## 3 Results and Discussion  
### Tuning of Fe-Rich Microwires by Stress-Annealing  
As expected for Fe-rich microwires with high and positive \(\lambda\)s values, the as-prepared sample presents rectangular hysteresis loop with coercivity, Hc, of about 55 A/m (see Figure 1a). Annealing without stress did not considerably affect the hysteresis loop shape. Upon annealing at T\({}_{\rm ann}\) = 350 \({}^{\circ}\)C, the hysteresis loop of as-prepared microwires maintained its rectangular shape; however, the coercivity, Hc, slightly decreased up to 50 A/m, as shown in Figure 1b. The hysteresis loop of the sample annealed under stress (Figure 1c) was changed completely: the stress-annealed sample presented a linear hysteresis loop with low values of coercivity (about 17 A/m). Both the stress applied during annealing (Figure 2) and the annealing temperatures (Figure 3) affected the character of hysteresis loops, showing a higher magnetic anisotropy field, H\({}_{\rm k}\), by raising \(\sigma_{\rm a}\) or T\({}_{\rm ann}\).  
Similar to a previously reported GMI effect for Fe-rich microwires, the GMI effect of the as-prepared sample is quite low (Figure 4a). The GMI ratio, AZ/Z presented a single peak dependence, with decay from H = 0, as predicted for wires with axial magnetic anisotropy [42; 43; 44; 45]. As can be seen in Figure 4b,c, stress-annealing allowed for considerable improvement of the GMI ratio. Additionally, the character of the \(\Delta\)Z/Z (H) dependencies became different: starting from \(f\geq\) 100 MHz double peak \(\Delta\)Z/Z (H), dependencies were observed for stress-annealed samples (Figure 4b,c). Rather unusual character of \(\Delta\)Z/Z (H) dependencies was observed for the sample annealed \(\sigma_{\rm a}\) = 900 MPa (T\({}_{\rm ann}\) = 300 \({}^{\circ}\)C):at intermediate \(f\)-values (\(f\) = 100 MHz), \(\Delta\)Z/Z (H) dependence showed an irregular shape, consisting of single and double-peak \(\Delta\)Z/Z (H) dependencies. Considering the core-shell model [46; 47] of the domain structure of magnetic wires (proved experimentally [48]), the radius of the inner axially magnetized core, \(\mathrm{R_{c}}\), can be evaluated based on its relationship with the squareness ratio, \(\mathrm{M_{r}/M_{o}}\):  
\[\mathrm{R_{c}}=\mathrm{R(M_{r}/M_{o})^{1/2}} \tag{2}\]  
where R is the metallic nucleus radius. From observed hysteresis loops in Figures 2 and 3, the reduction of \(\mathrm{M_{r}/M_{o}}\) upon stress-annealing can be evidenced.  
On the other hand, the skin depth of a cylindrical magnetic conductor, \(\delta\), is affected by the circumferential magnetic permeability, \(\mathrm{\mu_{\Phi}}\), and by the frequency, \(f\), as follows:  
\[\delta=(\pi\sigma\mathrm{\mu_{\Phi}}\,f)^{-1/2} \tag{3}\]  
where \(\sigma\) is the electrical conductivity. Considering the aforementioned, one can assume the contribution of the inner axially magnetized core for low frequencies and an increase in the contribution of the outer shell with increasing frequency. From frequency dependence of maximum GMI ratio, \(\Delta\)Z/Z\({}_{\mathrm{m}}\), evaluated for the as-prepared and stress-annealed samples (Figure 5), we can deduce that stress-annealing allowed the improvement of \(\Delta\)Z/Z\({}_{\mathrm{m}}\) for a wide frequency range.