## 1 Introduction  
Magnetic wires exhibit versatile physical properties such as the Giant Magnetoimpedance (GMI) effect [1; 2; 3] and fast propagation of a single domain wall (DW) [4; 5]. Although these properties are not solely restricted to amorphous magnetic wires [3; 6], the former family presents several advantages, like better mechanical properties [7; 8] as well as a fast and inexpensive preparation method involving rapid solidification from the melt [9; 10; 11]. Consequently, the highest GMI effect and the fastest DW propagation were reported in either Co-rich or Fe-rich amorphous microwires, respectively [4; 5; 12; 13; 14]. From the viewpoint of applications, excellent magnetic field sensitivity of the GMI effect reported for soft magnetic wires (up to 10 %/A/m) is certainly of great technological interest [12; 13; 14; 15]. In this context, a number of magnetic sensors and magnetometers enabling the detection of low magnetic field or external parameters (e.g., stresses, temperature) based on GMI effect were designed and reported [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28].  
On the other hand, thin magnetic wire inclusions can be relevant for some other recent technological developments, like metamaterials [29; 30]. In particular, specific magnetic structures containing arrays of amorphous magnetic wires allow us to achieve high sensitivity of the surface impedance to external stimuli and hence are useful for development of tunable metamaterials and metacomposites [30; 31; 32].  
As compared to conventional metamaterials [29], the special feature of tunable metamaterials and metacomposites with soft magnetic wire inclusions is that they can demonstrate strong tunabilitywith respect to the varying of external stimuli, such as magnetic field, mechanical load and heat [30; 31; 32]. Consequently, metamaterials incorporating arrays of magnetic wires in fiber-reinforced polymer composites are potentially suitable for engineering of electromagnetic functionalities and stress/temperature monitoring.  
Industrial applications based on the GMI effect demand a size reduction of the magnetic element [16; 17]. Therefore, the development of thin wires exhibiting GMI effect has become a topic of intensive research [4; 5; 11; 12; 13; 14; 15]. Among different preparation techniques of magnetic wires, the so-called Taylor-Ulitovsky method allows for the thinnest wires' fabrication and reduced dimensions [11; 12; 13; 14; 15; 16; 31; 32; 33]. In order to observe the GMI effect in thin wires, the skin depth should be lower than the radius of the wire. As such, a decrease in diameter should be associated with an increase in the frequency range for observation of the GMI effect [34; 35]. Besides these technical features, the overall cost should be also considered for applications (e.g., smart composites with wire inclusions) where substantial amounts of wires are required.  
Excellent soft magnetic properties with enhanced GMI effects are usually reported for as-prepared Co-rich [11; 12; 13; 14; 15] and nanocrystalline Fe-rich magnetic microwires [36; 37]. The latter are often accompanied with an inherent brittleness of samples over the course of the nanocrystallization process, and therefore alternative stress-annealing approaches have been proposed, to enhance the GMI effect retaining the amorphous structure [38; 39]. Stress-annealing can be performed in a temperature range well below the crystallization onset. In addition, the degree of stress-induced anisotropy can be selectively tuned through optimal annealing temperature, time and/or different values of applied stresses. Thus, this contribution aims at providing comparative studies on the effect of stress-induced anisotropy on magnetic softness and GMI effect in Fe-and Co-rich magnetic microwires.