Development of Magnetically Soft Amorphous Microwires for Technological Applications

Abstract

Amorphous magnetic microwires can be suitable for a variety of technological applications due to their excellent magnetic softness and giant magnetoimpedance (GMI) effect. Several approaches for optimization of soft magnetic properties and GMI effect of magnetic microwires covered with an insulating, flexible, and biocompatible glass coating with tunable magnetic properties are overviewed. The high GMI effect and soft magnetic properties, achieved even in as-prepared Co-rich microwires with a vanishing magnetostriction coefficient, can be further improved by appropriate heat treatment (including stress-annealing and Joule heating). Although as-prepared Fe-rich amorphous microwires exhibit low GMI ratio and rectangular hysteresis loops, stress-annealing, Joule heating, and combined stress-annealed followed by conventional furnace annealing can substantially improve the GMI effect (by more than an order of magnitude).

1. Introduction

Magnetic functional cost-effective materials with tunable magnetic properties and reduced dimensions are highly demanded by numerous technological applications, such as sensors, security electronic surveillance, microelectronics, medicine, automobile and aircraft industries, energy harvesting and conversion, home entertainment, electrical engineering, magnetic recording, magnetic memories, etc. [1,2,3,4,5,6].

Among the most demanded properties of magnetic functional materials can be listed: good magnetic softness, energyharvesting, magnetocaloric effect, magnetoresistance effects (AMR, GMR, TMR), giant magnetoimpedance effect, GMI, magnetocaloric effect, MCE, Hall effect, etc. [1,2,3,4,5,6,7,8,9]. Cost and performance of devices and sensors are linked to the magnetic material properties and cost/price.

Amorphous magnetic materials produced by rapid quenching from the melt are considered among the most appropriate materials due to excellent soft magnetic properties combined with high mechanical and anticorrosive properties, and relatively simple and cost-effective fabrication technology [3,4,10,11,12,13,14,15]. The origin of such unique combination of properties of amorphous materials is linked to their glassy-like structure characterized by the absence of defects typical for crystalline structure [10,11,12,13,14,15].

Generally, amorphous materials can be prepared in the form of ribbons or wires [3,4,10,11,12,13,14,15]. For the implementation of certain magnetic properties (such as high GMI effect or magnetic bistability), cylindrical geometry is more suitable [16,17]. Therefore, different families of amorphous wires became subjects of extensive studies, and numerous applications of amorphous wires have been proposed [16,17,18,19,20,21,22,23,24,25,26,27].

The excellent magnetic softness exhibited by amorphous materials is intrinsically related to the GMI effect originated by the dependence of the skin depth, δ, of a magnetic conductor on an applied magnetic field, H, given as [28,29,30,31]:

$$\delta = \frac{1}{\sqrt{{\pi \sigma \mu }_{\phi }f}}$$

(1)

where μ_φ is the circumferential magnetic permeability, σ is the electrical conductivity, and f is the AC current frequency.

High sensitivity of magnetic wire impedance, Z, to an applied magnetic field, H, or even to applied stresses is crucial for development of numerous high-performance magnetic and magnetoelastic sensors [30,31,32,33,34,35,36,37,38,39]. For characterization of the GMI effect, the commonly used parameter is the GMI ratio, ΔZ/Z, defined as [28,29,30,31,32,33]:

ΔZ/Z = [Z(H) − Z(H_max)]/Z(H_max)] × 100,

(2)

where H_max is the maximum applied DC magnetic field (as a rule, below a few kA/m).

The other value of merit is the field sensitivity, η, given as [40]:

$$\mathsf{\eta }=\frac{\partial \left(\frac{\mathsf{\Delta }Z}{Z}\right)}{\partial H}$$

(3)

Up until now, the highest ΔZ/Zs are reported in amorphous microwires. Therefore, almost all reported GMI applications involve the use of magnetically soft amorphous wires with vanishing magnetostriction coefficient, λ_s [16,18,33,34,35,36].

Another peculiar feature of amorphous magnetic wires is spontaneous magnetic bistability associated with magnetization reversal through single and large Barkhausen jump and hence perfectly rectangular hysteresis loops [41,42,43]. This behavior is typically observed in amorphous wires of magnetostrictive compositions (in glass-coated microwires for λ_s > 0) and explained by the domain structure of amorphous wires consisting of an inner single domain with axial orientation surrounded by an outer domain shell with transverse orientation (radial for λ_s > 0 or circumferential for λ_s < 0) [41,42,43,44,45]. The ultrafast propagation of a single domain wall (DW) within a single inner domain, which starts from the end closure domains, is responsible for spontaneous magnetic bistability [41,42,43,44,45].

Amorphous wires can be prepared by various methods, all of them involving rapid melt quenching [12,13,46,47,48,49,50]. The so-called Taylor–Ulitovsky technique allows preparation of magnetic microwires in a wider range of diameters, d, (0.2 ≤ d ≤ 100 μm) coated by flexible and insulating glass coating [49,50,51]. Glass coating provides additional functionalities, such as improved mechanical and anticorrosive properties and biocompatibility [13,14,22,24,25].

This combination of magnetic and physical properties (good magnetic softness, magnetic bistability, GMI effect, good mechanical and anticorrosive properties, and biocompatibility) makes glass-coated microwires highly attractive for various applications and provides unique possibilities for basic research (studies of single DW propagation, GMI effect at GHz frequencies, among others).

In this review, we present trends related to optimization of soft magnetic properties and GMI effect of amorphous glass magnetic microwires suitable for various technological applications. This review is organized as follows: the fabrication method and experimental methods are described in Section 2. In Section 3, we review magnetic properties of as-prepared amorphous magnetic microwires. Finally, trends of magnetic softness and GMI effect are provided in Section 4.

2. Materials and Methods

Preparation of metallic (Pb, Sb, Bi, Au, Ag, Cu, Fe, Sn, Cd, Co, Ga) microwires by drawing out of the molten metal from a heated by flame glass tube was first reported in 1924 [52]. Almost continuous process of metallic nonmagnetic wire preparation was developed in 1964 [53]. Amorphous magnetic microwire preparation using the technology developed initially for nonmagnetic alloys was reported in the 1970s and 1980s [13,54]. Finally, this technology has been substantially modified: the modern fabrication facility is provided by a feedback system allowing control of main manufacturing parameters and geometry of the microwire (metallic nucleus diameter, d, and total diameter of the microwire, D) using a PC [55,56]. In recent publications, this preparation method is usually referred to as the modified Taylor–Ulitovsky method and/or the quenching and drawing method [54,56].

This preparation method involves the simultaneous rapid solidification of a composite microwire (a metallic nucleus inside a glass capillary) as it passes through a stream of coolant (water or oil) (see Figure 1a). Previously, a metallic alloy ingot (typically a few grams) of the desired chemical composition is melted inside a glass (Pyrex or Duran-like) tube by a high frequency (typically 350–500 kHz) inductor. Then a glass capillary is formed from the softened glass, which is captured by a rotating pick-up spool. The molten metallic alloy fills the glass capillary and a microwire with a metallic nucleus completely covered by a continuous, thin and flexible glass coating is formed (see Figure 1a,b). The metallic nucleus diameter, d, and glass-coating thickness can be tuned by the speed at which the wire is drawn and by the glass tube feed rate.

The high-frequency magnetic field of the inductor, high temperature itself, and interaction of the metallic alloy and glass can affect the chemical homogeneity of the glass-coated microwire; small glass particles can be entrained in the melt under the action of high-frequency magnetic field of the inductor [56,57]. These glass particles can be captured by the metallic nucleus and by the glass capillary during casting and even interrupt the process [56,57].

Although insulating glass coating protects from the surface oxidation typically observed in conventional (uncoated) amorphous wires, the presence of an interfacial layer between the metallic nucleus and glass coating is reported for various chemical compositions of metallic alloys (including Co- and Fe-based magnetic alloys) [57,58,59]. One of the examples is provided in Figure 2, where the element mappings obtained by scanning electron microscope JEOL JSM-6610 for the Fe_72,2B_13,2Si_10,9C₂ microwires are provided. A modification in Fe, Si, and C contents along the microwire radius is observed between the metal core and the glass coating. The interfacial layer thickness evaluated for various Fe-rich microwires is about 0.5 μm [58,59], which is quite similar to those provided for microwires from nonmagnetic alloys obtained by various methods [57].

The interfacial layer origin has been attributed to various phenomena [57,58,59]: solid state solutions between glass coating and metal core, uncompensated molecular forces at the interface between the glass and the metal nucleus, or the formation of stable chemical compounds with a structure that is different (from a crystallographic viewpoint) from the interacting materials. For nonmagnetic metallic nucleus, existence of correlation between the content of nonmetallic inclusions in the interfacial layer and the ρ-ratio between metallic nucleus diameter, d, and total diameter, D (ρ = d/D) is observed: the content of nonmetallic inclusions decreased increasing ρ-ratio [57]. Accordingly, for a thin metallic nucleus the existence of an interfacial layer may be more relevant.

The presence of bubbles spontaneously distributed in the glass coating is reported in Fe- and Co-rich microwires [60,61]. One of the examples is shown in Figure 3. The presence of such bubbles can produce internal stress heterogeneity within the metallic nucleus [58,59,60,61]. The equilibrium melt droplet shape is affected by the shape of the HF inductor, the electromagnetic field inside the molten ingot, ingot mass, alloy viscosity, and glass properties (melting temperature and thermal expansion coefficient), among other parameters.

The simultaneous rapid solidification of a metallic nucleus surrounded by a glass coating with different thermal expansion coefficients is the source of additional internal stresses [62,63,64,65,66]. Accordingly, in addition to quenching internal stresses, σ_iq, arising from the rapid melt quenching itself [62], there are two more sources of internal stresses: stresses originating from the different thermal expansion coefficients of metallic alloy and glass, σ_it, and stresses produced by wire drawing, σ_id, [63,64,65,66]. Most of experimental and theoretical results point out that σ_it » σ_iq and σ_it »σ_id. Additionally, σ_it value is of tensor character and can be tuned by the microwire geometry through the ρ-ratio (ρ = d/D).

In the most simplified approximation, σ_i has been expressed as [49,65,67]:

σ_φ = σ_r = εEkΔ/(k/3 + 1)Δ + 4/3; σ_z = σ_r(k + 1)Δ + 2/(kΔ + 1)

(4)

where σ_φ, σ_r, and σ_z are circular, radial, and axial stresses, Δ = (1 − ρ²)/ρ², k = E_g/E_m, E_m, E_g—Young modulus of metallic nucleus and glass, respectively, ε = (α_m − α_g)(T_m − T_room), α_m, α_g are thermal expansion coefficients of metallic nucleus and glass, respectively, and T_m, T_room are melting and room temperatures.

The more detailed theoretical estimations give σ_it up to 4 GPa [63,64,66], since σ_z is the largest in most part of the metallic nucleus volume (roughly up to r~0.85 R, where R is the metallic nucleus radius) [63,64,66]; σ_iq and σ_id are roughly an order of magnitude lower than σ_it [63,64,66].

In spite of aforementioned peculiarities of the Taylor–Ulitovsky preparation process (some of them are common with other methods involving rapid melt quenching), this technique is suitable for preparation of up to 10 km-long continuous glass-coated magnetic microwires with metallic nucleus diameters from 0.2 up to 100 μm. For most typical d-values (about 10–30 μm), about 1 km of glass-coated microwires can be prepared from 1 g of metallic alloy ingot.

In this review, we give attention to the development of amorphous microwires with magnetically soft properties exhibiting GMI effect.

Geometries of the microwires (d and D-values) provided are the average values determined by optical microscopy at several places along the microwires. Typically, the spread in d and D-values is below 0.5 μm.

Hysteresis loops of as-prepared and heat-treated microwires were evaluated using the fluxmetric method, described in detail elsewhere [68]. Hysteresis loops have been represented as the dependence of normalized magnetization, M/M₀, (M—the magnetic moment at a given magnetic field and M₀—magnetic moment at the maximum magnetic field amplitude H_m) on magnetic field, H. Such hysteresis loops are useful for comparison of samples with different chemical compositions (and, hence, different saturation magnetization). The magnetic field is created by a long (about 12 cm) and thin (about 8 mm in diameter) solenoid. Hysteresis loops are measured using a 20 mm-long pick-up coil.

A vector network analyzer and a microstrip sample holder were employed to evaluate the microwire impedance, Z, from the reflection coefficient, S₁₁, as previously described [69,70]. This technique allows Z measurements at frequencies, f, up to GHz frequencies [69,70]. Magnetic field, H, dependence of Z has been evaluated by placing the microstrip sample holder with microwire inside a sufficiently long solenoid producing H up to 20 kA/m. The GMI ratio, ΔZ/Z, has been evaluated from Z(H) dependence by using Equation (2).

The X-ray diffraction (XRD) method was used to prove the amorphous structure of microwires studied: all present XRD patterns with a broad halo. X-ray studies were performed using a Bruker (D8 Advance) X-ray diffractometer with Cu K_α (λ = 1.54 Å) radiation. For annealing, we used a standard Thermolyne furnace. All samples were annealed at temperatures, T_ann, below the crystallization temperature. Typically, the crystallization of amorphous microwires was observed at T_ann ≥ 500 °C [68,71]. In the case of stress-annealing, the stress value in the metallic nucleus, σ_m, was evaluated considering different Young’s modulus of metal, E₂, and glass, E₁, as described elsewhere [68,71]:

$${\sigma }_m=\frac{K·P}{K·S_m+S_{gl}}$$

(5)

where K = E₂/E₁, S_m and S_gl are the metallic nucleus and glass coating cross sections, respectively, and P is the applied mechanical load. As a rule, σ_m values were below 900 MPa. The tensile stress was applied during annealing and during cooling of the sample in the furnace. Typically, annealing duration, t_ann, was 60 min.

Values of the magnetostriction coefficients, λ_s, were measured by the small angle magnetization rotation (SAMR) technique using the setup adapted for microwires [72].

The compositions, diameters, and λ_s values of the microwires studied are provided in

Table 1. Composition and geometry of the glass-coated microwires studied.

Composition	Metallic Nucleus Diameter, d (μm)	Total Diameter, D (μm)	Ratio ρ = d/D	Magnetostriction Coefficient, λs × 106
Fe74B13Si11C2	16.6	20.8	0.8	38
Fe74Si11B13C2	14.6	21.8	0.55	38
Fe75B9Si12C4	15.2	17.2	0.88	38
Fe65Si15B15C5	15	23.8	0.63	38
Fe65Si15B15C5	10.8	22.5	0.48	38
Fe65Si15B15C5	6	23.1	0.26	38
Fe36Co40B12.9Si11.1	19.8	23.9	0.83	25
Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7	6.6	15.7	0.42	−3
Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7	6.8	13.6	0.5	−3
Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7	9.8	18.5	0.53	−3
Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7	11.8	18.4	0.64	−3
Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7	13.4	20.9	0.64	−3
Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7	16.8	24	0.7	−3
Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7	16.8	21	0.8	−3
Fe3.8Co65.4Ni1B13.8Si13Mo1.35C1.65	18.8	22.2	0.85	−1
Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2	22.8	23.2	0.98	−0.3
Fe16Co60Si13B11	12	29	0.4	15
Co41.7Fe36.4Si10.1B11.8	13.6	34	0.4	25
Co41.7Fe36.4Si10.1B11.8	18	38	0.47	25
Co41.7Fe36.4Si10.1B11.8	13.6	24.6	0.55	25
Fe62Ni15.5Si7.5B15	14.35	33.25	0.43	27
Co77.5Si15B7.5	13.1	18	0.73	−5

.

3. Magnetic Properties of as-Prepared Glass-Coated Microwires

Magnetic properties of as-prepared microwires are reported elsewhere [4,17,31,32]. Therefore, we describe them very briefly. As described elsewhere [4,17,31,32], perfectly rectangular hysteresis loops are observed in microwires with positive λ_s (Fe, Fe–Co, and Fe–Ni based), while microwires with vanishing λ_s present a completely different (linear and almost unhysteretic with low coercivity, H_c) character of hysteresis loops (see Figure 4d,e).

This correlation of the hysteresis loop character and λ_s values and sign are determined by the role of the magnetoelastic anisotropy, K_me, given as [4,41,42]:

K_me ≈ 3/2λ_sσ

(6)

where σ = σ_i + σ_app is the total stress, σ_i is the total internal stress, and σ_app is the applied stress.

Accordingly, the easiest way to tune the shape of hysteresis loops is by modifying the chemical composition of metallic nucleus.

The character of hysteresis loops is intrinsically related to the domain structure of microwires, which is affected not only by λ_s value and sign, but also by the internal stress distribution and by the shape magnetic anisotropy [73,74]. Thus, the axial magnetization alignment in the core of thin magnetic wires is determined by the shape anisotropy [74]. However, the presence of strong internal stresses in Co-rich magnetic microwires with λ_s < 0 turns the magnetization to a circumferential direction [44,45,73,74,75]. Accordingly, low H_c (about 4–5 A/m) and almost linear hysteresis loops of Co-rich glass-coated microwires with low and negative λ_s must be attributed to the remagnetization mechanism by magnetization rotation (see Figure 4d,e). In these microwires with internal stresses of preferentially axial origin, the σ_i value can be modified by the ρ-ratio (see Equation (4)). Accordingly, circumferential anisotropy of such Co-rich microwires can be tuned by ρ-ratio: magnetic anisotropy field, H_k, can be represented as a function of ρ-ratio (see Figure 5a,b). Proof of this interpretation is the dependence of the hysteresis loops of Co_65.4Fe_3.8Ni₁B_13.8Si₁₃Mo_1.35C_1.65 microwire on σ_app: qualitatively, the same type of H_k(σ_app) dependence (showing an increase in H_k under the effect of tensile applied stress, σ_app) is observed (see Figure 5c).

Observed decrease in H_k values by increasing the ρ-ratio must be attributed to decreased internal stresses of preferentially axial stress. However, simultaneously with a decrease in H_k an increase in H_c is observed (see Figure 5a,c). To explain the observed increase in H_c we must consider a remarkable magnetic hardening upon annealing, observed in various Co-rich glass-coated microwires with vanishing λ_s [68,70,72]. Similarly, transformation of almost anhysteretic loops into almost perfectly rectangular and, hence, H_c increase is also observed upon gradual glass-coating removal by chemical etching in Co-rich microwires [75]. This unexpected magnetic hardening has been explained considering either magnetostriction coefficient change induced by relaxation of the internal stresses or just an increase in the volume of inner axially magnetized core originating from the counterbalance between the magnetoelastic and shape anisotropies [68,70,71,72,73,74,75]. In the present case, a decrease in σ_app must affect the hysteresis loops in the similar way as the relaxation of the partial stresses. Therefore, an increase in H_c is expected.

Completely different hysteresis loops are reported for Fe-rich microwires (see Figure 6a–c); perfectly rectangular hysteresis loops are reported for as-prepared microwires with λ_s > 0 (Fe, Fe–Co, and Fe–Ni rich microwires) [17,45,75]. For Fe-rich microwires of the same composition (Fe₇₀B₁₅Si₁₀C₅), an increase in H_c is observed with a decrease in the ρ-ratio (i.e., with an increase in the σ_i value) (see Figure 6). Similar to Co-rich microwires, H_c can be represented as a function of ρ-ratio (see Figure 6b). Moreover, modification of hysteresis loops under applied tensile stress shown in Figure 6c has the same tendency as the influence of ρ-ratio; an increase in H_c upon σ_app is observed.

As shown in Figure 6a,b, in such Fe-rich microwires with perfectly rectangular hysteresis loops, a change in the ρ-ratio allows one to substantially change H_c (from 85 to 250 A/m).

Similarly, to the case of Co-rich microwires, the H_c values for different D and d values can be represented as the H_c(ρ) dependence (see Figure 6b).

An increase in H_c upon applied tensile stresses, σ, observed in Fe-rich microwires, was interpreted considering the energy required to form the domain wall involved in the bistable magnetization process [76]. This approach suggests H_c~σ^1/2, which is roughly experimentally observed for Fe-rich microwires [76]. A decrease in H_c upon increase of ρ-ratio (see Figure 6b) must be attributed to a decrease in σ_i magnitude.

As expected from the results provided above on the correlation of hysteresis loops and the ρ-ratio, ΔZ/Z(H) dependencies of Co-rich microwires are affected by ρ-ratio (see Figure 7a). Similar correlation of ΔZ/Z(H) dependencies and the ρ-ratio (reflecting the σ_i value) has been previously reported elsewhere for various Co-rich microwires [31,32,68,69,70,77]. Compared to Co-rich microwires with vanishing λ_s values, ΔZ/Z values that are quite low (an order of magnitude less) are reported for as-prepared microwires with λ_s > 0 (see Figure 7b). Therefore, from the viewpoint of GMI applications, as-prepared microwires with λ_s > 0 (Fe, Fe–Co, and Fe–Ni rich microwires) are usually not considered.

However, in as-prepared microwires with λ_s > 0 (Fe, Fe–Co and Fe–Ni rich microwires) with perfectly rectangular hysteresis loops, the remagnetization process runs by fast single DW propagation [78,79,80,81].

The evident correlation of magnetic properties and σ_i (modified through the ρ-ratio) is limited by various factors. Thus, the insulating glass coating with relatively low thermal conductivity can affect the quenching rate. Accordingly, microwires with sufficiently thick glass coating may present either crystalline or mixed crystalline–amorphous structures and, hence, rather different magnetic properties [56]. On the other hand, for sufficiently thin glass coating, the σ_it can be of the same order as σ_iq and σ_id (σ_it~σ_iq~σ_id). Accordingly, such correlation may be broken.

4. Tuning of Magnetic Softness and GMI Effect in Amorphous Microwires

As shown above, hysteresis loops and GMI effect are substantially affected not only by chemical composition of microwires, but also by their geometry (ρ-ratio). Therefore, obviously, for a comparative analysis on the effect of post-processing, we need to fix the composition and geometry of the microwire. Accordingly, we selected two typical Co- and Fe-rich microwires with fixed chemical composition and geometry, and provide comparative analysis for the selected microwires.

4.1. Tailoring of Magnetic Properties and GMI Effect in Co-Rich Amorphous Microwires

As shown above, internal stress (magnitude and spatial distribution) is one of the main factors affecting magnetic properties of glass-coated microwires. Thermal treatment is the most traditional method for internal stress relaxation. However, after conventional furnace annealing at sufficiently high temperature the hysteresis loop shape of Co-rich microwires with vanishing λ_s usually turns into rectangular [82,83].

As discussed above, hysteresis loops and GMI effect of Co-rich microwires are substantially affected not only by the chemical composition, but also by the geometry. Therefore, for comprehensive analysis of the influence of post-processing on magnetic properties, we selected just one typical Co-rich microwire: Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 (d = 22.8 μm, D = 23.2 μm).

Similar to other Co-rich microwires, considerable magnetic hardening is observed upon conventional annealing: all annealed samples at 250 °C ≤ T_ann ≤ 350 °C (t_ann = 60 min) present considerable magnetic hardening. Hysteresis loops of annealed samples turn to rectangular; a remarkable increase in H_c (from 4 up to 90 A/m) and remanent magnetization, M_r/M_o, upon annealing is observed (see Figure 8a). Finally, an almost perfectly rectangular hysteresis loop is observed for the sample annealed at T_ann ≥ 350 °C (t_ann = 60 min).

A decrease in the maximum GMI ratio, ΔZ/Z_max, is observed after annealing at T_ann = 200 °C, while an increase in the ΔZ/Z_max is observed at higher T_ann (see Figure 8b,c). The character of ΔZ/Z(H) dependence gradually changes after annealing from double peak (for as-prepared microwire) to single peak (with ΔZ/Z_max at H = 0) (see Figure 8b).

As observed elsewhere [83,84], magnetic hardening can be suppressed by stress-annealing. The stress-annealing induced anisotropy is affected by several parameters, such as T_ann and σ_m; after stress-annealing at moderate T_ann and σ_m a decrease in H_c and increase in M_r/M_o are observed (see Figure 9a). At higher T_ann, however, while a decrease in H_c is still observed with increasing σ_m, M_r/M_o begins to also decrease with increasing σ_m (see Figure 9b,c). Accordingly, magnetic softness of stress-annealed at sufficiently high T_ann and σ_m Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 microwire can be substantially improved; H_c ≈ 14 A/m and H_k ≈ 50 A/m are observed for the sample stress-annealed at T_ann = 300 °C and σ_m = 472 MPa. Even better magnetic softness: H_c ≈ 2 A/m and H_k ≈ 50 A/m and M_r/M_o ≈ 0 have been obtained for Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 microwire stress-annealed at T_ann = 350 °C and σ_m = 472 MPa (see Figure 9c).

The influence of both T_ann and σ_m on hysteresis loops is illustrated in Figure 10; almost identical properties have been obtained in Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 microwires stress-annealed at different T_ann and σ_m. Thus, H_c ≈ 14 A/m and H_k ≈ 50 A/m have been obtained in the Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 microwires stress-annealed at T_ann = 300 °C, σ_m = 472 MPa and T_ann = 375 °C, σ_m = 354 MPa.

Accordingly, substantial GMI performance improvement was achieved in properly stress-annealed Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 microwires; ΔZ/Z_max ≥ 200% is observed in all stress-annealed (at σ_m = 472 MPa) Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 microwires (see Figure 11a,b). These ΔZ/Z_max values are almost twice those for as-prepared Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 microwires (see Figure 11c).

The frequency, f_m, at which the highest ΔZ/Z_max value is observed in ΔZ/Z_max(f) dependence for as-prepared Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 microwire is at about 80 MHz (ΔZ/Z_max ≈ 100%). However, in stress-annealed samples ΔZ/Z_max ≈ 220% are observed at f_m ≈ 150 MHz (see Figure 11c). The ΔZ/Z(H) dependence character is also affected by stress-annealing; a double peak ΔZ/Z(H) dependence is observed in stress-annealed Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 microwires (see Figure 11a,b). However, the maximum in the ΔZ/Z(H) dependence is observed at a magnetic field, H_m, lower than that of the as-prepared Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 microwire. This difference must be explained considering that H_m is linked to the magnetic anisotropy field [28,29,30].

The origin of induced magnetic anisotropy in amorphous materials is commonly attributed either to directional atomic pair ordering (chemical or topological), structural anisotropy, or “back stresses” [85,86,87,88,89]. This magnetic anisotropy can be induced either by stress or by magnetic field annealing [85,86,87,88,89]. Weak circumferential magnetic anisotropy is considered as one of the prerequisites for achievement of high GMI effect [28,29,30]. Therefore, Joule heating, allowing annealing due to the heat generated by the electrical current in the presence of a circumferential magnetic field, H_circ, created by the current, is considered among the alternative methods for GMI effect tuning in amorphous materials [66,90,91,92,93,94].

One of the problems related to Joule heating is reliable determination of the sample temperature. In most cases the sample temperature is determined by indirect methods. Thus, one of the most relevant parameters of Joule heating treatment is the current density [95]. In conventional amorphous materials (ribbons and amorphous wires prepared by in-rotating water method), the current density, j, of 30–45 A/mm² produced heating up to 400 °C [95]. However, in glass-coated microwires the heat exchange is affected by thermal conductivity of glass coating, by microwire diameter. Accordingly, recent estimations considering convection and radiation heat exchange along with the experimental results (i.e., control of resistivity) show that the crystallization of a glass-coated microwire is observed at j > 200 A/mm² [94,96]. However, DC and even pulsed currents, I, of 50 mA can produce irreversible changes in GMI effect related to Joule heating [97]. Accordingly, for studies of the effect of Joule heating on GMI effect and magnetic softness of Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 microwire, we used I = 24 and 32 mA, which correspond to j ≈ 58 and 78 A/mm², respectively [93]. These I and j values are selected to avoid crystallization and related deterioration of magnetic properties.

Unlike conventional furnace annealing, under Joule heating (at I = 32 mA) the hysteresis loops of the Co_69.2Fe_3.6Ni₁B_12.5Si₁₁Mo_1.5C_1.2 microwire remain linear (see Figure 12). However, some decrease in H_k, was observed (see Figure 12 inset).

Accordingly, the relevant advantage of Joule heating treatment is that it allows for preventing the magnetic hardening observed upon conventional furnace annealing of Co-rich microwires with vanishing λ_s [83]. As observed in Figure 13, a remarkable increase in ΔZ/Z_max is observed in Joule heated samples.

An increase in ΔZ/Z_max from ΔZ/Z_max ≈ 100% up to ΔZ/Z_max ≈ 300% (for I = 24 and 32 mA, t_ann = 10 min) is achieved by Joule heating of Co₆₇Fe_3.9Ni_1.4B_11.5Si_14.5Mo_1.6 microwire (see Figure 13 and Figure 14).

From a comparison of ΔZ/Z_max values we must emphasize that both stress-annealing and Joule heating allows a remarkable ΔZ/Z_max improvement. In frequencies up to the f = 400–500 MHz range, the highest ΔZ/Z_max values are observed in Joule heated Co₆₇Fe_3.9Ni_1.4B_11.5Si_14.5Mo_1.6 microwire, while for f ≥ 600 MHz, higher ΔZ/Z_max values are observed in stress-annealed Co₆₇Fe_3.9Ni_1.4B_11.5Si_14.5Mo_1.6 microwire.

The origin of the magnetic field annealing induced anisotropy is commonly discussed in terms of the preferred magnetization orientation during the annealing [86,87,88,89,98,99,100].

In the present case, the internal stress relaxation may be responsible for the domain structure transformation related to an increase in the volume of the inner axially magnetized core upon annealing. Indeed, the origin of core–shell domain structure of magnetic wires is commonly attributed to the counterbalance of the magnetoelastic anisotropy related to distribution of internal stresses and the shape anisotropy [40,41,73,74]. The increase in remanent magnetization, M_r/M_o, upon annealing (see Figure 8a) must be therefore attributed to the inner axially magnetized core, R_c, increase considering the link between R_c and M_r/M_o as [40,74]:

R_c = R(M_r/M_o)^1/2

(7)

where R is the metallic nucleus radius.

However, the modification in λ_s upon annealing of amorphous materials with vanishing λ_s can be a relevant factor [101]. Thus, an increase in λ_s upon annealing of Co-rich microwires is reported elsewhere [102]. This influence of annealing on λ_s value and even sign is explained by the stress, σ, (either applied or internal) dependence of λ_s, described as [101,102]:

$${\lambda }_{s,\sigma }={\lambda }_{s,0}-B\sigma$$

(8)

where ${\lambda }_{s,\sigma }$ is the magnetostriction coefficient under stress, λ_s,0 is the zero-stress magnetostriction coefficient, and B is a positive coefficient of order 10⁻¹⁰ MPa.

The other source of magnetic hardening observed in Co-rich amorphous microwires is discussed in terms of the DW stabilization [75,98,99]. The origin of such DWs stabilization is associated with the diffusion of interstitial atoms or directional atomic ordering in ferromagnetic alloys consisting of at least two magnetic elements in the positions occupied by the DWs during annealing [98,99]. The DWs stabilization can be usually suppressed by magnetic field/stress-annealing [98,99].

Consequently, we can assume that stress-annealing and Joule heating are promising methods for optimization of both magnetic softness and GMI effect of Co-rich microwires.

4.2. Engineering of Magnetic Softness and GMI Effect in Amorphous Microwires with Positive Magnetostriction

There are several advantages of Fe-rich microwires, such as higher saturation magnetization values and lower price of Fe, which make them potentially attractive for GMI applications. However, as-prepared microwires with positive λ_s, characterized by rectangular hysteresis loops (see Figure 4a–c), usually have poor GMI performance (see example in Figure 7b). Therefore, a search for appropriate post-processing that allows for magnetic softening and GMI effect improvement is essentially relevant for applications of microwires with positive λ_s.

However, the character of the hysteresis loops of Fe-rich microwires annealed in a conventional furnace remains unchanged; a slight decrease in coercivity is observed for different T_ann, while all hysteresis loops maintain a perfectly rectangular shape (see Figure 15a).

Similarly, as-prepared and annealed Fe–Ni based microwires maintain rectangular character of hysteresis loops and hence relatively low ΔZ/Z_max values (as compared to Co-rich microwires with vanishing λ_s) [104].

Similar to Co-rich microwires, transverse magnetic anisotropy can be induced by stress-annealing of Fe-rich microwires [32,71,103,105]. Indeed, a gradual change in hysteresis loops from rectangular to linear is observed in the Fe₇₅B₉Si₁₂C₄ microwire stress- annealed at the same annealing conditions (t_ann and T_ann) (see Figure 15b).

There are common features of stress-annealing induced magnetic anisotropy of Co- and Fe-rich microwires; in both cases induced anisotropy depends on T_ann, σ_m and t_ann. Thus, there is a similar tendency: a decrease in remnant magnetization, M_r/M_o, and coercivity, and increase in magnetic anisotropy field, which are observed after stress-annealing at fixed σ_m increasing T_ann (see Figure 15) or at fixed T_ann increasing t_ann or σ_m (see Figure 16 and Figure 17).

Accordingly, Fe₇₅B₉Si₁₂C₄ microwires stress-annealed at sufficiently high T_ann, σ_m, or t_ann present substantial transverse magnetic anisotropy (see Figure 16 and Figure 17).

The observed magnetic softening upon stress-annealing enables considerable improvement of GMI effect performance in Fe-rich microwires [71,103,105]. A comparison of ΔZ/Z(H) dependencies of as-prepared and stress-annealed Fe₇₅B₉Si₁₂C₄ microwires is shown in Figure 18. In addition to a noticeable ΔZ/Z_max value improvement in stress-annealed Fe₇₅B₉Si₁₂C₄ microwires, the character of the ΔZ/Z(H) dependencies changes from single to double peak (see Figure 18a,b). Previously, double peak ΔZ/Z(H) dependencies were predicted for magnetic wires with circumferential character of magnetic anisotropy, while single peak ΔZ/Z(H) dependencies were for wires with axial magnetic anisotropy [106]. Therefore, modification of both ΔZ/Z_max values and ΔZ/Z(H) dependencies satisfactorily correlate with change in hysteresis loop character upon stress-annealing.

One of the peculiarities of ΔZ/Z(H) dependencies of stress-annealed Fe-rich microwires is unusual and irregular ΔZ/Z(H) dependencies at intermediate frequencies, f, range (roughly between 50 and 400 MHz) (see Figure 19b). At low frequencies (10–50 MHz), ΔZ/Z(H) dependencies present single peak character similarly to as-prepared Fe₇₅B₉Si₁₂C₄ microwire (with a single maximum at H = 0). For f ≥ 500 MHz ΔZ/Z(H) dependencies transform to double peak typical for wires with transverse magnetic anisotropy (see Figure 19c). The irregular ΔZ/Z(H) dependencies have been explained by the contribution of the inner axially magnetized core superposition with single peak ΔZ/Z(H) dependence and the double peak ΔZ/Z(H) dependence from the outer shell [103]. Indeed, from the δ(f) dependence given by Equation (1), one can predict a decrease in δ with increasing f. Therefore, the inner axially magnetized core contribution must decrease with increasing frequency.

These irregular ΔZ/Z(H) dependencies have been suppressed by the subsequent conventional furnace annealing followed by stress-annealing (see Figure 20a,b) [107]. Additionally, subsequent conventional furnace annealing followed by stress-annealing allowed for further improvement of ΔZ/Z_max magnitude; values up to 160% have been achieved (see Figure 20a,b).

Recently, the influence of Joule heating on the magnetic properties and the GMI effect of the Fe₇₅B₉Si₁₂C₄ microwire has been evaluated [108,109]. As in the case of Co-rich microwires, an improvement of ΔZ/Z_max by almost an order of magnitude is observed in Joule heated (j ≈ 110 A/mm²) Fe₇₅B₉Si₁₂C₄ microwires (see Figure 21a). However, the hysteresis loop character of the Joule annealed Fe₇₅B₉Si₁₂C₄₂ microwire remains quite similar to the as-prepared sample (see Figure 21b).

Additionally, after Joule heating of the Fe₇₅B₉Si₁₂C₄₂ microwire, the ΔZ/Z(H) dependencies change from a single peak to a double peak (see Figure 21a). This evolution of ΔZ/Z(H) dependencies must be associated to low circumferential magnetic anisotropy induced by Joule heating.

As discussed above, the origin of stress-induced anisotropy in amorphous materials is still unclear and commonly discussed considering “back stresses”, the atomic directional pair ordering or topological short range ordering [86,87,88,89,110]. In the present case, stress-annealing induced anisotropy is observed in both types of microwires: Fe-rich with only one ferromagnetic element (Fe) and Co-rich microwires containing Fe and Ni.

The contributions of atomic directional pair ordering and back stresses cannot be completely excluded. However, the irreversible character of the stress-annealing induced magnetic anisotropy obtained upon stress-annealing at elevated σ_m indicates a relevant contribution from topological short-range ordering (also known as structural anisotropy) [107].

The yield stress of most amorphous materials at room temperature is of the order of 700 MPa. Therefore, a certain amount of creep and plastic deformation could occur for stress-annealed microwires, giving rise to irreversible stress-annealing induced anisotropy. On the other hand, the yield stress value is affected by the diameter and by the chemical composition [13,111]. Thus, the yield stress of glass-coated Fe–B microwires with diameter of the order of 10–20 μm can be substantially increased by additions of Co and Si up to 4.4 GPa [111].

The dependence of stress-annealing induced anisotropy on the stress-annealing conditions was recently employed to develop magnetic microwires with graded magnetic anisotropy [105,112]. Fe-rich microwires with a graded magnetic anisotropy were prepared by stress-annealing at a variable annealing temperature. In magnetic materials with graded magnetic anisotropy, a controllable spatial distribution of magnetic anisotropy can be obtained.

Controlled DW injection or trapping, previously predicted for thin films with graded magnetic anisotropy [113], were experimentally demonstrated in such magnetic microwires with graded magnetic anisotropy [105,112]. Earlier, to obtain the graded magnetic anisotropy in thin films, a rather complex method was used, consisting in the modification of the chemical composition during the thin film preparation [114,115].

As mentioned, reported elsewhere [3,4,10,11,12,13,14,15], amorphous magnetic materials can present not only excellent soft magnetic properties, but also high mechanical and anticorrosive properties. Although the nanocrystallization allows for considerable magnetic softening of certain amorphous alloys (for example, Finemet-type alloys) [3,10,56], the devitrification also involved drastic deterioration of mechanical properties [14]. In this review, we focused on only completely amorphous microwires coated by amorphous glass (which also prevents corrosion). Accordingly, all microwires studied were completely amorphous. The amorphous origin of structure was confirmed several times by different structural methods (X-ray diffraction, DSC) [82,83]. All annealing conditions (T_ann, t_ann) were selected in order to avoid the crystallization typically observed in the microwires studied at T_ann ≈ 500 °C [83].

The main pinning mechanisms of amorphous materials have been identified and discussed by Kronmüller et al. [116,117,118]. In amorphous materials, the domain structure is mostly determined by three different types of anisotropy energies: shape anisotropy (including the surface irregularities), magnetoelastic anisotropy, and structure anisotropy [116,117,118].

Accordingly, the existence of the interfacial layer (see Figure 2a–g) and the fluctuations of the internal stresses related to the presence of bubbles spontaneously distributed in the glass coating can affect the DW pinning.

The remarkable effect observed of stress-annealing induced magnetic anisotropy must be attributed to the contribution from structural anisotropy. This structure anisotropy in as-prepared amorphous materials is usually attributed to temperature gradients or magnetic fields occurring during the fabrication process. The possible origins are either gradients in the distribution of metalloid atoms, short range atomic pair ordering in amorphous materials containing two or more ferromagnetic elements, or the angular distribution of atomic bonds and small anisotropic structural rearrangements at the temperature near glass transition [87,118]. The evidence of such structural anisotropy in amorphous materials has been confirmed by energy dispersive X-ray diffraction (EDXD) [87].

Recently, we observed that such stress-annealing induced anisotropy in Fe-rich microwires can be annealed out only partially [107]. Therefore, the magnetic anisotropy related to back stresses can be responsible for the reversible stress-annealing induced anisotropy [107].

In certain cases, such as thicker magnetic wires prepared by melt extraction, strong stresses produced by cold-drawn can produce the mechanical deformation that induces the precipitation of nanocrystals [119]. However, this was not the case for studied as-prepared and annealed glass-coated amorphous microwires.

On the other hand, the origin of the GMI effect is commonly attributed to the magnetic field dependence of skin depth, δ, of magnetically soft conductor and explained in terms of classical electrodynamics [16,28,29,30,31]. The GMI effect features are linked to magnetic properties of the surface layer. In several publications, δ(H) dependencies were evaluated and showed that the minimum skin depth values, δ_min, at f ≥ 100 MHz are of about 1–2 µm, reaching values of δ_min ≈ 1.2 µm at 1 GHz [68]. These δ_min values are comparable to the thickness of the interfacial layer (about 0.5 μm) (see Figure 2). Accordingly, we can assume that the spatial distribution of magnetic anisotropy in the surface layer of metallic nucleus can be affected by the interfacial layer.

Evolution of the ΔZ/Z/(H) dependencies and ΔZ/Zmax for Fe₇₅B₉Si₁₂C₄ and Co₆₇Fe_3.9Ni_1.4B_11.5Si_14.5Mo_1.6 microwires subjected to various heat treatments (annealing, stress-annealing, and Joule heating) at selected frequencies, f, (10, 100, 200, and 500 MHz) is shown in Figure 22. Intermediate frequencies are selected considering that the highest ΔZ/Zmax values are usually observed at f ≈ 100–200 MHz.

Generally, the link between magnetic anisotropy and ΔZ/Z/(H) dependencies and ΔZ/Zmax can be clearly identified in most of the microwires studied. Thus, a decay in ΔZ/Z(H) from H = 0 for all f-values and rather low ΔZ/Zmax value are observed for as-prepared Fe₇₅B₉Si₁₂C₄ microwires with rectangular hysteresis loop (see Figure 22a). These single peak ΔZ/Z(H) dependencies are predicted and observed experimentally for magnetic wires with axial magnetic anisotropy [28,29,30,31,106].

However, almost an order of magnitude higher ΔZ/Zmax value and double peak ΔZ/Z(H) dependencies are observed in as-prepared Co₆₇Fe_3.9Ni_1.4B_11.5Si_14.5Mo_1.6 microwires (Figure 22e), and in stress-annealed Fe₇₅B₉Si₁₂C₄ microwires with transverse induced magnetic anisotropy (Figure 22b). These double peak ΔZ/Z(H) dependencies are typical for magnetic wires with transverse magnetic anisotropy [28,29,30,31,106].

The ΔZ/Z(H) dependencies shown in Figure 22b were obtained for Fe₇₅B₉Si₁₂C₄ microwires stress-annealed at σ_m = 760 MPA, with a rather strong induced transverse magnetic anisotropy. Therefore, the ΔZ/Zmax values observed in these Fe₇₅B₉Si₁₂C₄ microwires are lower than those observed for the same microwires stress-annealed at σ_m = 190 MPa (see Figure 19). The irregularity in the ΔZ/Z(H) dependencies at intermediate frequencies (f = 100 and 200 MHz), observed in both stress-annealed microwires, was attributed to the superposition of the contributions coming from the inner axially magnetized core (having a single peak ΔZ/Z(H) dependence) and a double peak ΔZ/Z(H) dependence from the outer shell with transverse magnetic anisotropy. This irregularity in the ΔZ/Z(H) dependencies can be suppressed by subsequent annealing (see Figure 22c), which also allows for the reduction of strong transverse induced magnetic anisotropy due to partial relaxation of the reversible part of the stress-annealing induced anisotropy. In this case, the double peak ΔZ/Z(H) dependence is observed at f ≥ 100 MHz (see Figure 22) and higher ΔZ/Zmax values are observed. Joule heating is an alternative route for ΔZ/Zmax improvement in Fe- and Co-rich microwires (see Figure 22d,g). However, the hysteresis loops of Joule heated microwires are rather similar to those of as-prepared microwires. Therefore, the GMI ratio improvement in Joule heated microwires can be attributed to heating in the presence of the Oersted magnetic field during Joule heating.

The magnetic softness and GMI effect of Co-rich microwires stress-annealed at appropriate annealing conditions (T_ann, t_ann or σ_m) can be substantially improved (see Figure 22f). The double peak ΔZ/Z(H) dependence is observed over the entire f range, while the maxima in the ΔZ/Z(H) dependencies are observed at a lower magnetic field, H_m.

Despite the rectangular hysteresis loop of the annealed Co-rich microwire, the double peak ΔZ/Z(H) dependence observed at f ≥ 200 MHz in this microwire is attributed to the circumferential magnetization alignment of the outer domain shell [44].

In general, higher ΔZ/Z_maxvalues are observed in properly processed Co-rich microwires. However, higher ΔZ/Z_max are observed at elevated (e.g., f = 500 MHz) frequencies in stress-annealed or Joule heated Fe-rich microwires.

Although magnetic softness is one of the prerequisites for GMI effect optimization, the domain walls become strongly damped by eddy currents at frequencies above 10 MHz [120]. All of the results provided consider frequencies above 10 MHz (most are above 100 MHz). Consequently, the GMI effect at elevated frequencies is discussed in terms of the fundamental link between ferromagnetic resonance, FMR, and GMI [69,120,121,122]. However, the AC Oersted field distribution is influenced by the skin effect, and therefore it is necessary to consider the FMR for the heterogeneous driving field [122].

Aforementioned results on effect of stress-annealing and Joule heating on magnetic properties and GMI effect provide efficient routes to enhance magnetic softness and GMI effect in magnetic microwires. A remarkable GMI effect improvement can be achieved by appropriate post-processing.

5. Conclusions

We summarized the magnetic properties and GMI performance of amorphous magnetic glass-coated microwires and the methods that allow for improving magnetic softness and GMI effect. Glass-coated magnetic microwires with amorphous structure present a unique combination of soft magnetic properties together with thin dimensions and excellent mechanical and anticorrosive properties. Tunable magnetic properties together with new functionalities provided by an insulating, flexible, and biocompatible glass coating make these microwires suitable for various technological applications, including magnetic and magnetoelastic sensors.

Several routes for optimization of the magnetic properties of magnetic microwires are provided. Magnetic softness and GMI effect of microwires with a vanishing magnetostriction coefficient can be substantially improved by appropriate annealing (including stress-annealing and Joule heating). As-prepared amorphous microwires with positive magnetostriction coefficient and rectangular hysteresis loops are unsuitable for GMI applications. However, magnetic softness and GMI effect have been remarkably improved through appropriate post-processing, including stress-annealing, Joule heating, and combined stress-annealing, followed by conventional furnace annealing, which can significantly improve the GMI effect (by more than an order of magnitude).