Electronic Surveillance and Security Applications of Magnetic Microwires

: Applications in security and electronic surveillance require a combination of excellent magnetic softness with good mechanical and anticorrosive properties and low dimensionality. We overviewed the feasibility of using glass-coated microwires for electronic article surveillance and security applications, as well as different routes of tuning the magnetic properties of individual microwires or microwire arrays, making them quite attractive for electronic article surveillance and security applications. We provide the routes for tuning the hysteresis loops’ nonlinearity by the magnetostatic interaction between the microwires in the arrays of different types of amorphous microwires. The presence of neighboring microwire (either Fe- or Co-based) signiﬁcantly affects the hysteresis loop of the whole microwires array. In a microwires array containing magnetically bistable microwires, we observed splitting of the initially rectangular hysteresis loop with a number of Barkhausen jumps correlated with the number of magnetically bistable microwires. Essentially, nonlinear and irregular hysteresis loops have been observed in mixed arrays containing Fe- and Co-rich microwires. The obtained nonlinearity in hysteresis loops allowed to increase the harmonics and tune their magnetic ﬁeld dependencies. On the other hand, several routes allowing to tune the switching ﬁeld by either postprocessing or modifying the magnetoelastic anisotropy have been reviewed. Nonlinear hysteresis loops have been also observed upon devitriﬁcation of amorphous microwires. Semihard magnetic microwires have been obtained by annealing of Fe–Pt–Si microwires. The observed unique combination of magnetic properties together with thin dimensions and excellent mechanical and anticorrosive properties provide excellent perspectives for the use of glass-coated microwires for security and electronic surveillance applications.


Introduction
Soft magnetic materials are an essential part of magnetic sensors and devices demanded by several industries, including (but not limited to) microelectronics, electrical engineering, car, aerospace, and aircraft industries, medicine, magnetic refrigerators, home entertainment, energy harvesting and conversion, informatics, magnetic recording, and security and electronic surveillance [1][2][3]. In most cases, like in the case of security and electronic surveillance, in addition to excellent magnetic softness, a combination of mechanical and anticorrosive properties and low dimensionality is required [4][5][6].
Almost all department stores, supermarkets, airports, libraries, museums, etc. are provided with different types of security and anti-thief systems. The principle of elec- The provided microwires geometry (d-and D-values) gives the average values determined by the optical microscopy at several places of the microwires. Typically, the spread in dand D-values is below 0.5 µm [5].
The amorphous structure of all the microwires has been proved by the X-ray diffraction (XRD) method. All amorphous microwires present a broad halo in the XRD patterns. The XRD patterns have been obtained by the Bruker (D8 Advance) X-ray diffractometer with Cu K α (λ = 1.54 Å) radiation. Several samples have been annealed in a conventional furnace at temperatures below the crystallization temperature. Typically, the crystallization of amorphous microwires was observed at T ann ≥ 500 • C [49].
The induction method previously was used for the hysteresis loops measurements. The details of the experimental set-up are described in details elsewhere [46]. The hysteresis loops were represented as the magnetic field, H, dependence of the normalized magnetization, M/M 0 , where M is the magnetic moment at a given magnetic field, and M 0 is the magnetic moment at the maximum magnetic field amplitude, H m . Such hysteresis loops are useful for comparison of the samples with different chemical compositions (hence, different saturation magnetization).
In several cases, the hysteresis loops were measured with a conventional superconducting quantum interference device, SQUID.
The magnetostriction coefficients, λ s , of the investigated microwires, were evaluated using the SAMR method adapted for microwires, as described elsewhere [46,49].
The experimental set-up allowing to measure the electromagnetic response of a magnetic tag consisting of an exciting coil, a pick-up coil, a preamplifier, and registration facilities is described elsewhere (see Figure 1) [47]. The experimental set-up allowing to measure the electromagnetic response of a magnetic tag consisting of an exciting coil, a pick-up coil, a preamplifier, and registration facilities is described elsewhere (see Figure 1) [47].  The magnetic tag (up to 4 cm long) is magnetized by 5 cm long exciting coil producing a nearly uniform magnetic field up to 640 A/m with frequency f = 332 Hz. We used a squared pick-up coil containing 20 turns with a side of 20 cm. An exciting coil with a magnetic tag inside was located perpendicular to the pick-up coil plane. The electromagnetic signal from the tag was amplified by a preamplifier with a voltage gain~100 and detected by the registration facilities, i.e., spectrum analyzer CF 5210 and a digital oscilloscope. The noise voltage level at a frequency higher than 1 kHz is given by~10 µV/Hz 1/2 . The tag placed inside the exciting coil produces a periodic signal of negative and positive pulses detected in the digital oscilloscope.
We also measured the amplitudes of the first seven harmonics of the voltage induced in the pick-up coil using a lock-in amplifier. For these measurements, the fundamental frequency was 200 Hz.

Feasibility of Using Magnetic Microwires for Magnetic Tags
For magnetic tag applications, the magnetic response must be as high as possible. Fe-rich microwires present a higher saturation magnetization. Additionally, as-prepared Fe-rich microwires have perfectly rectangular hysteresis loops (see Figure 2a). To assess the feasibility of using Fe-rich microwires for magnetic tags, we measured the fifth harmonic as a function of the distance between the tag and the pick-up coil. As can be seen from Figure 2b, the fifth harmonic of 3 cm long Fe 74 B 13 Si 11 C 2 microwire (metallic nucleus diameter, d = 17.3 µm) can be detected at a distance up to 25 cm. Similar studies of Fe-rich microwires with d ≈ 100 µm show that in this case, the signal can be detected at a distance up to 50 cm [48].
ducing a nearly uniform magnetic field up to 640 A/m with frequency f = 332 Hz. We used a squared pick-up coil containing 20 turns with a side of 20 cm. An exciting coil with a magnetic tag inside was located perpendicular to the pick-up coil plane. The electromagnetic signal from the tag was amplified by a preamplifier with a voltage gain ~100 and detected by the registration facilities, i.e., spectrum analyzer CF 5210 and a digital oscilloscope. The noise voltage level at a frequency higher than 1 kHz is given by ~ 10 μV/Hz 1/2 . The tag placed inside the exciting coil produces a periodic signal of negative and positive pulses detected in the digital oscilloscope.
We also measured the amplitudes of the first seven harmonics of the voltage induced in the pick-up coil using a lock-in amplifier. For these measurements, the fundamental frequency was 200 Hz.

Feasibility of Using Magnetic Microwires for Magnetic Tags
For magnetic tag applications, the magnetic response must be as high as possible. Fe-rich microwires present a higher saturation magnetization. Additionally, as-prepared Fe-rich microwires have perfectly rectangular hysteresis loops (see Figure 2a). To assess the feasibility of using Fe-rich microwires for magnetic tags, we measured the fifth harmonic as a function of the distance between the tag and the pick-up coil. As can be seen from Figure 2b, the fifth harmonic of 3 cm long Fe74B13Si11C2 microwire (metallic nucleus diameter, d = 17.3 μm) can be detected at a distance up to 25 cm. Similar studies of Fe-rich microwires with d ≈ 100 μm show that in this case, the signal can be detected at a distance up to 50 cm [48].  Figure 2b is adapted [47].
Perfectly rectangular hysteresis loops of Fe-rich microwires are quite stable: the character of hysteresis loops remains the same even after long annealing (180 min) at an elevated annealing temperature, Tann = 400 °C (see Figure 3a,b).
Only slight coercivity, Hc, decrease is observed upon annealing at Tann = 400 °C (Figure 3c). The crystallization temperature of the Fe74B13Si11C2 microwire is about 522 °C [49]. Therefore, a slight coercivity decrease must be associated with internal stresses relaxation. On the other hand, quite sharp voltage peaks (about 10 μs) in the pick-up coils are produced upon magnetization switching in such Fe-rich microwires (Figure 3d). Perfectly rectangular hysteresis loops of Fe-rich microwires are quite stable: the character of hysteresis loops remains the same even after long annealing (180 min) at an elevated annealing temperature, T ann = 400 • C (see Figure 3a,b).
Only slight coercivity, H c , decrease is observed upon annealing at T ann = 400 • C ( Figure 3c). The crystallization temperature of the Fe 74 B 13 Si 11 C 2 microwire is about 522 • C [49]. Therefore, a slight coercivity decrease must be associated with internal stresses relaxation. On the other hand, quite sharp voltage peaks (about 10 µs) in the pick-up coils are produced upon magnetization switching in such Fe-rich microwires (Figure 3d).

Tuning of Hysteresis Loop Nonlinearity by the Magnetostatic Interaction between Microwires
Magnetic tags applications require a nonlinear hysteresis loop that contains the characteristic distribution of harmonic frequencies. It is believed that the steeper the magnetization reversal, the higher the harmonic content of the signal. Accordingly, perfectly rectangular hysteresis loops with low coercivity observed in Fe-rich microwires (Figures 2 and 3) are attractive for use as magnetic tags.

Tuning of Hysteresis Loop Nonlinearity by the Magnetostatic Interaction between Microwires
Magnetic tags applications require a nonlinear hysteresis loop that contains the characteristic distribution of harmonic frequencies. It is believed that the steeper the magnetization reversal, the higher the harmonic content of the signal. Accordingly, perfectly rectangular hysteresis loops with low coercivity observed in Fe-rich microwires (Figures 2 and 3) are attractive for use as magnetic tags.
On the other hand, the nonlinearity of the hysteresis loop of the magnetic microwires can be further improved using the magnetostatic interaction of microwires. Below, we will present several experimental results on magnetic response of two kinds of individual microwires (Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 and Fe74B13Si11C2) as well as the arrays containing either microwires of the same type or containing two different kinds of microwires. Microwires in each array were located close to each other, that is, the magnetic nucleuses were separated only by the glass coatings.
The hysteresis loops of such microwires are rather different: microwire with high and positive magnetostriction coefficient, λs, exhibits perfectly a rectangular hysteresis loop with Hc ≈ 100 A/m (Figure 4a), however, an inclined hysteresis loop with quite low Hc (Hc ≈ 5 A/m) is observed in Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwires (see Figure 4b).  On the other hand, the nonlinearity of the hysteresis loop of the magnetic microwires can be further improved using the magnetostatic interaction of microwires. Below, we will present several experimental results on magnetic response of two kinds of individual microwires (Co 67 Fe 3.9 Ni 1.5 B 11.5 Si 14.5 Mo 1.6 and Fe 74 B 13 Si 11 C 2 ) as well as the arrays containing either microwires of the same type or containing two different kinds of microwires. Microwires in each array were located close to each other, that is, the magnetic nucleuses were separated only by the glass coatings.
The hysteresis loops of such microwires are rather different: microwire with high and positive magnetostriction coefficient, λ s , exhibits perfectly a rectangular hysteresis loop with H c ≈ 100 A/m (Figure 4a), however, an inclined hysteresis loop with quite low H c (H c ≈ 5 A/m) is observed in Co 67 Fe 3.9 Ni 1.5 B 11.5 Si 14.5 Mo 1.6 microwires (see Figure 4b).  As discussed elsewhere, the hysteresis loop of even individual Fe-rich magnetically bistable microwires is remarkably affected by the magnetic field amplitude. The most relevant hysteresis loop change in a single Fe-rich magnetically bistable microwire takes place when the magnetic field amplitude, H0, exceeds the switching field, Hs, value [50,51]: below certain "critical" magnetic field amplitude, Hc,crit, value (for studied Fe75B9Si12C4 microwire at Hc,crit ≈ 100 A/m), the hysteresis loop abruptly disappears (see Figure 5a). Above Hc,crit, the magnetization switching by single and large Barkhausen jump occurs. Accordingly, such critical magnetic field is commonly referred to as the aforementioned switching field, Hs, at which the irreversible magnetization switching begins. It is worth noting that in AC hysteresis loops at low H0 and magnetic field frequency, f, Hs ≈ Hc (see Figure 4a and Figure 5a). However, with increasing H0, one can observe a deviation from the perfectly rectangular hysteresis loop typical of magnetically bistable Fe-based microwires (Figure 5a). This modification of the hysteresis loop shape (more noticeable for high H0-values) was explained by taking into account the counterbalance between the sweep rate, dH/dt, and the magnetization switching time required for single domain wall (DW) propagation over the sample [50,52]. In the case of a triangular input signal, dH/dt is given as the following equation [52]: Accordingly, increasing of H0 or f results in faster sweep rate, dH/dt. Such change of the hysteresis loops is linked with Hc increase. Previously, the frequency and magnetic field amplitude dependence of coercivity in various magnetic materials has been described as follows [52,53]: where Hco is the static coercivity, H0 is the magnetic field amplitude, and n is a coefficient ranging from 1 to 4, which depends on the sample geometry and the type of the hysteresis loop of the studied materials, and B-a coefficient depending on the intrinsic material parameters [52,53]. Additionally, even the switching field, Hs, increases with increasing H0 and f (see Figure 5a). However, Hs increases slower than Hc with increasing H0 and f (see Figure 5a for H0). The origin of such Hc (f), Hs(f), Hc (H0), and Hs (H0) dependencies has been discussed considering a reversible magnetization process associated with reversible DW movement at low magnetic field (below magnetization switching) and the irreversible DW movement associated to large and single Barkhausen jump [52,53]. As discussed elsewhere, the hysteresis loop of even individual Fe-rich magnetically bistable microwires is remarkably affected by the magnetic field amplitude. The most relevant hysteresis loop change in a single Fe-rich magnetically bistable microwire takes place when the magnetic field amplitude, H 0 , exceeds the switching field, H s , value [50,51]: below certain "critical" magnetic field amplitude, H c,crit , value (for studied Fe 75 B 9 Si 12 C 4 microwire at H c,crit ≈ 100 A/m), the hysteresis loop abruptly disappears (see Figure 5a). Above H c,crit , the magnetization switching by single and large Barkhausen jump occurs. Accordingly, such critical magnetic field is commonly referred to as the aforementioned switching field, H s , at which the irreversible magnetization switching begins. It is worth noting that in AC hysteresis loops at low H 0 and magnetic field frequency, f, H s ≈ H c (see Figures 4a and 5a). However, with increasing H 0 , one can observe a deviation from the perfectly rectangular hysteresis loop typical of magnetically bistable Fe-based microwires ( Figure 5a). This modification of the hysteresis loop shape (more noticeable for high H 0 -values) was explained by taking into account the counterbalance between the sweep rate, dH/dt, and the magnetization switching time required for single domain wall (DW) propagation over the sample [50,52]. In the case of a triangular input signal, dH/dt is given as the following equation [52]: dH/dt = 4fH 0 (1) Accordingly, increasing of H 0 or f results in faster sweep rate, dH/dt. Such change of the hysteresis loops is linked with H c increase. Previously, the frequency and magnetic field amplitude dependence of coercivity in various magnetic materials has been described as follows [52,53]: where H co is the static coercivity, H 0 is the magnetic field amplitude, and n is a coefficient ranging from 1 to 4, which depends on the sample geometry and the type of the hysteresis loop of the studied materials, and B-a coefficient depending on the intrinsic material parameters [52,53]. The hysteresis loop of an array containing two Fe74B13Si11C2 microwires is rather different from that of a single Fe74B13Si11C2 microwire. Two Barkhausen jumps can be observed at H0 > 80 A/m (see Figure 5b). Such peculiar hysteresis loop shape has been explained by considering the magnetostatic interaction in the two-microwire array [50,51]. Such magnetostatic interaction is a consequence of stray fields created by magnetically bistable microwires: the superposition of external and stray fields causes magnetization reversal in one of the samples, when the external field is below the switching field of a single microwire. Single rectangular hysteresis loop (similar to the case of single microwire shown in Figure 5a) is observed for 60 A/m <H0 < 80 A/m (see Figure 5b).
In the array consisting of two microwires, the lower switching field of the first Barkhausen jump, Hs1, decreases, while the switching field of the second Barkhausen jump, Hs2, increases (Figure 5c). Such difference must be attributed to the stray field created by neighboring microwire [50,51]. The origin of the different Hs-values of individual microwires can be related with metallic nucleus diameters or glass-coating thickness fluctuations, stresses induced by cutting, and so forth.
At an increasing magnetic field amplitude (approximately at H0 > 250 A/m), this splitting of the hysteresis loop disappears (Figure 5d). Such dependence of the hysteresis loop of two microwires array can be understood from the counterbalance between the dH/dt and the switching time determined by the velocity of the DW propagation along the whole wire. Additionally, even the switching field, H s , increases with increasing H 0 and f (see Figure 5a). However, H s increases slower than H c with increasing H 0 and f (see Figure 5a for H 0 ). The origin of such H c (f ), H s (f ), H c (H 0 ), and H s (H 0 ) dependencies has been discussed considering a reversible magnetization process associated with reversible DW movement at low magnetic field (below magnetization switching) and the irreversible DW movement associated to large and single Barkhausen jump [52,53].
The hysteresis loop of an array containing two Fe 74 B 13 Si 11 C 2 microwires is rather different from that of a single Fe 74 B 13 Si 11 C 2 microwire. Two Barkhausen jumps can be observed at H 0 > 80 A/m (see Figure 5b). Such peculiar hysteresis loop shape has been explained by considering the magnetostatic interaction in the two-microwire array [50,51]. Such magnetostatic interaction is a consequence of stray fields created by magnetically bistable microwires: the superposition of external and stray fields causes magnetization reversal in one of the samples, when the external field is below the switching field of a single microwire. Single rectangular hysteresis loop (similar to the case of single microwire shown in Figure 5a) is observed for 60 A/m < H 0 < 80 A/m (see Figure 5b).
In the array consisting of two microwires, the lower switching field of the first Barkhausen jump, H s1 , decreases, while the switching field of the second Barkhausen jump, H s2 , increases (Figure 5c). Such difference must be attributed to the stray field created by neighboring microwire [50,51]. The origin of the different H s -values of individual microwires can be related with metallic nucleus diameters or glass-coating thickness fluctuations, stresses induced by cutting, and so forth.
At an increasing magnetic field amplitude (approximately at H 0 > 250 A/m), this splitting of the hysteresis loop disappears (Figure 5d). Such dependence of the hysteresis loop of two microwires array can be understood from the counterbalance between the dH/dt and the switching time determined by the velocity of the DW propagation along the whole wire.
As can be appreciated from Equation (2), H c is also affected by the frequency, f. Accordingly, H c , as well as overall hysteresis loops of the two-microwires array are affected by f in a similar way as by H 0 (see Figure 5c,d). For a two-microwires array, two-steps hysteresis loops are observed for f < 150 Hz. At f > 150 Hz, the hysteresis loop splitting disappears, and at 150 < f < 1000 Hz, a single smooth magnetization jump is observed.
Accordingly, the odd and even harmonics of the signal of two Fe-rich microwires array are affected by H 0 and f (see Figure 6a,b). osensors 2021, 9, x FOR PEER REVIEW 10 of 23 As can be appreciated from Equation (2), Hc is also affected by the frequency, f. Accordingly, Hc, as well as overall hysteresis loops of the two-microwires array are affected by f in a similar way as by H0 (see Figure 5c,d). For a two-microwires array, two-steps hysteresis loops are observed for f < 150 Hz. At f > 150 Hz, the hysteresis loop splitting disappears, and at 150 < f < 1000 Hz, a single smooth magnetization jump is observed.
Accordingly, the odd and even harmonics of the signal of two Fe-rich microwires array are affected by H0 and f (see Figure 6a A sharp increase in the harmonics amplitudes is observed when H0 exceeds Hs1 and Hs2 (see Figure 6a,b). The even harmonics amplitudes are significantly inferior to the odd harmonics amplitudes. The field dependences of odd harmonics have a "plateau" between 60 and 90 A/m, which reflects the hysteresis loops splitting (see Figure 6a).
Another example of tuning the nonlinearity of hysteresis loops and harmonics is the magnetostatic interaction of microwires with different character of hysteresis loops. Rather nonlinear hysteresis loops can be obtained in an array consisting of one Fe74B13Si11C2 and one Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire (see Figure 7a). In such array, at H0 < 90 A/m (which corresponds to Hs of Fe74B13Si11C2 microwire), the hysteresis loops character is typical of those for a single Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire. Essentially, nonlinear hysteresis loops have been observed at H0 > 110 A/m (Figure 7a). Such peculiar hysteresis loops can be interpreted as the superposition of two hysteresis loops: one from magnetically bistable Fe74B13Si11C2 microwire (shown in Figure 4a) and the other one from Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire with linear hysteresis loop (shown in Figure 4b A sharp increase in the harmonics amplitudes is observed when H 0 exceeds H s1 and H s2 (see Figure 6a,b). The even harmonics amplitudes are significantly inferior to the odd harmonics amplitudes. The field dependences of odd harmonics have a "plateau" between 60 and 90 A/m, which reflects the hysteresis loops splitting (see Figure 6a).
Another example of tuning the nonlinearity of hysteresis loops and harmonics is the magnetostatic interaction of microwires with different character of hysteresis loops. Rather nonlinear hysteresis loops can be obtained in an array consisting of one Fe 74 B 13 Si 11 C 2 and one Co 67 Fe 3.9 Ni 1.5 B 11.5 Si 14.5 Mo 1.6 microwire (see Figure 7a). In such array, at H 0 < 90 A/m (which corresponds to H s of Fe 74 B 13 Si 11 C 2 microwire), the hysteresis loops character is typical of those for a single Co 67 Fe 3.9 Ni 1.5 B 11.5 Si 14.5 Mo 1.6 microwire. Essentially, nonlinear hysteresis loops have been observed at H 0 > 110 A/m (Figure 7a). Such peculiar hysteresis loops can be interpreted as the superposition of two hysteresis loops: one from magnetically bistable Fe 74 B 13 Si 11 C 2 microwire (shown in Figure 4a) and the other one from Co 67 Fe 3.9 Ni 1.5 B 11.5 Si 14.5 Mo 1.6 microwire with linear hysteresis loop (shown in Figure 4b A/m (which corresponds to Hs of Fe74B13Si11C2 microwire), the hysteresis loops character is typical of those for a single Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire. Essentially, nonlinear hysteresis loops have been observed at H0 > 110 A/m (Figure 7a). Such peculiar hysteresis loops can be interpreted as the superposition of two hysteresis loops: one from magnetically bistable Fe74B13Si11C2 microwire (shown in Figure 4a) and the other one from Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire with linear hysteresis loop (shown in Figure 4b). At intermediate H0-values, the shape of the hysteresis loop depends on H0. The peculiar hysteresis loop character at H 0 ≤ 120 A/m can be explained by the partial magnetization reversal of the magnetically bistable wire under the influence of the stray field from the Co-based wire. The stray field is affected by the sample demagnetizing factor and the sample magnetization [54,55]. In the case of Co-rich microwire, the magnetization and hence, the stray field are affected by the applied magnetic field (as can be appreciated from the hysteresis loops shown in Figure 4b). In contrast, the magnetization of Fe-rich sample change by abrupt jump and below and above H s is almost independent of magnetic field (see Figure 4a).
Accordingly, such microwire array consisting of two microwires (Fe-rich and Co-rich) with different hysteresis loops presents odd and even harmonics quite different from the case of the array with two Fe-rich microwires (see Figure 7b,c). A single, sharp jump of odd and even harmonics is observed at H 0 ≈ H s . There is also a change in the odd and even harmonics in the weak (H 0 < H s ) field region (see Figure 7b,c).
Further tuning of harmonic spectra is observed in the array consisting of three Fe 74 B 13 Si 11 C 2 and one Co 67 Fe 3.9 Ni 1.5 B 11.5 Si 14.5 Mo 1.6 microwires (see Figure 8). The hysteresis loop of such array, consisting of three magnetically bistable microwires and one microwire with inclined hysteresis loop, is essentially nonlinear and has a complex shape (see Figure 8a). The peculiar hysteresis loop character at H0 ≤ 120 A/m can be explained by the partial magnetization reversal of the magnetically bistable wire under the influence of the stray field from the Co-based wire. The stray field is affected by the sample demagnetizing factor and the sample magnetization [54,55]. In the case of Co-rich microwire, the magnetization and hence, the stray field are affected by the applied magnetic field (as can be appreciated from the hysteresis loops shown in Figure 4b). In contrast, the magnetization of Fe-rich sample change by abrupt jump and below and above Hs is almost independent of magnetic field (see Figure 4a).
Accordingly, such microwire array consisting of two microwires (Fe-rich and Co-rich) with different hysteresis loops presents odd and even harmonics quite different from the case of the array with two Fe-rich microwires (see Figure 7b,c). A single, sharp jump of odd and even harmonics is observed at H0 ≈ Hs. There is also a change in the odd and even harmonics in the weak (H0 < Hs) field region (see Figure 7b,c).
Further tuning of harmonic spectra is observed in the array consisting of three Fe74B13Si11C2 and one Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwires (see Figure 8). The hysteresis loop of such array, consisting of three magnetically bistable microwires and one microwire with inclined hysteresis loop, is essentially nonlinear and has a complex shape (see Figure 8a). Basically, the hysteresis loop observed in low H0 region is similar to those of a single Co-rich microwire (see Figure 8a). The superposition of a linear hysteresis loop and three rectangular hysteresis loops with three Barkhausen jumps is observed with increasing H0 (see Figure 8a).
The harmonic spectra also reflect the multistep magnetization process of the array consisting of four microwires with different hysteresis loops with regions of gradual changes and abrupt jumps (see Figure 8b,c).
Thus, the use of arrays consisting of magnetic microwires allows us to create a complex and unique spectra of magnetic harmonics in magnetic microwires.
One of the main features of magnetically bistable amorphous microwires is that such Basically, the hysteresis loop observed in low H 0 region is similar to those of a single Co-rich microwire (see Figure 8a). The superposition of a linear hysteresis loop and three rectangular hysteresis loops with three Barkhausen jumps is observed with increasing H 0 (see Figure 8a).
The harmonic spectra also reflect the multistep magnetization process of the array consisting of four microwires with different hysteresis loops with regions of gradual changes and abrupt jumps (see Figure 8b,c).
Thus, the use of arrays consisting of magnetic microwires allows us to create a complex and unique spectra of magnetic harmonics in magnetic microwires.
One of the main features of magnetically bistable amorphous microwires is that such microwires behave similarly to single-domain magnets. Such behavior is linked to perfectly rectangular hysteresis loops of Fe-rich microwires (see Figures 4a and 9a) and the magnetostatic interaction described above. Accordingly, the hysteresis loops of a single magnetically bistable microwire and of the array of magnetically bistable microwires are substantially different. In the case of a single Fe 65 Si 15 B 15 C 5 microwire and arrays consisting of 2, 5, and 10 Fe 65 Si 15 B 15 C 5 microwires, the hysteresis loops are rather different (see Figure 9). The hysteresis loops shown in Figure 9 have been obtained when the microwires in the array were placed touching each other: the distance between the magnetic nucleuses was equal to the double glass-coating thickness (7.4 μm). For a single microwire, a single Barkhausen jump is observed (Figure 9a). An increase in the number of microwires causes an increase in the number of jumps (see Figure 9b-d) that correlates with the number of microwires.
As discussed above, the different Hs-values of the two jumps are explained by the influence of the stray field on the magnetization reversal in the array of a pair of microwires. The hysteresis loop splitting, ΔH, defined as the difference between Hs2 and Hs1, depends on the distance between the microwires (see Figure 9e). At a distance of about 2 mm, such splitting becomes negligible (Figure 9e). It is worth mentioning that such magnetostatic interaction in Co-rich microwires with inclined hysteresis loops is not quite pronounced. Thus, the presence of the second Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire in two Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwires array causes a slight increase in the effective The hysteresis loops shown in Figure 9 have been obtained when the microwires in the array were placed touching each other: the distance between the magnetic nucleuses was equal to the double glass-coating thickness (7.4 µm). For a single microwire, a single Barkhausen jump is observed (Figure 9a). An increase in the number of microwires causes an increase in the number of jumps (see Figure 9b-d) that correlates with the number of microwires.
As discussed above, the different H s -values of the two jumps are explained by the influence of the stray field on the magnetization reversal in the array of a pair of microwires. The hysteresis loop splitting, ∆H, defined as the difference between H s2 and H s1 , depends on the distance between the microwires (see Figure 9e). At a distance of about 2 mm, such splitting becomes negligible (Figure 9e). It is worth mentioning that such magnetostatic interaction in Co-rich microwires with inclined hysteresis loops is not quite pronounced. Thus, the presence of the second Co 67 Fe 3.9 Ni 1.5 B 11.5 Si 14.5 Mo 1.6 microwire in two Co 67 Fe 3.9 Ni 1.5 B 11.5 Si 14.5 Mo 1.6 microwires array causes a slight increase in the effective anisotropy field (see Figure 9f). The hysteresis loop shape remains almost the same.

Multi-Bit Magnetic Tags Applications of Magnetic Microwires
Hysteresis loops with several sharp jumps, observed in magnetically bistable microwire arrays, seem to be suitable for multi-bit magnetic tags. Such magnetic tags, consisting of several magnetically bistable microwires and presenting an overall hysteresis loop with several Barkhausen jumps, have been proposed for the magnetic codification method [25,27,56]. In such a magnetic tag, exposed to an AC magnetic field, each particular microwire is remagnetized in a different magnetic field, giving rise to an electrical signal on the detection system (see Figure 10).
Chemosensors 2021, 9, x FOR PEER REVIEW 12 of 21 ular microwire is remagnetized in a different magnetic field, giving rise to an electrical signal on the detection system (see Figure 10). In a magnetic tag consisting of magnetically bistable microwires of the same composition, the hysteresis loop splitting, among other factors, is substantially affected by the distance between microwires. Therefore, multi-bit magnetic tags consisting of magnetically bistable microwires with rather different switching fields are considered more suitable for such application [25,56]. The extended range of switching fields provides a possibility to use a large number of combinations for magnetic codification.
A variety of Hs-values can be achieved either by compositional Hs dependence or by the effect of internal stress or thermal treatments on Hs.
The influence of chemical composition on the Hs-values of amorphous microwires is originated by the compositional dependence of λs: a decrease in λs is observed in FexCo1−x amorphous alloys upon doping Fe-rich microwires with λs ≈ 40 × 10 −6 for x = 1, by Co up In a magnetic tag consisting of magnetically bistable microwires of the same composition, the hysteresis loop splitting, among other factors, is substantially affected by the distance between microwires. Therefore, multi-bit magnetic tags consisting of magnetically bistable microwires with rather different switching fields are considered more suitable for such application [25,56]. The extended range of switching fields provides a possibility to use a large number of combinations for magnetic codification.
A variety of H s -values can be achieved either by compositional H s dependence or by the effect of internal stress or thermal treatments on H s .
The influence of chemical composition on the H s -values of amorphous microwires is originated by the compositional dependence of λ s : a decrease in λ s is observed in Fe x Co 1−x amorphous alloys upon doping Fe-rich microwires with λ s ≈ 40 × 10 −6 for x = 1, by Co up to λ s~− (5−3) × 10 −6 for x = 0 [57][58][59]. Similarly, a decrease in λ s is reported in Fe x Ni 1−x alloys with an increase in Ni content [59,60].
However, even for microwires with fixed chemical composition, the Hs-values can be tuned by the internal stresses, σi, values. The main (though, not the unique) origin of the internal stresses in glass-coated microwires is the different thermal expansion coefficients of the metallic nucleus and the glass coating [36,[61][62][63][64]. Accordingly, it is assumed (and experimentally confirmed) that σi-magnitude inside the metallic nucleus is affected by the ρ-ratio between the metallic nucleus diameter, d, and the total microwire diameter, [36,[62][63][64].
As can be appreciated from Figure 12, even for the same microwire composition, Hs can be modified by almost an order of magnitude (from 85 to 630 A/m) by changing the ρ-ratio. The correlation of Hs and ρ-ratio is evidenced by the Hs(ρ) shown in Figure 12e.
The main problem with magnetic tags consisting of microwires with different d-values is that the magnetic moments of microwires with different d-values are rather different. Accordingly, the alternative approach lies in the use of heat treatment allowing internal stresses relaxation keeping the magnetization values the same.
For the Fe75B9Si12C4 microwires, annealing is not very effective: annealing allows only a slight Hs decrease (see Figure 3a-c). The lower coercivity of Fe 47.4 Ni 26.6 Si 11 B 13 C 2 and Fe 16 Co 60 Si 13 B 11 microwires as compared with Fe 77.5 Si 7.5 B 15 microwire correlates with lower λ s -values (see Figure 11).
However, even for microwires with fixed chemical composition, the H s -values can be tuned by the internal stresses, σ i , values. The main (though, not the unique) origin of the internal stresses in glass-coated microwires is the different thermal expansion coefficients of the metallic nucleus and the glass coating [36,[61][62][63][64]. Accordingly, it is assumed (and experimentally confirmed) that σ i -magnitude inside the metallic nucleus is affected by the ρ-ratio between the metallic nucleus diameter, d, and the total microwire diameter, [36,[62][63][64].
As can be appreciated from Figure 12, even for the same microwire composition, H s can be modified by almost an order of magnitude (from 85 to 630 A/m) by changing the ρ-ratio. The correlation of H s and ρ-ratio is evidenced by the H s (ρ) shown in Figure 12e Annealing is the more effective route for Hs tuning in Fe62Ni15.5Si7.5B15 and Fe49.6Ni27.9Si7.5B15 microwires with positive magnetostriction (λs ≈27 × 10 −6 and 20 × 10 −6 , respectively) [61,65,66].
The magnetic hardening, observed in Fe-Ni-based amorphous microwires upon annealing, has been explained considering the effect of DW stabilization [60,[65][66][67][68]. The mechanism of such DW stabilization is linked to directional atomic pair ordering along a preferred magnetization direction during the annealing and is usually observed for amorphous alloys with two or more ferromagnetic elements [60]. The nonmonotonic Hc(tann) dependence (see Figure 14e) was explained in terms of the simultaneous effect of internal stresses relaxation (allowing a decrease in Hc) and DW stabilization (leading to an increase in Hc) [65,66].  Figures 13 and 14). However, a remarkable increase in H s is observed in both Fe-Ni-based microwires upon annealing (see Figures 13b-d and 14b-d). The magnetic hardening, observed in Fe-Ni-based amorphous microwires upon annealing, has been explained considering the effect of DW stabilization [60,[65][66][67][68]. The mechanism of such DW stabilization is linked to directional atomic pair ordering along a preferred magnetization direction during the annealing and is usually observed for amorphous alloys with two or more ferromagnetic elements [60]. The nonmonotonic H c (t ann ) dependence (see Figure 14e) was explained in terms of the simultaneous effect of internal stresses relaxation (allowing a decrease in H c ) and DW stabilization (leading to an increase in H c ) [65,66].
The observed possibility to tune coercivity of Fe-Ni-based microwires by annealing makes them suitable for multi-bit tags applications.
Even a wider range of coercivities can be achieved by partial or complete devitrification of amorphous microwires. The main attractive feature of nanocrystalline materials is their magnetic softening upon nanocrystallization [17,60]. Such magnetic softening is commonly attributed to the mixed amorphous nanocrystalline (average grain size of 10-15 nm) structure of properly annealed amorphous Fe-based alloys doped by Cu and Nb [17,60,69]. Such nanocrystalline FeSiBCuNb alloys are commonly known as Finemet [60,69]. More recently, another family of nanocrystalline FeCoB-M-Cu (Hitperm) alloys has been proposed [69].
As shown in Figure 15, as-prepared Finemet-like and Hitperm-like glass-coated microwires also present perfectly rectangular hysteresis loops. In the present case, the Fe 38.5 Co 38.5 B 18 Mo 4 Cu 1 microwire presents a nanocrystalline structure in the as-prepared state [70,71]. The advantage of as-prepared nanocrystalline materials is that they can present better mechanical properties [70,72]. On the other hand, a rectangular hysteresis loop can be observed in nanocrystalline microwires devitrified by annealing of an amorphous precursor [70,74]. Thus, a rectangular hysteresis loop with H c ≈ 2000 A/m is observed in Fe 71,8 Cu 1 Nb 3,1 Si 15 B 9,1 microwire (ρ = 0.282) annealed at T ann = 700 • C (see Figure 16a).
Even a wider range of coercivities can be achieved by partial or complete devitrification of amorphous microwires. The main attractive feature of nanocrystalline materials is their magnetic softening upon nanocrystallization [17,60]. Such magnetic softening is commonly attributed to the mixed amorphous nanocrystalline (average grain size of 10-15 nm) structure of properly annealed amorphous Fe-based alloys doped by Cu and Nb [17,60,69]. Such nanocrystalline FeSiBCuNb alloys are commonly known as Finemet [60,69]. More recently, another family of nanocrystalline FeCoB-M-Cu (Hitperm) alloys has been proposed [69].
The second magnetic phase can also be created on the glass shell. Accordingly, bimagnetic glass-coated microwires consisting of glass-coated microwire surrounded by an external magnetic microtube have been reported [77,78]. However, such technology requires one more technological process related to precise sputtering or electroplating of the magnetic microtube [77,78]. Considering thousands of security systems and millions of tags required for such applications on a daily basis, such a technological scheme can be challenging.
The above-described magnetostatic interaction between various microwires requires certain precision and special attention to magnetic multi-bit tag design. Accordingly, appropriate digital algorithms have been developed for the multi-bit tag recognition [26]. Additionally, the magnetization process of microwire arrays with different geometrical configurations has been analyzed theoretically by considering dipole-dipole interaction [79][80][81].
On the other hand, magnetically hard and semihard microwires are required for the development of smart markers for the electronic article surveillance [82]. A semihard magnetic material is proposed as a "deactivating element". When the deactivating element is magnetized, it creates a stray magnetic field that saturates the neighboring soft magnetic element, making the soft magnetic element undetectable by the interrogator used in the interrogation zone.
One of the routes allowing magnetic hardening is the use of Fe-Pt-based microwires and proper annealing, allowing the formation of an L10-type superstructure [83]. Elevated coercivity, H c ≈ 40 kA/m, has been achieved in properly annealed Fe 50 Pt 40 Si 10 microwires upon devitrification of the amorphous precursor (see Figure 17).
Several alternative routes allowing magnetic hardening include controllable crystallization of Co-or Fe-rich microwires by Joule heating [84,85], by directional crystallization [86], by conventional furnace annealing [74], or by employing novel chemical compositions [87]. ment is magnetized, it creates a stray magnetic field that saturates the neighboring soft magnetic element, making the soft magnetic element undetectable by the interrogator used in the interrogation zone.
One of the routes allowing magnetic hardening is the use of Fe-Pt-based microwires and proper annealing, allowing the formation of an L10-type superstructure [83]. Elevated coercivity, Hc ≈ 40 kA/m, has been achieved in properly annealed Fe50Pt40Si10 microwires upon devitrification of the amorphous precursor (see Figure 17). Several alternative routes allowing magnetic hardening include controllable crystallization of Co-or Fe-rich microwires by Joule heating [84,85], by directional crystallization [86], by conventional furnace annealing [74], or by employing novel chemical compositions [87].
Provided routes for the design of nonlinear hysteresis loops allow us to consider amorphous and devitrified Fe-, Co-Fe-, Fe-Ni-, and Fe-Pt-rich microwires as quite promising candidates for the use in security and electronic surveillance applications. We Provided routes for the design of nonlinear hysteresis loops allow us to consider amorphous and devitrified Fe-, Co-Fe-, Fe-Ni-, and Fe-Pt-rich microwires as quite promising candidates for the use in security and electronic surveillance applications. We were able to tune the switching field of magnetically bistable microwires, by chemical composition of the metallic nucleus, by the internal stresses value (through the glass-coating thickness), by heat treatment as well as by magnetostatic interaction between magnetic microwires (through the magnetic field dependencies of even and odd harmonics). A predictable design of nonlinear hysteresis loops can serve as a good basis for magnetic tags application using glass-coated microwires.

Conclusions
We overviewed the properties of soft magnetic glass-coated microwires and the routes allowing to obtain nonlinear hysteresis loops either by different postprocessing or by using magnetostatic interaction between the microwires, making them quite attractive for electronic article surveillance and security applications.
The feasibility studies show that the fifth harmonics of 3 cm long typical Fe-rich microwire can be detected at a distance up to 25 cm.
We showed that the presence of neighboring microwire (either Fe-or Co-based) significantly affects the hysteresis loop of the whole microwires array. In a microwires array containing magnetically bistable microwires, we observed splitting of the initially rectangular hysteresis loop with a number of Barkhausen jumps correlated with the number of magnetically bistable microwires. Essentially, nonlinear and irregular hysteresis loops have been observed in mixed arrays containing Fe-and Co-rich microwires. The observed nonlinear hysteresis loops allowed to increase the harmonics and to tune their magnetic field dependencies.
Nonlinear hysteresis loops have been also observed upon devitrification of amorphous microwires.
On the other hand, several routes allowing to tune the switching field by either postprocessing or modifying the magnetoelastic anisotropy have been reviewed.
The observed unique combination of magnetic properties, together with thin dimensions and excellent mechanical and anticorrosive properties, provide excellent perspectives for the use of glass-coated microwires for security and electronic surveillance applications. and AVANSITE) projects and by the University of Basque Country under the scheme of "Ayuda a Grupos Consolidados" (Ref.: GIU18/192).

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the restrictions associated with the conditions of projects under development.