Impact of Stress Annealing on the Magnetization Process of Amorphous and Nanocrystalline Co-Based Microwires

The domain wall (DW) dynamics of amorphous and nanocrystalline Co-based glass-coated microwires are explored under the influence of stress annealing. Different annealing profiles have enabled remarkable changes in coercivity and magnetostriction values of Co-based amorphous microwires with initially negative magnitude, allowing induced magnetic bistability in stress-annealed samples and, consequently, high DW velocity has been observed. Similarly, Co-based nanocrystalline microwires with positive magnetostriction and spontaneous bistability have featured high DW velocity. Different values of tensile stresses applied during annealing have resulted in a redistribution of magnetoelastic anisotropy showing a decreasing trend in both DW velocities and coercivity of nanocrystalline samples. Observed results are discussed in terms of the stress dependence on magnetostriction and microstructural relaxation.


Introduction
Domain wall (DW) propagation has become a topic in the spate of a number of emerging applications including a wide range of magnetic logics and nano-sized data storage devices [1][2][3][4]. The dynamic behavior of magnetic DWs determines the operational speed of such devices, and thereby knowledge of such dynamics and their dependence on external stimuli (e.g., magnetic field, current, tensile stress, frequency) is crucial on both device and materials levels [3][4][5]. To this end, amorphous and nanocrystalline soft magnetic glass-coated microwires have attracted great attention as a result of their outstanding magnetic properties (with low coercivities down to 4 A/m) and production techniques allowing considerable diameter reductions in comparison with other rapidly quenched materials [6][7][8].
Glass-coated microwires are composite materials made of a metallic nucleus (amorphous alloy) covered by a glass-coating layer [7,9,10]. The variety of dimensions at the micro-scale, as well as different chemical compositions, are easily obtainable by the modified Taylor-Ulitovsky fabrication method based on rapid solidification phenomena [10]. The interaction of local magnetic moments with stresses arising from fast drawing, as well as different thermal expansion coefficients of the metallic nucleus and glass shell during a microwire's production, defines the magnetoelastic anisotropy. Hence, the magnetoelastic anisotropy is regulated by Taylor-Ulitovsky technique described elsewhere [9,10]. Scanning electron microscopy (SEM, TESCAN model VEGA, UPJS, Kosice, Slovakia) was used to examine the wires' topologies ( Figure 1a). The diameters of the metallic nucleus and the glass shell were determined using an optical microscope (Axio Scope A1, Carl Zeiss, Jena, Germany), as shown in Figure 1b,c.  Structure and phase compositions of as-prepared microwires were characterized by a BRUKER (D8 Advance, Karlsruhe, Germany) X-ray diffractometer with Cu-Kα (λ= 0.15406 nm) radiation. The samples were attached to the diffractometer, at which each scan was made over a two-theta angular range of 30-90 degrees with a step size of 0.05° and a step time of 30 seconds for each step.
We performed DW measurements with a set-up system consisting of three pickup coils based on the classic Sixtus-Tonks experiments [26]. Stress-annealed microwire samples (10 cm long) were placed coaxially inside of pickup coils. A magnetic field was generated by a solenoid upon applying rectangular-shaped voltage. As described previously [22,23,27], the DW propagation induces electromotive force (EMF) in the coil that is picked up at an oscilloscope upon passing the propagating wall. The DW velocity was estimated as where l is the distance between pick-up coils and Δt is the time difference between the maximum in the induced EMF. In reported DW velocities, we excluded the non-linearity at high values of magnetic fields from the discussion and aimed only at the DW characteristics in the viscous regime. Hysteresis loops of as-prepared and stress-annealed samples were measured by the flux metric methods used in [8]. We represented the hysteresis loops as normalized magnetization, M/Ms, versus the applied magnetic field, H, where Ms is the magnetic moment of the sample at the maximum magnetic field amplitude Ho.
The stress-annealing process was carried out in a conventional furnace where a mechanical load was attached into one end of the microwire and axially placed via the furnace nozzle. Values of the applied stresses were calculated based on Young moduli of the metallic nuclei and the glass shell, as well as the microwire cross-sectional area, described in [25].
Magnetostriction coefficients were measured by the small-angle magnetization rotation (SMAR) methods described elsewhere [12,28]. Briefly, the magnetostriction coefficient was evaluated according to dependence of the axial magnetic field on an applied stress at the fixed value of the induction voltage V(2f), according to the expression Structure and phase compositions of as-prepared microwires were characterized by a BRUKER (D8 Advance, Karlsruhe, Germany) X-ray diffractometer with Cu-Kα (λ = 0.15406 nm) radiation. The samples were attached to the diffractometer, at which each scan was made over a two-theta angular range of 30-90 degrees with a step size of 0.05 • and a step time of 30 seconds for each step.
We performed DW measurements with a set-up system consisting of three pickup coils based on the classic Sixtus-Tonks experiments [26]. Stress-annealed microwire samples (10 cm long) were placed coaxially inside of pickup coils. A magnetic field was generated by a solenoid upon applying rectangular-shaped voltage. As described previously [22,23,27], the DW propagation induces electromotive force (EMF) in the coil that is picked up at an oscilloscope upon passing the propagating wall. The DW velocity was estimated as υ = l/∆t where l is the distance between pick-up coils and ∆t is the time difference between the maximum in the induced EMF. In reported DW velocities, we excluded the non-linearity at high values of magnetic fields from the discussion and aimed only at the DW characteristics in the viscous regime. Hysteresis loops of as-prepared and stress-annealed samples were measured by the flux metric methods used in [8]. We represented the hysteresis loops as normalized magnetization, M/Ms, versus the applied magnetic field, H, where Ms is the magnetic moment of the sample at the maximum magnetic field amplitude H o .
The stress-annealing process was carried out in a conventional furnace where a mechanical load was attached into one end of the microwire and axially placed via the furnace nozzle. Values of the applied stresses were calculated based on Young moduli of the metallic nuclei and the glass shell, as well as the microwire cross-sectional area, described in [25].
Magnetostriction coefficients were measured by the small-angle magnetization rotation (SMAR) methods described elsewhere [12,28]. Briefly, the magnetostriction coefficient was evaluated according to dependence of the axial magnetic field on an applied stress at the fixed value of the induction voltage V(2f), according to the expression where µ o M s is the saturation magnetization, and σ app is the applied tensile stress. Figure 2 shows XRD patterns of as-prepared Co 69.2 Fe 4.1 B 11.8 Si 13.8 C 1.1 and Co 38.5 Fe 38.5 B 18 Mo 4 Cu 1 glass-coated microwires. As can be clearly seen, the Co 69.2 Fe 4.1 B 11.8 Si 13.8 C 1.1 microwires presented an amorphous structure confirmed by a diffuse halo, without observation of any crystalline peaks. In contrast, notable crystalline peaks corresponding with α-FeCo phase (33 nm average grain size) were shown for Co 38.5 Fe 38.5 B 18 Mo 4 Cu 1 microwires. It is worth underlining that, in some cases, decreasing the quenching speed during the fabrication process resulted in formation of nanocrystallites embedded within an amorphous matrix. Analysis of the crystalline peak features and average grain size calculation have been reported earlier by us for different Fe-and Co-based of nanocrystalline microwires [29]. where μοMs is the saturation magnetization, and σapp is the applied tensile stress. Figure 2 shows XRD patterns of as-prepared Co69.2Fe4.1B11.8Si13.8C1.1 and Co38.5Fe38.5B18Mo4Cu1 glass-coated microwires. As can be clearly seen, the Co69.2Fe4.1B11.8Si13.8C1.1 microwires presented an amorphous structure confirmed by a diffuse halo, without observation of any crystalline peaks. In contrast, notable crystalline peaks corresponding with α-FeCo phase (33 nm average grain size) were shown for Co38.5Fe38.5B18Mo4Cu1 microwires. It is worth underlining that, in some cases, decreasing the quenching speed during the fabrication process resulted in formation of nanocrystallites embedded within an amorphous matrix. Analysis of the crystalline peak features and average grain size calculation have been reported earlier by us for different Fe-and Co-based of nanocrystalline microwires [29]. As-prepared amorphous Co69.2Fe4.1B11.8Si13.8C1.1 microwires presented an almost unhysteretic shape with low coercivity, Hc≈ 4A/m (Figure 3), as previously reported for Co-based glass-coated microwires with low and negative λs (λs ≈ -10 -7 ). Slightly irregular hysteresis loop shapes can be related either to the interface layer between the metallic nucleus and glass coating [30], or to a contribution of the small inner axially magnetized domain that usually presents higher coercivity.

Results and Discussion
For Co69.2Fe4.1B11.8Si13.8C1.1 amorphous samples, we performed a series of stress-annealing steps varying the annealing time from 5 to 30 min at a fixed annealing temperature (300 °C) and 80 MPa applied stress. The evaluation of coercivity as well as magnetostriction with annealing time are plotted in Figure 4a. As can be appreciated, stress annealing resulted in an increase of coercivity (Hc increased from 4 A/m in as-prepared samples to 33 A/m in stress-annealed samples at tann 30 min). In most cases, conventional annealing methods result in decreasing coercivity due to internal stress relaxation induced by the fabrication process. However, in the case of Co-based microwires, considerable magnetic hardening upon annealing has been recently observed [18]. In the present case, observed Hc values were considerably lower than those reported in [18]. Such magnetic hardening can be explained by considering the effect of annealing on the magnetostriction coefficient.
Consequently, we evaluated the λs values upon stress annealing. The magnetostriction shifted from highly negative to nearly zero in as-prepared versus stress-annealed Co69.2Fe4.1B11.8Si13.8C1.1 microwire samples at tann = 30 min, respectively. In the present case of stress annealing (i.e., conventional annealing simultaneously under tensile stress) the situation was rather complex. As-prepared amorphous Co 69.2 Fe 4.1 B 11.8 Si 13.8 C 1.1 microwires presented an almost unhysteretic shape with low coercivity, H c ≈ 4A/m (Figure 3), as previously reported for Co-based glass-coated microwires with low and negative λ s (λs ≈ −10 −7 ). Slightly irregular hysteresis loop shapes can be related either to the interface layer between the metallic nucleus and glass coating [30], or to a contribution of the small inner axially magnetized domain that usually presents higher coercivity.
For Co 69.2 Fe 4.1 B 11.8 Si 13.8 C 1.1 amorphous samples, we performed a series of stress-annealing steps varying the annealing time from 5 to 30 min at a fixed annealing temperature (300 • C) and 80 MPa applied stress. The evaluation of coercivity as well as magnetostriction with annealing time are plotted in Figure 4a. As can be appreciated, stress annealing resulted in an increase of coercivity (Hc increased from 4 A/m in as-prepared samples to 33 A/m in stress-annealed samples at t ann 30 min). In most cases, conventional annealing methods result in decreasing coercivity due to internal stress relaxation induced by the fabrication process. However, in the case of Co-based microwires, considerable magnetic hardening upon annealing has been recently observed [18]. In the present case, observed Hc values were considerably lower than those reported in [18]. Such magnetic hardening can be explained by considering the effect of annealing on the magnetostriction coefficient.     Consequently, we evaluated the λ s values upon stress annealing. The magnetostriction shifted from highly negative to nearly zero in as-prepared versus stress-annealed Co 69.2 Fe 4.1 B 11.8 Si 13.8 C 1.1 microwire samples at t ann = 30 min, respectively. In the present case of stress annealing (i.e., conventional annealing simultaneously under tensile stress) the situation was rather complex.
As such, two different induced anisotropies were present: one arising from the mechanical load (transversal), and the other from annealing (stress relaxation and hence magnetostriction modification), leading to a redistribution of the internal stresses and/or local microstructures of the sample. In addition, if the initial magnetostriction coefficient is low and negative, we must consider two opposite consequences on the internal stresses. The first contribution is an increase of the total magnetoelastic energy. The second must be related to stress dependence (either applied or internal stresses: σ total = σ applied + σ internal ) on the magnetostriction coefficient, described in Equation (2), which is quite relevant in the case of a low magnetostriction constant, λ s,0 .
We analyzed DW dynamics in consideration of the observed rectangular character of hysteresis loops and induced magnetic bistability of stress-annealed Co 69.2 Fe 4.1 B 11.8 Si 13.8 C 1.1 microwire (presented in Figure 4b). Due to a rectangular hysteresis loop, the remagnetization of this sample ran through the DW propagation within an inner single-domain core [18,25]. As can be clearly seen in Figure 5, the DW velocity dependencies on applied magnetic fields presented typical DW linear growth velocity with the magnetic field. As such, two different induced anisotropies were present: one arising from the mechanical load (transversal), and the other from annealing (stress relaxation and hence magnetostriction modification), leading to a redistribution of the internal stresses and/or local microstructures of the sample. In addition, if the initial magnetostriction coefficient is low and negative, we must consider two opposite consequences on the internal stresses. The first contribution is an increase of the total magnetoelastic energy. The second must be related to stress dependence (either applied or internal stresses: σtotal = σapplied + σinternal) on the magnetostriction coefficient, described in Equation (2), which is quite relevant in the case of a low magnetostriction constant, λs,0.
We analyzed DW dynamics in consideration of the observed rectangular character of hysteresis loops and induced magnetic bistability of stress-annealed Co69.2Fe4.1B11.8Si13.8C1.1 microwire (presented in Figure 4b). Due to a rectangular hysteresis loop, the remagnetization of this sample ran through the DW propagation within an inner single-domain core [18,25]. As can be clearly seen in Figure 5, the DW velocity dependencies on applied magnetic fields presented typical DW linear growth velocity with the magnetic field.  The response of a DW to a magnetic field in a viscous medium is described by the classical equation of motion [31]. This leads to the following expression for the steady-state wall velocity: where H is the axial magnetic field, H0 is the critical propagation field below which DW propagation is not possible, and S is the DW mobility regulated by S ≈ δ ≈ (A/Kme) 1/2 , where A is the exchange stiffness constant and Kme (Equation (1)) is the magnetic anisotropy constant. Consequently, both DW velocity and mobility are strongly dependent on magnetoelastic anisotropy. Reasonably high DW velocities and DW mobilities are both shown in Figure 5. In parallel to the hysteresis loops presented in Figure 4b, stress-annealed samples for tann = 30 min showed either higher DW velocity or mobility than those annealed for tann = 20 min. In particular, DW mobility increased from 22.80 m 2 /A.s for samples stress annealed for 20 min, to 26.68 m 2 /A.s after 30 min annealing. Higher DW mobility should be ascribed to lower magnetoelastic anisotropy, deduced from the low coercivity, as well as the near-zero magnetostriction, which is shown in Figure 4.
On the other hand, as-prepared Co38.5Fe38.5B18Mo4Cu1 nanocrystalline microwires presented higher values of coercivity and rectangular hysteresis loops with spontaneous magnetic bistability, as shown in Figure 6a. Stress annealing resulted in a considerable decrease of coercivity; the coercivity decreased from 760 A/m in as-prepared samples to 610 A/m in stress-annealed samples at 300 °C for The response of a DW to a magnetic field in a viscous medium is described by the classical equation of motion [31]. This leads to the following expression for the steady-state wall velocity: where H is the axial magnetic field, H 0 is the critical propagation field below which DW propagation is not possible, and S is the DW mobility regulated by S ≈ δ ≈ (A/K me ) 1/2 , where A is the exchange stiffness constant and K me (Equation (1)) is the magnetic anisotropy constant. Consequently, both DW velocity and mobility are strongly dependent on magnetoelastic anisotropy. Reasonably high DW velocities and DW mobilities are both shown in Figure 5. In parallel to the hysteresis loops presented in Figure 4b, stress-annealed samples for t ann = 30 min showed either higher DW velocity or mobility than those annealed for t ann = 20 min. In particular, DW mobility increased from 22.80 m 2 /A.s for samples stress annealed for 20 min, to 26.68 m 2 /A.s after 30 min annealing. Higher DW mobility should be ascribed to lower magnetoelastic anisotropy, deduced from the low coercivity, as well as the near-zero magnetostriction, which is shown in Figure 4.
On the other hand, as-prepared Co 38.5 Fe 38.5 B 18 Mo 4 Cu 1 nanocrystalline microwires presented higher values of coercivity and rectangular hysteresis loops with spontaneous magnetic bistability, as shown in Figure 6a. Stress annealing resulted in a considerable decrease of coercivity; the coercivity decreased from 760 A/m in as-prepared samples to 610 A/m in stress-annealed samples at 300 • C for 1 h under 556.8 MPa applied stress. The dependence of coercivity on different values of applied stresses during annealing is presented in Figure 6b. As can be appreciated, a decreasing trend of coercivity after stress annealing is observed. This is due to the compressive and back stresses induced by the mechanical loads during annealing as well as the glass shell (i.e., upon removing the mechanical loads, compressive or back stresses evolved) as reported previously for Fe-based amorphous microwires [32]. A similar tendency of the DW velocity dependence on magnetic fields of stress-annealed Co 38.5 Fe 38.5 B 18 Mo 4 Cu 1 microwires was also observed, as shown in Figure 7.  Figure 6b. As can be appreciated, a decreasing trend of coercivity after stress annealing is observed. This is due to the compressive and back stresses induced by the mechanical loads during annealing as well as the glass shell (i.e., upon removing the mechanical loads, compressive or back stresses evolved) as reported previously for Fe-based amorphous microwires [32]. A similar tendency of the DW velocity dependence on magnetic fields of stress-annealed Co38.5Fe38.5B18Mo4Cu1 microwires was also observed, as shown in Figure 7.  As shown, DW velocities decreased upon stress annealing. It is well known that in nanocrystalline alloys, the internal stresses are heterogeneously distributed into two phases (i.e., an amorphous phase and a nanocrystalline phase). As reported previously [33,34], the easy magnetization axis in nanocrystalline alloys can be either parallel or perpendicular to the direction of stresses applied during annealing, depending on the sign of the magnetostriction and chemical alloy compositions. Accordingly, Equation (2) can be reproduced as where Vcr is crystalline volume fraction, and σcr and σam denote the stresses located in the volume fraction of nanocrystallites and the amorphous phase, respectively. In the case of Fe-based nanocrystalline microwires (for example Finemet alloys), negative magnetostriction of nanocrystallites (α-FeSi) compensate for the positive magnetostriction of the parent amorphous phase yielding to vanishing magnetostriction values and overall low magnetoelastic anisotropy. The application of tensile stresses during annealing of Finemet alloys develops inclined hysteresis loops with an easy magnetization axis that is perpendicular to the direction of the tensile stress [34]. In contrast, α-FeCo nanocrystallites have been observed with positive magnetostriction in Co38.5Fe38.5B18Mo4Cu1 nanocrystalline microwires, and for that reason overall magnetostriction has remained positive, with rectangular hysteresis loops. The character of such hysteresis loops preserves rectangular with spontaneous magnetic bistability even after annealing (cf. Figure 6 in [35]). Consequently, it can be deduced that the easy magnetization axis is parallel to the direction of stresses. As such, the overall magnetoelastic anisotropy is reasonably higher (according to Equation (6)), resulting finally in the lower DW dynamics observed in Figure 7. The DW mobility decreased from 0.97 m 2 /A.s in as-prepared Co38.5Fe38.5B18Mo4Cu1 nanocrystalline samples to 0.71 m 2 /A.s in stress-annealed samples at 556.8 MPa.

Conclusions
In summary, we have evaluated different stress-annealing conditions to study the magnetization process and DW dynamics of Co-based amorphous and nanocrystalline glass-coated microwires. Stress annealing of amorphous Co69.2Fe4.1B11.8Si13.8C1.1 microwires resulted in increasing coercivity with induced magnetic bistability and considerable changes in magnetostriction. The latter was elevated from highly negative to vanishing values. Fast DW velocities and mobilities appeared with unusual features in stress-annealed amorphous microwires. The opposite tendency of DW dynamics was observed in the case of nanocrystalline Co38.5Fe38.5B18Mo4Cu1 microwires with highly positive As shown, DW velocities decreased upon stress annealing. It is well known that in nanocrystalline alloys, the internal stresses are heterogeneously distributed into two phases (i.e., an amorphous phase and a nanocrystalline phase). As reported previously [33,34], the easy magnetization axis in nanocrystalline alloys can be either parallel or perpendicular to the direction of stresses applied during annealing, depending on the sign of the magnetostriction and chemical alloy compositions. Accordingly, Equation (2) can be reproduced as where V cr is crystalline volume fraction, and σ cr and σ am denote the stresses located in the volume fraction of nanocrystallites and the amorphous phase, respectively. In the case of Fe-based nanocrystalline microwires (for example Finemet alloys), negative magnetostriction of nanocrystallites (α-FeSi) compensate for the positive magnetostriction of the parent amorphous phase yielding to vanishing magnetostriction values and overall low magnetoelastic anisotropy. The application of tensile stresses during annealing of Finemet alloys develops inclined hysteresis loops with an easy magnetization axis that is perpendicular to the direction of the tensile stress [34]. In contrast, α-FeCo nanocrystallites have been observed with positive magnetostriction in Co 38.5 Fe 38.5 B 18 Mo 4 Cu 1 nanocrystalline microwires, and for that reason overall magnetostriction has remained positive, with rectangular hysteresis loops. The character of such hysteresis loops preserves rectangular with spontaneous magnetic bistability even after annealing (cf. Figure 6 in [35]). Consequently, it can be deduced that the easy magnetization axis is parallel to the direction of stresses. As such, the overall magnetoelastic anisotropy is reasonably higher (according to Equation (6)), resulting finally in the lower DW dynamics observed in Figure 7. The DW mobility decreased from 0.97 m 2 /A.s in as-prepared Co 38.5 Fe 38.5 B 18 Mo 4 Cu 1 nanocrystalline samples to 0.71 m 2 /A.s in stress-annealed samples at 556.8 MPa.

Conclusions
In summary, we have evaluated different stress-annealing conditions to study the magnetization process and DW dynamics of Co-based amorphous and nanocrystalline glass-coated microwires. Stress annealing of amorphous Co 69.2 Fe 4.1 B 11.8 Si 13.8 C 1.1 microwires resulted in increasing coercivity with induced magnetic bistability and considerable changes in magnetostriction. The latter was elevated from highly negative to vanishing values. Fast DW velocities and mobilities appeared with unusual features in stress-annealed amorphous microwires. The opposite tendency of DW dynamics was observed in the case of nanocrystalline Co 38.5 Fe 38.5 B 18 Mo 4 Cu 1 microwires with highly positive magnetostriction. Induced magnetoelastic anisotropy upon increasing applied stresses during annealing resulted in decreasing the coercivity and hence lowering DW dynamics.