## 2 Materials and Methods
### Operational Physical Basis and High-Frequency Characterization  
Metallic MWs interact with the electromagnetic waves as micro-antennas with a resonance that is defined by the effective permittivity of the surrounding medium (\(\epsilon_{\mathrm{eff}}\)) and by the length (\(L\)) of the order of cm in the GHz range [2]. However, in the case of Co-based MWs, the possibility of magnetically tuning the present dipole resonances is conferred by the high-permeability of the MWs when their radius (\(r\)) are in the same order of the magnetic skin depth (\(\delta_{\mathrm{m}}\sim\upmu\)m). Therefore, the \(r\sim\delta_{\mathrm{m}}\) condition ensures a good interaction between the electromagnetic waves and ferromagnetic core. The arrays are built by hand with an equidistant distance between the MWs of 0.5 cm, and they are placed in a plastic plate (dielectric substrate) with a thickness (\(d\)) of 700 \(\upmu\)m to ensure the structural stability of the arrays. The fixed distance between MWs is chosen according to the reported theoretical study in which an enhanced GMI effect is obtained with MWs with a diameter of 30 \(\upmu\)m [33]. The MWs were clamped in the plastic sheet without stress by a commercial tape to avoid changes in the permittivity media during the microwave experiments. The microwave scattering properties of the MWs were experimentally measured using two double-ridged guide horn antennas with an operation frequency from 800 MHz to 18 GHz. The distance between the horn antennas is 1.2 m, with the sample being placed at 0.6 m from the emitting and the receiver antenna (equidistant point). Because the transmission electromagnetic horn antennas are in the far-field range, the electromagnetic waves can be considered as plane waves with a propagation constant \(\mathbf{k}\) towards the MWs array. The antennas were connected to a programmable network analyzer (Agilent E8362B PNA Series Network Analyzer), and the transmission coefficient \(S_{21}\) that gives the relation between the power of the emitting antenna (\(P_{1}\)) and the power of the receiving antenna (\(P_{2}\)) is measured after calibration procedures that are based on open-air measurements (Equation (1)). This coefficient is directly related with the electrical current induced along the MW axis by the incident wave, since the scattered wave is generated by this current [36; 46]. \[S_{21}=20\ \text{log}_{10}\frac{P_{2}}{P_{1}} \tag{1}\]  
The magnetic field of the incident microwave radiation is oriented perpendicular to the MW axis, whereas the electric field is parallel to this axis to obtain both a polarization and a current induction along the MW axis. In turn, two Helmholtz coils (current, \(I=0.2\) A and operating frequency \(f_{\text{operating}}=10\) Hz) are used to apply both DC and AC magnetic fields parallel to the axis of the MWs to study the influence of their magnetic response on the microwave scattering spectra in the frequency and time domain representations. The distance between the two Helmholtz coils is 0.4 m, the same length as the radius of the coils. Those that are applied DC or AC magnetic fields are the controlling factors of the microwave spectrum, since the surface impedance is related with the MW permeability that depends on its magnetic structure [46; 49]. To conclude the experimental section, two types of measurements are performed in the microwave scattering experiments: in the frequency and time domains. Figure 1 shows an illustration of the microwave scattering experimental setup in transmission mode. In the frequency domain, the \(S_{21}\) scattering coefficient shows a minimum at the dipole resonance frequency (\(f_{\text{min}}\)) [35], which is related to the electric permittivity of the surrounding media of the MWs (\(\epsilon_{\text{d}}\)), MW length (\(L\)), and speed of light (\(c\)) by the Equation (2). \(S_{21}\) coefficient was modulated by applied DC-magnetic fields from 0 to 17 Oe, where these values are previously calibrated with a Hall probe.