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Microwave programmable response of Co-based microwire polymer composites through wire microstructure and arrangement optimization

Traditional approaches to realize microwave tunability in microwire polymer composites which mainly rely on topological factors, magnetic field/stress stimuli, and hybridization prove to be burdensome and restricted to rather narrow band frequencies. This work presents a novel yet facile strategy based on a single component tunable medium to program the transmission response over wide frequency bands. To this end, we demonstrated that structural modification of one type of microwire through suitable current annealing and arrangement of the annealed wires in multiple combinations were sufficient to distinctly red-shift the transmission dip frequency of the composites. Such one wire control-strategy endorsed a programmable multivariable system grounded on the variations in both the overall array conductivity or"effectiv"area determined by the wires arrangement and the relaxation time dictated by the annealing degree of microwires. These results can be used to prescribe transmission frequency bands of desired features via diverse microwire arrays and microwave performance from a single component to a composite system design.


Introduction
Recently, polymer-based composites incorporating arrays of ferromagnetic glass-coated microwires have gained much attention due to their Giant Magneto-impedance (GMI) effect and tunable soft magnetic properties which confer them potential applications in electronic sensing, electromagnetic shielding, microwave absorption and structural health monitoring [1,2]. Although electromagnetic functionalities (e.g., metamaterial wave conditions on Co-based wires of the same composition and tune their transmission parameters through distinct dynamic wire-wire interactions, which is enabled by the arrangement of structurally different wires within the microwire array composite. Both transmission magnitude and transmission dip frequency proved to be tunable with the systematic combination of the as-cast and annealed wires. Our single component-control strategy provides an accessible platform for programming and prescribing the ultimate electromagnetic properties of microwire array composites for a wide frequency range, which is hard to design and often requires plenty of components to fulfill requirements for each particular application.

Current Annealing of Co60Fe15Si10B15 glass-coated microwires
Co60Fe15Si10B15 glass-coated microwires with total wire diameter Dw=35.4 µm and metallic core diameter of Dm=27.2 µm were selected for our study. The microwires were fabricated by a modified Taylor-Ulitovsky method [14] by simultaneously drawing and quenching the molten master alloy. 5 grams of the master alloy with the selected composition were put into a Pyrex glass tube and placed within a high-frequency inductor heater. While the metal melted, the portion of the glass tube adjacent to the melting metal softened; enveloping the metal droplet. A glass capillary was then drawn from the softened glass portion and wound on a rotating coil. By adjusting the drawing conditions, the molten metal filled the glass capillary and the microwire was formed in which the metal core was completely coated by the glass shell. To modify the structural features of the microwires and therefore, electromagnetic properties, as-cast wires (labeled as A) of about 12 cm in length were annealed at different DC currents of 20 mA, 30 mA and 40 mA for 10 minutes. Prior to current-annealing, the glass coating of the wire was mechanically removed from both ends to allow electrical contact (Fig. 1). In addition, the DC resistance was monitored after each current application with a digital multimeter showing a considerable drop for the wire treated at 40 mA, which indicates a possible onset of crystallization. Such drop is related to large grain size due to the rise in temperature caused by the current that will lead to less electron scattering at the reduced grain boundaries [15]. The crystallization starts initially at the surface of the wire and grows slowly with islands of crystallites nucleating homogeneously all over the wire (as will be elucidated in Section 3.2). This leads to bigger grain size formation and lower resistance as it crystallizes. After current-annealing, the morphology and topography of the wires were studied by scanning electron microscopy (SEM) in a Hitachi S-4800 cold field emission scanning electron microscope and a Bruker icon atomic force microscope (AFM). Thermal, structural and magnetic properties of the microwires were evaluated by Differential Scanning Calorimetry (DSC 204 HP Phoenix, the heating rate of 10K/min), X-Ray Diffraction (BEDE multi-function high-resolution X-ray diffractometer) and Quantum Design PPMS-VSM at room temperature, respectively.

Preparation and electromagnetic characterization of Co60Fe15Si10B15 glass-coated microwire/ silicon resin composites
The as-cast and annealed wires were incorporated into silicon-resin matrix in different arrangements and combinations (Fig. 2). The initial arrays were composed of the same type of microwire, either as-cast A (0 mA), annealed wires B (30 mA) or C (40 mA), Fig.   2 a. Subsequently, the as-cast wires were combined with B annealed wire (Fig. 2 b) and C annealed wire (Fig. 2 c) [16].

Structural and thermal properties of Co60Fe15Si10B15 glass-coated microwires
In order to check the effect of annealing treatment on the structural and thermal properties of the microwires, we explored DSC and XRD analyses. The increase in temperature during current annealing depends not only on the current density but also on the microwire diameter [17]. To evaluate the temperature reached due to current annealing, the following equation of conversion of electrical-to-thermal energy can be used [17]: where ρ is the electric resistivity, h is the coefficient of Newton's law of convection cooling, ε is the emissivity coefficient, α=5.67·10 -8 W/m 2 /K 4 is the Stefan-Boltzmann constant and Tex is the ambient temperature. In the case of microwires with a metallic core diameter in the range of 20 microns, currents of 25-50 mA correspond to temperatures of 400-550 K which are high enough for structural relaxation and partial relief of internal stresses [18], but lower than the crystallization temperature, Tx of 720 K shown in Fig. 3 a. DSC curves of the as-cast wires and 30mA and 40mA annealed wires reveal the influence of current annealing on the structural relaxation and crystallization processes.
For the as-cast wire, a very small Curie peak, around Tc of 635 K reflects a large concentration of internal stresses [19]. In addition, a two-step crystallization process is also noticed. Annealing the wire at 30 and 40mA results in a splitting of the Tc into two peaks confirming the presence of two magnetic phases and appearance of small clusters with different local environment [20]. The higher intensity of these peaks and increase of Tc are related to a reduction in internal stresses and structural relaxation processes [19,20].
In addition, the broadening of the crystallization peak after annealing and increase of Tx with respect to the as-cast wire, demonstrate the larger fraction of nanocrystals (area under this peak is proportional to the fraction of nanocrystals) and stress relief in the annealed samples [19].
The XRD spectra further confirm that the microwire maintains its amorphous structure when annealed at the maximum current intensity of 40 mA (Fig. 3 b). Therefore, annealing of the microwires mainly induced stress relief, structural relaxation, and homogenization. However, these subtle structural changes in the microwires will have a considerable influence on the magnetic and electromagnetic properties of arrays composites, as will be elucidated in the following sections.
[ Figure 3 here] [ Figure 4 here] [ Figure 5 here] Figure 6 shows the magnetic hysteresis loops (Fig. 6 a) and the magnetic field dependence of the magneto-impedance ratio for the as-cast and annealed samples annealed with different currents (Fig. 6 b). Both the magnetization process and magnetoimpedance ratio of microwires are defined by the magnetic anisotropy affected e.g. by current annealing [18,22]. Large internal stresses give rise to a large anisotropy which is evidenced in the M-H loop of the as-cast wire (Fig. 6 a). Annealing the microwires progressively induce anisotropies along local magnetizations (slope of the loops gradually decreases) due to short-range pair ordering and a circular magnetic field generated by the current which aligns the easy anisotropy axes. The slightly larger anisotropy of 40 mA sample compared to that of 30 mA sample (inset Fig. 6 a) may be due to the closeness of crystallization, as mentioned previously. Current annealing also improves the magnetic softness evidenced by the drastic decrease in coercivity from 15 Oe for the as-cast wire to 0.8 Oe for the wire annealed at 40 mA due to stress and structural relaxation during the annealing process. From the magneto-impedance plot at 200 MHz ( Fig. 6 b), the as-cast wire is characterized by a slightly distorted single peak which evidences a system with the easy anisotropy parallel to the high-frequency current [23]. This is in disagreement with the M-H loop of the as-cast wire in which an inclined shape is indicative of the presence of circumferential anisotropy. To explain such discrepancy, we first should consider the differences between these two measurements. M-H curves correspond to static magnetization and thus bulk magnetic properties can be obtained while magnetoimpedance measurements are of dynamic character in which magnetization processes depend on ac current and frequency. Second, we should consider the magnetic structure of these type of wires in which both circumferentially magnetized shell and longitudinally magnetized inner core exist [24]. Both conductivity channels are subjected to the frequency dispersion due to the ac magnetic susceptibilities and their interplay especially near the ferromagnetic resonance results in complex transformations of MI when changing the frequency from MHz to GHz. In previously published reports, only the influence of the shell is taken into account to explain the impedance field dependence of these wires, but thanks to our recently developed broadband impedance measurements (which will be reported in next works) we are able to disclose the role of the inner core as well. At 200 MHz, the single peak is indicative that the main contribution to the magnetization comes from the longitudinally magnetized inner core. At such frequency, the ac excitation current will penetrate deeper into the wire. Another evidence of the contribution of the longitudinally magnetized core is delivered by the dispersion curves of magnetoimpedance measured in a wide range, as explained in the Supporting Information (Section 1, Fig. S1 b). With increasing the frequency, the single peak transforms into asymmetrical double peaks (Fig. S1 a) demonstrating the gradual contribution to the magnetization of the circular domains at the wire surface shell which will be reflected in the shape of the M-H loops.

Magnetic and magneto-impedance properties of Co60Fe15Si10B15 glass-coated microwires
Annealing the wire originates a double peak asymmetrical magneto-impedance response due to a slight deflection of the longitudinal anisotropy. It should be noted that such improvement in magnetic softness does not benefit GMI; this can be ascribed to the increase in surface defects and roughness, as evidenced by the morphological and topological characterization of the microwires ( Fig. S2 and Fig. S3). It causes fluctuation of local magnetic anisotropy at the surface and immobilization of surface spins [24][25][26][27].
[ Figure 6 here] Anyhow, the general magnetic behavior of the microwires depends intimately on the domain structure, which is determined by minimization of the magnetoelastic energy Kme given by: where λs refers to magnetostriction coefficient, σii refers to the dominant internal stress component [28]. By adjusting the microstructure of the wires through annealing treatment, the internal stresses σii of the wires can be relieved or redistributed. The internal stresses can be expressed as: where the term (Hkfin−Hkin) refers to the decrease in anisotropy field due to the annealing treatment, µ0 represents the vacuum permeability and Ms the saturation magnetization.
Such internal stresses are introduced while fabricating the wires coupled with magnetostriction and are distributed in a complex way forming a unique domain structure [29]. From the above equation decreasing the anisotropy field results in a decrease in internal stresses. Such a decrease in internal stresses [30] reduces the magnetoelastic energy which modifies the domain structure [31] by inducing relatively well-defined magnetic domains in the 40 mA annealed wire (inset Fig. 6 a). The changes in magnetic properties of the wires after annealing will have an important influence on the electromagnetic properties of the composites, as will be elucidated in the next section.

Transmission spectra of composites incorporating as-cast and current annealed wires
In this section, we will show that by incorporating microwires with different structural features arranged in different combinations into a polymer matrix the electromagnetic parameters are readily programmable, in particular, the transmission coefficient, S21/S12 being a measure for the transmission loss is crucial in understanding the microwave properties of the composite samples. When the wires are arranged in an alternate manner i.e. ABABAB and ACACAC, the transmission dip follows the same trend with frequency, i.e., red-shifting with the incorporation of 40 mA-annealed wire C (Fig. 7 a). Finally, when the middle microwires in the array ABABAB and ACACAC are switched, i.e. ABBAAB and ACCAAC, the critical frequency once again shifts on the side of the 40 mA-annealed wire C. In addition, the transmission amplitude of the composites also decreases as wire C is incorporated in the array (Fig. 7 a-c). Therefore, one can infer a dominant influence of the annealed microwires over the as-cast microwires on dictating the electromagnetic response of the composites.
[ Figure 7 here] The variations in transmission spectra feature in the composites could be explained by the dynamic wire-wire interactions considering the differences in domain structure and magnetic tensors between the as-cast and annealed wires incorporated in the array [30,32].
In this case, the dynamic magnetic interactions resulted from the coupling with an electrical component of incident waves rather than the magneto-static coupling, since 2 mm spacing is still too wide to induce meaningful magneto-elastic energy [28]. In the first case AAAXXX (where X corresponds to either 30 or 40 mA annealed wires), we can consider the largest "effective" area composed of equally structural microwires (three ascast wires plus three-annealed wires) with different conductivity, larger for the annealed wires (Fig. 8 a). The same type of wires in a parallel manner constitute an increase of the total cross-sectional area of the wires, resulting in a diminution of the effective resistivity and hence a stronger skin effect [33]. Such "effective" area is decreased when varying the order of the wires in the arrangement, three wires of the same type are reduced to two (AXXAAX, Fig. 8 b) and one (AXAXAX, Fig. 8 c), therefore affecting the equivalent conductivity and shifting the transmission dip frequency of the composites.
[ Figure 8 here] In addition to structural relaxation, annealing also reduces the internal damping or relaxation rate Γ on nanostructures which is inversely proportional to the electron relaxation time τ, i.e., Γ =hτ -1 , where h is Planck's constant [34]. The increase in relaxation time with annealing might be related to the progressive switching of the transmission dip to low frequency for the arrays containing the annealed samples (Fig. 7). In fact, the decrease in resistivity for the 40 mA annealed-sample is due to the enhancement in nanocrystallinity (Fig. 4 c), carrier concentration and carrier mobility [35,36] therefore decreasing the internal damping.
Let us summarize our programming strategy in Fig. 9, in which a horizontal line represents the transmission dip frequency for the different arrays containing the as-cast A, annealed wires X and their combinations. The initial frequency band, i.e. the frequency ranges from the frequency of the composites containing merely as-cast wires fA to the frequency of the composites containing merely annealed wires fX can be broaden or shorten according to the annealing degree of the wires, which will modify fX. Random combinations of as-cast and annealed wires will locate the transmission dip frequency between the critical band determined by fA and fX. Finally, using the same amount of ascast and annealed wires in a consecutive manner, the frequency falls out of fA-fX range, red-shifting progressively with the current annealing intensity. Our approach shows that incorporating wires having diverse structural features arranged in different combinations, the electromagnetic properties could be largely anticipated and programmed. Moreover, stress-relaxation and structural change of the wires through low-current annealing without varying the general nanocrystalline structure and without crystalline degradation are only necessary to induce a significant change in the signature of the transmission spectra.
Because of the final electromagnetic properties are decided not only by the structural differences of the wires but also by the dynamic wire-wire interaction, changing the distance between the wire arrays could offer further tunability of the microwave response.
Relevant work is now underway.

Conclusion
We proposed a strategy to program and formulate the microwave properties of