## 3 Results and Discussion
### Evolution of the Microwave Scattering Properties in Co-Based MWs Linear Arrays  
In previous works, the position of the dipole resonance varies with the length \(L\) of the MW, while considering Equation (2) [48; 51]. In accordance with those, lengths of 4 cm and 8 cm are chosen to evaluate the microwave scattering behavior of the MWs, when they are arranged in a linear array. Figure 3a shows how the \(f_{\mathrm{min}}\) that is associated to the maximum scattering for a single MW falls around 3.03 GHz and 1.64 GHz for the lengths of 4 cm and 8 cm, respectively. Accordingly, their maximum scatterings are located in the S-band (short wave region) and in the L-band (long wave region). As the number of parallel MWs increases, noticeable changes are detected in the intensity, bandwidth, and position of the minimum \(S_{21}\). Specifically, the \(\left.\right|S_{21}\left.\right|\) coefficient at \(f_{\mathrm{min}}\) of both array configurations shows an almost linear trend with an increase of \(-3.8\) dB and \(-4.0\) dB for 4 cm and 8 cm length, respectively, from 1 MW to 15 MWs (Figure 3b). These experiments confirm a behavior equivalent to that observed in antenna arrays widely used in point-to-point communication systems, where a very high directive beam of radiation is needed [52]. In our previous work [48], it demonstrates how, with parallel MWs equidistantly placed at a constant distance of \(\lambda/2\), the radiation is concentrated in one axis becoming a more directional scattering of the electromagnetic wave coming from the emitting antenna as the number of MWs increases from 1 to 4. The MWs behave as a dipole antenna with a resonance at \(\lambda/2\) condition resulting in an enhancement of the S\({}_{21}\) scattering parameter [48]. Therefore, these results reveal no MWs length dependence for the gain obtained. Instead, while the \(f_{\mathrm{min}}\) of 8-cm-length MWs barely varies with the number de MWs, \(f_{\mathrm{min}}\) shifts from 3.03 GHz to 2.54 GHz for 4-cm-length MWs (Figure 3c). The present results prove that these simple system configurations are potentially interesting for tuning the frequency of the bandpass. Figure 2: (**a**) The scanning electron microscopy (SEM) image, (**b**) X-ray diffraction (XRD) pattern, and (**c**) magnetic hysteresis loop of Co-based MWs. The amorphous contributions of the Pyrex and the Co-based alloy are indicated by red and black asterisks, respectively, in Figure 2b. The hysteresis loop is performed in one single Co-based MW at 25 \({}^{\circ}\)C.  
Microwave Scattering Experiments Performed in Co-Based MWs Sensing Array Platforms by Applying DC/AC Magnetic Fields  
The possibility to tune the scattering parameter \(S_{21}\) with an external DC magnetic field is an important property of these array configurations [2]. The surface impedance tensor, \(\xi\), of MWs is linked to the tangential components of the electric, \(E_{t}\), and the magnetic, \(\mathbf{H}_{t}\), fields at the MW surface [2]:  
\[E_{t}=\xi\left(\mathbf{H}_{t}\times\mathbf{n}_{r}\right) \tag{3}\]  
with \(\mathbf{n}_{r}\) the unit radial vector directed through the MW. The diagonal component of the surface impedance tensor, \(\zeta_{zz}\), relates the longitudinal electric field \(E_{Z}\) and circular magnetic field \(\mathbf{H}_{\varphi}\) created by the induced current in the MW [53]:  
\[E_{Z}=\zeta_{zz}\ \mathbf{H}_{\varphi} \tag{4}\]  
In the case of the MW radius \(\,r\,\sim\,\delta_{m}\), the electric polarization can be modulated by the MW magnetization and \(\zeta_{zz}\) has the form [53]:  
\[\zeta_{zz}\ =\ \frac{c(1-\tilde{j})}{4\pi\sigma\delta}\bigg{(}\sqrt{\tilde{ \mu}}\ \cos^{2}\theta+\ \sin^{2}\theta\bigg{)} \tag{5}\]  
with \(\theta\) the angle between the uniform magnetization vector and the MW axis, \(\sigma\) the electrical conductivity of the MW, \(\delta=c/\sqrt{2\pi\sigma\omega}\) the electric skin depth, \(\tilde{\mu}\) the dynamic permeability (\(\tilde{\mu}=\frac{\partial M}{\partial H}\)), and \(\delta_{m}=c/\sqrt{2\pi\sigma\omega\tilde{\mu}}\) the magnetic skin depth.