in glass-coated microwires can be attractive to transmit the information along the magnetic microwire, like it was observed recently in wires of submicrometer diameter [30,31]. Clear advantage of glass-coated microwires is that the domain wall velocity is few times higher, achieving few km/s [5,34,43,45,47].