Unveiling the Magnetic and Structural Properties of (X 2 YZ; X = Co and Ni, Y = Fe and Mn, and Z = Si) Full-Heusler Alloy Microwires with Fixed Geometrical Parameters

: We studied Ni 2 FeSi-, Co 2 FeSi-, and Co 2 MnSi-based full-Heusler alloy glass-coated mi-crowires with the same geometric parameters, i.e., ﬁxed nucleus and total diameters, prepared using the Taylor–Ulitovsky method. The fabrication of X 2 YZ (X = Co and Ni, Y = Fe and Mn, and Z = Si)-based glass-coated microwires with ﬁxed geometric parameters is quite challenging due to the different sample preparation conditions. The XRD analysis showed a nanocrystalline microstructure for all the samples. The space groups Fm3 ¯ m (FCC) and Im3 ¯ m (BCC) with disordered B2 and A2 types are observed for Ni 2 FeSi and Co 2 FeSi, respectively. Meanwhile, a well-deﬁned, ordered L2 1 type was observed for Co 2 MnSi GCMWs. The change in the positions of Ni, Co and Mn, Fe in X 2 YSi resulted in a variation in the lattice cell parameters and average grain size of the sample. The room-temperature magnetic behavior showed a dramatic change depending on the chemical composition, where Ni 2 FeSi MWs showed the highest coercivity (H c ) compared to Co 2 FeSi and Co 2 MnSi MWs. The H c value of Ni 2 FeSi MWs was 16 times higher than that of Co 2 MnSi MWs and 3 times higher than that of Co 2 FeSi MWs. Meanwhile, the highest reduced remanence was reported for Co 2 FeSi MWs (Mr = 0.92), being about 0.82 and 0.22 for Ni 2 FeSi and Co 2 MnSi MWs, respectively. From the analysis of the temperature dependence of the magnetic properties (H c and M r ) of X 2 YZ MWs, we deduced that the H c showed a stable tendency for Co 2 MnSi and Co 2 FeSi MWs. Meanwhile, two ﬂipped points were observed for Ni 2 FeSi MWs, where the behavior of H c changed with temperature. For M r , a monotonic increase on decreasing the temperature was observed for Co 2 FeSi and Ni 2 FeSi MWs, and it remained roughly stable for Co 2 MnSi MWs. The thermomagnetic curves at low magnetic ﬁeld showed irreversible magnetic behavior for Co 2 MnSi and Co 2 FeSi MWs and regular ferromagnetic behavior for Ni 2 FeSi MWs. The current result illustrates the ability to tailor the structure and magnetic behavior of X 2 YZ MWs at ﬁxed geometric parameters. Additionally, a different behavior was revealed in X 2 YZ MWs depending on the degree of ordering and element distribution. The tunability of the magnetic properties of X 2 YZ MWs makes them suitable for sensing applications.

Arc melting, followed by additional thermal treatment, is the main technique used to produce Heusler alloys [2,3,10].This method makes it possible to produce Heusler alloys in bulk form.However, miniaturization has been investigated as an alternative approach to improve the aforementioned characteristics of Heusler alloys [10].The performance of Heusler alloys can be improved noticeably by minimizing the dimensions of the alloys.For instance, in the context of magnetic cooling applications, the surface-to-volume ratio can be enhanced to significantly improve the heat-exchange rate by using low-dimensional Heusler alloys.
In recent years, growing attention has been paid to the synthesis and investigation of different families of Heusler alloys with reduced dimensions, such as thin micro/nanowires, ribbons, nanoparticles, and thin films [13][14][15].However, the inherent brittleness of Heusler compounds, including Co-, Fe-, and Ni-based full-Heusler alloys, poses a challenge for their fabrication using conventional metallurgical techniques.Consequently, significant efforts have been directed toward the development of novel fabrication methods for producing Heusler alloys in different physical forms for a specified application.These endeavors aim to overcome the limitations imposed by brittleness and explore the potential of lowdimensional Heusler alloys.Additionally, the preparation of composites incorporating Heusler alloys has emerged as a promising approach to address the aforementioned brittleness issue, becoming a topic of considerable interest in the development of this family of functional materials [3,10].
Rapid melt quenching has been recognized by scientists since the 1960s as a commonly used method to produe innovative materials with a variety of morphological characteristics, including amorphous or crystalline (micro/nanocrystalline) structures, as well as metastable phases with reduced dimensions [16,17].Using this technology, it is possible to obtain alloys with specified chemical compositions using rapid solidification, obtaining materials with more effective mechanical, magnetic, and corrosion properties [18][19][20].Rapid melt quenching techniques have been developed to produce ribbons, wires, flakes, microwires, composite microwires, and other materials.The chosen alloy's phase diagram, the quenching conditions, and the geometry of the prepared materials are only a few of the specific fabrication features that are critical in determining the final structure of the materials that are produced.
As previously mentioned, crystalline rapidly quenched materials generally exhibit inferior mechanical properties compared to their amorphous counterparts [20].However, other properties relevant to various applications, such as enhanced corrosion resistance and biocompatibility, are desirable [21].Furthermore, the miniaturization of rapidly quenched materials has emerged as a challenge for numerous applications.Consequently, the development of preparation methods capable of meeting these expectations has garnered significant attention in recent years.
One of the peculiarities of the Taylor-Ulitovsky technique is that it allows the preparation of metallic microwires coated with insulating glass by simultaneous rapid solidification from the melt.This manufacturing method is intrinsically linked with internal stresses arising mostly due to the difference in the thermal expansion coefficients of the glass coating and the metallic alloy [18,[42][43][44].The magnitude of the internal stresses, σ i , correlates with the ratio, ρ, between the metallic nucleus diameter, d metal , and the total diameter, D total .In this way, σ i can be modified by changing the ρ-ratio [42,44].
In this study, we present an endeavor to produce a set of glass-coated microwires based on the X 2 YZ composition.These microwires were designed with fixed geometric parameters and a high Curie temperature exceeding 900 K.The objective was to examine the impact of the uniform internal stress induced by the glass layer coating on the magnetic and structural behavior of the samples, utilizing the Taylor-Ulitovsky process.The selection of this fabrication method was driven by the intriguing magneto-structural characteristics exhibited by glass-coated microwires derived from Heusler alloys, along with the advantageous functional properties associated with such microwires.We chose a series of Heusler alloys, i.e., Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi, with a high Curie temperature, which have a significant contribution in advanced spintronic applications due to their unique physical, electronic, and magnetic properties [2,12,14,17].A strong dependence of the magnetic and structural properties of X 2 YZ-based glass-coated microwires on fixed geometric parameters was observed, and this reveals the sensitivity of the internal stress to the microstructure ordering and the chemical composition of the metallic nuclei of X 2 YZ-based glass-coated microwires.

Materials and Methods
The experimental conditions for the preparation Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi in bulk and glass-coated microwires are described in detail in our previous works [12,14,17].
The key point and objective of the current study is to fabricate the samples with fixed geometric parameters to investigate the effect of the internal stresses originated by the covering glass layer on the magnetic properties and microstructure in different series of X 2 YZ-based full-Heusler glass-coated microwires.
The following procedures were used to prepare Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi alloys by arc melting.The precursor elements for the Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi alloys were weighed to fit with the nominal ratio (X)2:(Y)1:(Z)1) and deposited in a graphite crucible, containing Ni (99.99%),Co (99.99%),Fe (99.9%),Mn (99.99%), and Si (99.99%).The ingots of Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi alloys (ingot) were created by combining the ingredients.For all alloys, the melting process was repeated five times to make the alloys homogenous.The chemical compositions and the nominal ratio of the X 2 YZ alloys were tested before proceeding to the glass-covering process.By using the Taylor-Ulitovsky technique, we can obtain a wide range of Heusler-based glass-coated microwires with proper dimensions and length depending on the application and the purpose of the investigations [22,26,37,[41][42][43][44][45][46][47].Controlling the casting process rate of the melting ingot, i.e., Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi, enabled us to obtain glass-coated microwires with a fixed nuclei diameter and well-controlled thickness of the covering glass layer.Thus, fixed geometric parameters were easily obtained in the current alloys.After preparation of the Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MWs, we estimated the geometrical parameters d metal (µm), D total (µm), and the aspect ratio (ρ = d metal /D total ) by using an optical microscope and Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray (EDX) (JEOL-6610LV, JEOL Ltd., Tokyo, Japan) to determine the geometric parameters of the Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MW samples and their related nominal chemical compositions (see Table 1).After confirming the nominal ratio and the chemical compositions of the Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MWs, microstructure analysis was performed at room temperature by using X-ray diffraction (XRD) (D8 Advance, Bruker AXS GmbH, Karlsruhe, Germany).The magnetic characterizations were performed as follows: First, we measured the hysteresis (M-H) loops at room temperature by applying a magnetic field parallel and perpendicular to the metallic nuclei axis of the Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MW samples to check the magnetic anisotropy and confirm the easy axis of the magnetization.Then, we checked the magnetic behavior of the samples in a wide range of temperature (5-400 K) by measuring the M-H loops parallel to the wire's axis, i.e., the easy magnetization axis.Finally, we analyzed the thermal magnetization curves, i.e., the field cooling (FC) and field heating (FH) magnetizations curves at applied low external magnetic field, to check the irreversibility behavior or magnetic phase transition in the Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MWs.All magnetization curves were measured using a PPMS (Physical Property Magnetic System, Quantum Design Inc., San Diego, CA, USA) vibrating-sample magnetometer.

Chemical, Nominal Composition, and Microstructure Analysis
As mentioned in the previous section, the morphological and main geometrical parameters were evaluated using an optical microscope and SEM. Figure 1 illustrates the SEM images of the Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MWs with fixed geometrical parameters.Table 1 shows the estimation of the metallic nucleus, d metal , and the total diameters, D total , of the Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MWs.By calculating d metal (µm) and D total (µm), we can easily confirm that the samples have nearly the same geometrical parameters.The difference in the aspect ratios of all samples was around ± 0.1.We used EDX analysis to confirm the chemical compositions of the samples.As shown in Table 1, all the samples had the same stoichiometry 2:1:1.A higher amount of Si compared to Mn and Fe was observed in Ni 2 FeSi GCMWs, Co 2 FeSi MWs, and Co 2 MnSi MWs due to the additional signal of Si coming from the covering glass layer.
X-ray diffraction (XRD) (D8 Advance, Bruker AXS GmbH, Karlsruhe, Germany).The magnetic characterizations were performed as follows: First, we measured the hysteresis (M-H) loops at room temperature by applying a magnetic field parallel and perpendicular to the metallic nuclei axis of the Ni2FeSi, Co2FeSi, and Co2MnSi MW samples to check the magnetic anisotropy and confirm the easy axis of the magnetization.Then, we checked the magnetic behavior of the samples in a wide range of temperature (5-400 K) by measuring the M-H loops parallel to the wire's axis, i.e., the easy magnetization axis.Finally, we analyzed the thermal magnetization curves, i.e., the field cooling (FC) and field heating (FH) magnetizations curves at applied low external magnetic field, to check the irreversibility behavior or magnetic phase transition in the Ni2FeSi, Co2FeSi, and Co2MnSi MWs.All magnetization curves were measured using a PPMS (Physical Property Magnetic System, Quantum Design Inc., San Diego, CA, USA) vibrating-sample magnetometer.

Chemical, Nominal Composition, and Microstructure Analysis
As mentioned in the previous section, the morphological and main geometrical parameters were evaluated using an optical microscope and SEM. Figure 1 illustrates the SEM images of the Ni2FeSi, Co2FeSi, and Co2MnSi MWs with fixed geometrical parameters.Table 1 shows the estimation of the metallic nucleus, dmetal, and the total diameters, Dtotal, of the Ni2FeSi, Co2FeSi, and Co2MnSi MWs.By calculating dmetal (µm) and Dtotal (µm), we can easily confirm that the samples have nearly the same geometrical parameters.The difference in the aspect ratios of all samples was around ± 0.1.We used EDX analysis to confirm the chemical compositions of the samples.As shown in Table 1, all the samples had the same stoichiometry 2:1:1.A higher amount of Si compared to Mn and Fe was observed in Ni2FeSi GCMWs, Co2FeSi MWs, and Co2MnSi MWs due to the additional signal of Si coming from the covering glass layer.400) and (420) reflections, respectively.Due to the absence of a (111) reflection in the Ni 2 FeSi MWs, the BCC single-phase microstructure with B2 type, i.e., (disordered) is supposed.Meanwhile, a well-defined FCC single phase with L2 1 ordered type was found for the Co 2 MnSi MWs.However, the two superlattice diffraction (111) and (200) peaks were significantly weaker compared to those for other elements belonging to the same period of the periodic table [48].The intensities of these peaks may, therefore, be essentially undetectable if the majority or all the elements in the presented alloys belong to the same period in the elemental periodic table.For Co 2 FeSi MWs, the existence of two peaks only at 2Ө = 46.3• and 2Ө = 85.1 • , corresponding with (220) and (420) reflections, fit very well with the FCC single phase with A2 type, i.e., disordered.
From detailed analysis of the XRD pattern of the Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MW samples, we found that the lowest lattice parameters were detected for Co 2 FeSi MWs, where a = 2.81Å.The cell parameters for Ni 2 FeSi and Co 2 MnSi MWs were very similar, where a = 5.78 Å and 5.71 Å, respectively.However, although the samples had the same space group, i.e., Im3 m (BCC) type, the crystallite size was different as illustrated in Table 2.The Co 2 FeSi and Co 2 MnSi glass-coated microwires had a roughly similar crystallite size (≈ 37 nm), while for Ni 2 FeSi MWs, it reduced to ≈ 21 nm.The values for crystallite size and the degree of microstructure order have a strong effect on the magnetic behavior of the samples.Thus, the diffraction peak at 2Ө = 46.3• for Ni 2 FeSi GCMWs appeared broader than those for the other samples.
Figure 2, all the samples showed a crystalline structure with main peaks at 2Ө = 46.3°.Although the samples had the same geometrical parameters, changes in the microstructure were observed.The Ni2FeSi and Co2MnSi MWs shared two peaks at 2Ө = 68.6°and 2Ө = 85.1° with (400) and (420) reflections, respectively.Due to the absence of a (111) reflection in the Ni2FeSi MWs, the BCC single-phase microstructure with B2 type, i.e., (disordered) is supposed.Meanwhile, a well-defined FCC single phase with L21 ordered type was found for the Co2MnSi MWs.However, the two superlattice diffraction (111) and (200) peaks were significantly weaker compared to those for other elements belonging to the same period of the periodic table [48].The intensities of these peaks may, therefore, be essentially undetectable if the majority or all the elements in the presented alloys belong to the same period in the elemental periodic table.For Co2FeSi MWs, the existence of two peaks only at 2Ө = 46.3°and 2Ө = 85.1°, corresponding with (220) and (420) reflections, fit very well with the FCC single phase with A2 type, i.e., disordered.
From detailed analysis of the XRD pattern of the Ni2FeSi, Co2FeSi, and Co2MnSi MW samples, we found that the lowest lattice parameters were detected for Co2FeSi MWs, where a = 2.81Å.The cell parameters for Ni2FeSi and Co2MnSi MWs were very similar, where a = 5.78 Å and 5.71 Å, respectively.However, although the samples had the same space group, i.e., Im3ˉm (BCC) type, the crystallite size was different as illustrated in Table 2.The Co2FeSi and Co2MnSi glass-coated microwires had a roughly similar crystallite size (≈ 37 nm), while for Ni2FeSi MWs, it reduced to ≈ 21 nm.The values for crystallite size and the degree of microstructure order have a strong effect on the magnetic behavior of the samples.Thus, the diffraction peak at 2Ө = 46.3°for Ni2FeSi GCMWs appeared broader than those for the other samples.To check the magnetic behavior of the Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MWs at room temperature, we performed the magnetic measurements in two directions, axial, i.e., parallel to the metallic nuclei axis, and out-of-plane, i.e., perpendicular to the wire axis by using a PPMS magnetometer.The out-of-plane loops appeared linear with a vanishing coercivity and a reduced remanence, i.e., H c and M r ≈ zero (not shown).The vanishing out-of-plane H c and M r indicate that all the magnetization lies in the in-plane (axial) direction and the out-of-plane direction is the hard magnetization axis for all the MW samples.
Figure 3 shows the M-H loops of the Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MWs at room temperature with an applied magnetic field parallel to the microwire axis, i.e., the axial direction.For Co 2 MnSi MWs, it appears that the easy magnetization axis is not perfectly axial and is possibly tilted at an angle, away from the wire axis.Unfortunately, we do not have a way to measure the angular magnetic behavior to accurately determine the magnetic anisotropy of the sample.Ni 2 FeSi MWs showed hard magnetic behavior with a coercivity of 138 Oe, which was 16 times higher than that of the Co 2 MnSi MWs and 3 times higher than that of the Co 2 FeSi MWs (see Table 3).The increase in the coercivity and the inplane anisotropy field of Ni 2 FeSi MWs must be attributed to their different microstructure.Surprisingly, the smallest value for crystallite size was observed for the Ni 2 FeSi sample.Therefore, the high coercivity of the Ni 2 FeSi sample may be associated with its disordered microstructure of B2 type, which strongly affects the magnetization reversal process, the domain structure, and its movement.In addition, the magnetocrystalline anisotropy plays an important role in the overall magnetic behavior.Thus, the enhanced coercivity detected in Ni 2 FeSi MWs and the high reduced remanent magnetization of Co 2 FeSi MWs suggest a scenario in which the crystalline texture affects the magnetic anisotropy.In particular, the easy magnetization axis can be aligned along the ( 220) and (420) reflections.However, although the Co 2 MnSi MW sample showed a well-defined ordered structure with L2 1 type, the low reduced remanence and coercivity observed in the Co 2 MnSi MW sample can be due to the mismatching between the magnetocrystalline anisotropy and the crystalline structure.As demonstrated in our previous research, the magnetic anisotropy behavior of Heusler-based glass-coated microwires is primarily influenced by two main factors: uniaxial magnetic anisotropy and cubic magnetocrystalline anisotropy [14,17].It has been reported elsewhere [18][19][20][21]30] that the ρ-ratio is directly related to the strength of internal stresses.Therefore, it is expected, that the ρ-ratio affects the relative content of the crystalline phase and correlates with modifications in the magnetic properties.Specifically, cubic magnetocrystalline anisotropy emerges as the predominant factor governing magnetic anisotropy.Regrettably, at present, experimental measurement of this type of anisotropy remains unfeasible.However, the presence of a roughly squared hysteresis loop strongly indicates its significant impact on the magnetic properties of the Ni 2 FeSi and Co 2 FeSi MW samples.It is worth noting that the temperature stability of ferromagnetic materials is a crucial characteristic for their possible applications in spintronic and sensing devices.Hence, we investigated the magnetic behavior of the Ni2FeSi, Co2FeSi, and Co2MnSi MWs with a fixed ρ-ratio for a wide range of measurement temperatures, 5-400 K.The shape of the loops follows the same trend observed at room temperature: non-squared for the Co2MnSi MWs and quite squared for the Ni2FeSi and Co2FeSi MW samples.In Figures 4 and 5, the M-H loops and the evolution of Hc and Mr with the temperature are shown.This behavior can be explained by considering that, for the Ni2FeSi and Co2FeSi MW samples, cubic magnetocrystalline anisotropy prevails up to 400 K.

Temperature Dependence of Magnetic Properties
It is worth noting that the temperature stability of ferromagnetic materials is a crucial characteristic for their possible applications in spintronic and sensing devices.Hence, we investigated the magnetic behavior of the Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MWs with a fixed ρ-ratio for a wide range of measurement temperatures, 5-400 K.The shape of the loops follows the same trend observed at room temperature: non-squared for the Co 2 MnSi MWs and quite squared for the Ni 2 FeSi and Co 2 FeSi MW samples.In Figures 4 and 5, the M-H loops and the evolution of H c and M r with the temperature are shown.This behavior can be explained by considering that, for the Ni 2 FeSi and Co 2 FeSi MW samples, cubic magnetocrystalline anisotropy prevails up to 400 K.By analyzing the M-H loops measured at the temperature range 5-350 K for Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MWs with a fixed ρ-ratio, an interesting magnetic behavior was observed for the temperature dependence of H c in Ni 2 FeSi MWs.First, the Ni 2 FeSi MWs showed the highest coercivity value at all temperature ranges compared to the Co 2 -based glass-coated samples with the same aspect ratio.In addition, the H c temperature dependence did not show uniform behavior; two flipped points at T = 200 K and 50 K were observed.At these points, the tendency of H c dramatically changed with temperature (see Figure 4a).Meanwhile, the temperature dependence of H c for Co 2 FeSi and Co 2 MnSi MWs showed quite a stable tendency with temperature.The improved coercivity stability observed in Co 2 MnSi MWs is strongly related to the high-ordered microstructure with L2 1 type (see Figure 1).However, both the Ni 2 FeSi and the Co 2 FeSi MWs had a disordered microstructure with B2 type and A2 type, respectively.The Co 2 FeSi MWs showed higher coercivity thermal stability due to their A2 type microstructure, which shows higher energy stability compared to the B2 type [49][50][51].Thus, the Co 2 FeSi MWs' Hc vs. T appeared more stable compared to that of Ni 2 FeSi MWs.Additionally, the M r vs. T tendency displayed regular ferromagnetic behavior with temperature, where a monotonic increase in M r was observed with decreasing T (see Figure 4b).Both Ni 2 FeSi and Co 2 FeSi MWs had higher M r values for the entire range of measuring temperatures compared to Co 2 MnSi MWs.The higher values of M r for Ni 2 FeSi and Co 2 FeSi MWs suggest a dominant cubic magnetocrystalline anisotropy at a wide range of measuring temperatures.
Figure 6 shows the complete thermomagnetic behavior of Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MWs with a fixed ρ-ratio.We studied the FC and FH temperature dependence of magnetization to check any possible phase transition.Thus, the measurements were performed at a low magnetic field of 50 Oe.The Ni 2 FeSi MWs showed regular ferromagnetic Crystals 2023, 13, 1550 9 of 13 behavior wherein the FC and FH curves increased on decreasing the temperature from 400 to 5 K.For Co 2 FeSi and Co 2 MnSi MWs, the FC and FH magnetization curves showed non-homogonous behavior, besides an irreversible magnetic behavior that occurred at T = 125 K.Among the factors that affect irreversible behavior of the magnetization versus temperature are the induced martensitic transition and the change in the internal stresses associated with the glass-coating layer with temperature.As illustrated in Figure 6, the FC and FH magnetizations curves showed a perfect matching and monotonic increase on decreasing the temperature from 400 to 5 K in the Ni 2 FeSi sample (see Figure 6a).Accordingly, we can assume that the internal stress induced by the covering glass-layer during the fabrication process had a stable and uniform effect on the magnetic properties of the Ni 2 FeSi sample.Meanwhile, for Co 2 FeSi and Co 2 MnSi MWs, the internal stress did not show a uniform effect at all temperature ranges; from 400 to 300 K, the FC and FH had a good matching behavior, but on decreasing the temperature below 300 K, mismatching started to appear.Due to the disordered microstructure nature of the Co 2 FeSi MWs, the FC and FH did not have a smooth behavior with temperature unlike the Co 2 MnSi MWs.
The current results reveal that the influence of the internal stress induced by the glass coating layer is very sensitive to the chemical composition and the microstructure ordering of X 2 YZ-based glass-coated microwires.As a result, different magnetic and structural responses were observed in glass-coated microwires with different metallic nucleus chemical compositions.In our previous work, we illustrated how the internal stress is strongly related to the geometric dimensions and showed the importance of the external applied field, the annealing temperature/time condition, and the microstructure ordering of the host metallic alloys.

Discussion
During the preparation process of ferromagnetic glass-coated microwires, complex internal stresses of a tensor character are induced, determining their magnetic/structural properties.The difference between the thermal expansion coefficients of the metallic alloy

Discussion
During the preparation process of ferromagnetic glass-coated microwires, internal stresses of a tensor character are induced, determining their magnetic/structural properties.The difference between the thermal expansion coefficients of the metallic alloy and glass, quenching internal stresses associated with the fast solidification of the metallic alloy, and drawing stresses are the three main sources of internal stresses, σ i , in glass-coated microwires [18][19][20][21]30].It is generally accepted that the largest are the internal stresses arising due to the difference in the thermal expansion coefficients of the glass coating and the metallic alloy [18][19][20][21]30,[43][44][45].Moreover, all the internal stress components are affected by the geometrical parameter (ρ = d metal /D total ).Thus, we can simply estimate σ i as follows [24,45]: where σ z , σ ϕ , and σ r are axial, circular, and radial stresses, respectively; ∆ = (1 − ρ 2 )/ρ 2 ; k =E g /E m , E m , E g -Young modulus of metallic nucleus and glass, respectively; ε = (α m − α g )(T m − T room ), α m , α g are thermal expansion coefficients of metallic nucleus and glass, respectively, and T m and T room are the melting temperature and the room temperature, respectively.Therefore, a correlation is usually assumed between the magnitude of internal stresses and the geometric ratio ρ [45].However, the metallic alloy composition is also relevant when using the Taylor-Ulitovsky method [24].Thus, the alloy melting temperature, good wetting with glass, and the diffusion coefficients can substantially affect the microstructure and, hence, the magnetic properties of GCMWs [24].The origin of the quenching internal stress is related to the solidification of the metallic alloy from the surface toward the wire axis [24,44].Due to the different conditions for the solidification process for Co 2 FeSi, Co 2 MnSi, and Ni 2 FeSi GCMWs, the microstructure and even the magnitude of the quenching internal stress can be different.The same scenario is expected for the stresses induced by the difference in thermal expansion coefficients of the metallic alloy and glass and the drawing stresses, which are dependent on the metallic alloy as well.The previous investigations to evaluate such internal stress components took into consideration the successive concentric cylindrical shells solidifying consecutively, starting from the outside, due to the temperature gradient at the glass transition temperature [19,24,44,45].The introduction of differences in ε, k, T m , and T room while keeping the geometrical parameters fixed is one of the routes to control the magnetic behavior of the different metallic nuclei of X 2 YZ-based glass-coated microwires.

Conclusions
In summary, we succeeded in preparing X 2 YZ-based glass-coated microwires with the same aspect ratio.In such X 2 YZ-based glass-coated microwires, we studied the effect of different chemical compositions of magnetic materials, i.e., metallic nuclei, on the internal stress.Also, we illustrated three main sources of the internal stresses that control the magneto-structural behavior of the X 2 YZ-based glass-coated microwires (thermal expansion coefficients of the metallic alloy and glass, quenching internal stresses, and drawing stresses).By fixing the internal stress, which mainly depends on the geometrical parameters, a notable variation in the magnetic and structural properties was observed.In the microstructure investigation, for Co 2 FeSi and Ni 2 FeSi MWs, the microstructure features were found to be disordered, varying between the A2 type and the B2 type, respectively.Meanwhile, a well-defined, ordered L2 1 type microstructure was observed for Co 2 MnSibased glass-coated microwires.The variation in the microstructure has a strong effect on the magnetic behavior of the samples, resulting in a notable change in the H c , H k , M r , FC, and FH tendency with temperature and magnetic field.There were also differences in the quenching internal stress and the internal stresses originated by different thermal expansion coefficients of the metallic alloy and glass, i.e., changing the metallic nucleus composition leads to changes in the magnetic and structural properties.The high thermal

Figure 2
Figure 2 illustrates the microstructure investigation of Ni2FeSi, Co2FeSi, and Co2MnSi MWs measured by XRD at room temperature.The pattern starts from 2Ө = 23.8° to exclude the amorphous halo that comes from the covering glass layers.As shown in

Figure 2
Figure 2 illustrates the microstructure investigation of Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi MWs measured by XRD at room temperature.The pattern starts from 2Ө = 23.8• to exclude the amorphous halo that comes from the covering glass layers.As shown in Figure 2, all the samples showed a crystalline structure with main peaks at 2Ө = 46.3• .Although the samples had the same geometrical parameters, changes in the microstructure were

Figure 4 .Figure 4 .
Figure 4. Hysteresis loops at different temperatures of as-prepared Ni2FeSi, Co2FeSi, and Co2MnSi glass-coated microwires with fixed aspect ratio.All loops were measured at a temperature range from 350 K to 5 K.

Figure 4 .
Figure 4. Hysteresis loops at different temperatures of as-prepared Ni2FeSi, Co2FeSi, and Co2MnSi glass-coated microwires with fixed aspect ratio.All loops were measured at a temperature range from 350 K to 5 K.

Figure 5 .
Figure 5. Temperature dependence of the coercivity (a) and normalized remanence (b) of as-prepared Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi glass-coated microwires with fixed aspect ratio.(Lines for eye guide).

Crystals 2023 , 14 Figure 6 .
Figure 6.Temperature dependence of the measured magnetization of as-prepared (a) Ni2FeSi, (b) Co2FeSi, and (c) Co2MnSi glass-coated microwires with a fixed aspect ratio and an applied external magnetic field of 50 Oe.

Figure 6 .
Figure 6.Temperature dependence of the measured magnetization of as-prepared (a) Ni 2 FeSi, (b) Co 2 FeSi, and (c) Co 2 MnSi glass-coated microwires with a fixed aspect ratio and an applied external magnetic field of 50 Oe.

Table 3 .
The coercivity (H c ), reduced remanence (M r ), and in-plane anisotropy field (H k ) of asprepared Ni 2 FeSi, Co 2 FeSi, and Co 2 MnSi glass-coated microwires with a fixed aspect ratio measured at room temperature.
Figure 3. Hysteresis loops at room temperature of as-prepared Ni2FeSi, Co2FeSi, and Co2MnSi glasscoated microwires with fixed geometric parameters.