One of the main sources of information with respect to the magnetization processes in ultrathin magnetic nanowires and submicron wires prepared by rapid solidification is represented by experimental hysteresis loops. There are two types of hysteresis loop measurements that give an overall picture of the magnetic behavior of glass-coated amorphous wires in general: bulk hysteresis loops, usually measured by means of inductive methods (Zhukov et al., 1995), and surface hysteresis loops, typically measured using magneto-optical Kerr effect (MOKE) techniques (Chizhik et al., 2006). In the case of the ultrathin wires, such as glass-coated amorphous nanowires and submicron wires, the typical inductive experimental setup is not suitable because of the very small signal induced in the pickup coils given by the very small transverse dimensions of the samples.

To be able to measure the bulk hysteresis loops of amorphous nanowires and submicron wires, a new method has been recently developed and used (Corodeanu et al., 2011a). The novel method is based on the magnetic bistability of the wires, which always results in rectangular hysteresis loops, and uses a digital integration technique. Figure 7.3 shows a schematic of the experimental setup. The main components are

• a magnetizing solenoid;

• a system of pickup coils;

• a low-noise preamplifier;

• a function generator; and

• a data acquisition board.

The length of the samples measured with this system is about 4 cm, whereas the diameter can take any value between 90 and 1000 nm. The technique, which uses a so-called window method (Butta et al., 2009), works for any magnetically bistable ultrathin wire, and the resulting hysteresis loop is free of noise, as illustrated in Figure 7.4.

MOKE, on the other hand, is an effective tool for studying the surface magnetization of magnetic materials. It has been successfully used for wire-shaped materials, starting from conventional amorphous wires quenched in rotating water with diameters larger than 100 μm (e.g., Chizhik et al., 2002; Chiriac et al., 2011c), continuing with thinner glass-coated amorphous microwires (Chizhik et al., 2012; Chiriac et al., 2010b), and finishing with glass-coated, ultrathin amorphous submicron wires (Chiriac et al., 2011b) and nanowires (Țibu et al., 2012). Given that the magnetic properties of the near-surface region are particularly interesting in amorphous microwires (Óvári et al., 2009), investigation of these properties in much thinner submicron wires and nanowires is essential. For instance, the MOKE axial surface hysteresis loop of a Co_68.15Fe_4.35Si_12.5B₁₅ amorphous glass-coated submicron wire with a nucleus diameter of 800 nm is shown in Figure 7.5.

MOKE measurements in ultrathin wire-shaped samples have been typically performed using a NanoMOKE II magnetometer produced by Durham Magneto Optics Ltd. In a longitudinal configuration, the rotation of the plane of polarization is proportional to the magnetization component parallel to the plane of incidence. The plane of incidence is parallel to the wire axis. Polarized light from a helium–neon laser, with a wavelength of 635 nm, is reflected from the wire to the detector. The diameter of the light beam is about 2 μm, whereas the penetration depth of the laser light is about 9 nm.

To fill the eventual gaps in the experimental study of the magnetization process of rapidly solidified amorphous nanowires and submicron wires, ferromagnetic resonance (FMR) measurements have been performed. These investigations are aimed at studying the magnetic anisotropy distribution within the near-surface region of the nanowires and submicron wires (Chiriac et al., 2010a). The correlation between FMR and MOKE results can offer comprehensive information about the magnetic characteristics within the wire surface region. FMR spectra are typically measured using an X-band spectrometer (Chiriac et al., 2000). A modulation technique is applied, in which the direct current magnetic field is modulated with an alternating field with a low frequency (1 kHz) and an amplitude of about 800 A/m. Changing the working frequencies, for example, from 8.5 to 10.5 GHz, results in the modification of the magnetic penetration depth.

7.2.2 Main aspects of the magnetic behavior

As was pointed out in the Introduction section, magnetic bistability is the main characteristic of glass-coated amorphous nanowires and submicron wires prepared by means of rapid solidification. It has been emphasized in highly positive magnetostrictive compositions, such as Fe_77.5Si_7.5B₁₅, in nearly zero magnetostrictive ones, for example, Co_68.15Fe_4.35Si_12.5B₁₅, as well as in FINEMET- and NANOMET-type compositions.

Figure 7.6 illustrates the inductive hysteresis loop of a glass-coated, amorphous Fe_77.5Si_7.5B₁₅ submicron wire with a nucleus diameter of 500 nm, whereas Figure 7.7 shows the inductive loop of a Co_68.15Fe_4.35Si_12.5B₁₅ glass-coated, amorphous submicron wire with the same nucleus diameter. The coercivities are one order of magnitude larger in the Fe-rich sample compared with the cobalt (Co)-rich one. This shows the importance of the magnetomechanical coupling between internal stresses induced during preparation and the magnetostriction of the alloy in the case of highly magnetostrictive samples. Based on the results obtained in the case of amorphous glass-coated microwires, one can expect to have two main contributions that decide the overall characteristics of the magnetic behavior in the case of ferromagnetic, amorphous glass-coated nanowires and submicron wires prepared using a similar technique: (1) the magnetoelastic term, which is the result of the above-mentioned coupling between mechanical internal stresses and magnetostriction, and (2) the magnetostatic term, which gives rise to so-called magnetic shape anisotropy. The magnetoelastic term is expected to be preponderant in the case of highly magnetostrictive alloy compositions, whereas the magnetostatic one should be more important in samples with low magnetostriction. Hysteresis loop and coercivity data are not sufficient to clearly understand the impact of each contribution. Therefore, further investigations were required to obtain additional information on the magnetization reversal characteristics in these new wire-shaped materials.

The study of nanowires and submicron wires made from FINEMET-type alloys (Fe_73.5Cu₁Nb₃Si_13.5B₉) is important for trying to clarify such aspects. In the as-cast amorphous state, they exhibit a typical amorphous structure with a large and positive magnetostriction constant, as the main alloy group from which they originate (Fe–silicon–boron). However, the copper and niobium additions lead to the controlled formation and growth of α-FeSi nanosized grains, which are randomly spread through the remaining amorphous matrix. The fine balance between the two phases, which also implies certain limits to the size of the grains and certain distances among them, leads to the formation of a special structure called the nanocrystalline structure, whose main attribute is a vanishing magnetostriction (Herzer, 1997). This structure is obtained after well-defined stages of annealing to achieve the right density of grains and suitable grain dimensions to average out the overall magnetostriction. This recipe applies to FINEMET materials of any shape. Therefore, it was expected to work for rapidly solidified nanowires and submicron wires as well. Figure 7.8 illustrates the dependence of the maximum relative magnetic permeability on the annealing temperature for FINEMET nanowires and submicron wires with various diameters. The peak value corresponds to the formation of the nanocrystalline structure, whereas the subsequent decrease is determined by the growth of the crystalline grains, which alters the zero magnetostriction state. It is important to emphasize that the FINEMET nanowires and submicron wires are magnetically bistable in the as-cast state, and bistability is maintained after the various stages of annealing (1 h at temperatures between 500 and 650 °C). The nanocrystalline structure appears after annealing at 600 °C. This means that in this case, magnetic bistability is the result of the magnetostatic contribution (shape anisotropy), rather than of the magnetoelastic term. Thus, both terms are able to yield a magnetically bistable behavior.

Initial hysteresis studies have been extended to samples with different dimensions to analyze the influence of wire dimensions on coercivity values. The dependence of coercivity on nanowire diameter for a fixed glass coating thickness is represented in Figure 7.9 for Fe_77.5Si_7.5B₁₅ amorphous samples (Óvári and Chiriac, 2014). Figure 7.10 shows the normalized coercivity and normalized magnetoelastic anisotropy constant values (calculated based on the internal stress distributions) versus wire diameter. The two curves display a similar shape. They are basically overlapped in the range of 100–300 nm, proving the magnetoelastic nature of the magnetization reversal process in the case of the thinnest samples. As the diameter increases, however, there is a continuously widening gap between the two curves, with the switching field versus diameter curve dropping below the other one. This clearly indicates that the magnetoelastic term is not solely responsible for magnetic switching, even in highly magnetostrictive amorphous nanowires and submicron wires. The magnetostatic term is expected to play a significant role as well. This means that shape anisotropy produces various effects on the magnetization process of amorphous nanowires and submicron wires prepared by rapid solidification, depending on their dimensions and composition.

To extend the investigations and to explain these aspects, the actual magnetization reversal mechanism has been brought into focus, that is, the domain wall displacement along the wire length. Understanding the peculiarities of domain wall propagation allows one to understand the basic aspects of magnetization reversal and constitutes the basis for future applications, mainly domain wall logic applications.

7.3.1 Experimental techniques

Similar to the case of the specific experimental setup required for studying the hysteresis loops of such ultrathin wires, a special setup was designed to measure the domain wall propagation characteristics of glass-coated amorphous nanowires and submicron wires (Corodeanu et al., 2011b). The method is based on the classical Sixtus–Tonks method (Sixtus and Tonks, 1932); however, it addresses a couple of shortcomings, one in particular that is related to the small transverse dimensions of the rapidly solidified nanowires and submicron wires:

1. it picks up very small signals associated with the ultrathin wires of interest; and

2. it allows the detection of additional domain walls, which appear as a result of newly nucleated domains anywhere along the wire, to avoid having false readings of unrealistic and very large domain wall velocities.

The issue of small signals has been addressed using two identical systems of pickup coils that are connected in series-opposition to obtain a compensated system that provides only the signal because of the propagating domain walls. The detection of additional domain walls—those due to the generated domains with reversed magnetization anywhere else on the wire length during the propagation of the end domain walls—has been addressed using a number of four pickup coils in each of the compensated systems. Moreover, to easily detect the direction of the propagating domain walls, each of the four pickup coils has had three windings; the middle one is wound in the opposite direction with respect to the other two. Figure 7.12 shows a schematic of the improved system used to measure domain wall velocity in amorphous glass-coated nanowires and submicron wires.

More recently, a significant development has allowed the experimentally investigation of the shape of the propagating domain wall in rapidly solidified amorphous glass-coated nanowires and submicron wires (Țibu et al., 2012). This investigation is based on simultaneously using MOKE and the Sixtus–Tonks method in the same setup, as illustrated in Figure 7.13.

7.3.2 Domain wall velocity and mobility

Figure 7.14 shows the field dependence of the domain wall velocity for Fe_77.5Si_7.5B₁₅ amorphous glass-coated submicron wires prepared by rapid solidification, whereas Figure 7.15 shows the same dependence in Co_68.15Fe_4.35Si_12.5B₁₅ samples.

In general, a higher wall velocity corresponds to a thinner wire, which also exhibits higher coercivity because of larger internal stresses. This is also valid for the thinnest Fe_77.5Si_7.5B₁₅ submicron wire, shown in Figure 7.14, although in this case a significantly different slope is observed. A slight increment in slope with the decrease in the wire diameter is also observed for Co_68.15Fe_4.35Si_12.5B₁₅ submicron wires (Figure 7.15). A decrease in the wire diameter is equivalent to an increase in shape anisotropy. On the other hand, in the nearly zero magnetostrictive samples (Co_68.15Fe_4.35Si_12.5B₁₅), shape anisotropy is expected to be more influential with respect to magnetostrictive samples. Therefore, the slope of the velocity versus field dependence curve seems to be a key element in understanding the effect of each of the two main types of magnetic anisotropy encountered in ultrathin amorphous nanowires and submicron wires prepared by rapid solidification.

Maximum domain wall velocity values are usually larger in nearly zero magnetostrictive submicron wires. For even thinner samples, for example, Co_68.15Fe_4.35Si_12.5B₁₅ and Fe_77.5Si_7.5B₁₅ amorphous nanowires, the situation is somewhat similar, as illustrated in Figures 7.16 and 7.17.

It is important to note that compared with the highly magnetostrictive wires, nearly zero magnetostrictive wires require a much smaller axially applied magnetic field to reach high values of domain wall velocity. This is also clearly visible in the case of as-cast and nanocrystallized FINEMET nanowires (Figure 7.18).

As mentioned in the Introduction section, the maximum wall velocity values in rapidly solidified amorphous glass-coated nanowires and submicron wires are quite large—in most cases larger than those measured in planar nanowires. Moreover, the applied fields required to propagate the walls are generally smaller, and they can be tailored in a wide range to respond to the specifications of the envisaged applications. These propagation fields are related to the depinning of the preexistent domain walls and, therefore, to the preponderant type of magnetic anisotropy within the wires.

Based on the discussions above, a close connection between the domain wall propagation-related parameters and the type of preponderant magnetic anisotropy can be inferred. Therefore, the next step was to analyze the domain wall mobility in these ultrathin amorphous wires and its connection with the magnetic anisotropy.

Figures 7.19 and 7.20 show the domain wall mobility versus the diameter of the metallic nucleus for Fe_77.5Si_7.5B₁₅ and Co_68.15Fe_4.35Si_12.5B₁₅ glass-coated amorphous nanowires and submicron wires, respectively. In the case of positive magnetostrictive samples, the mobility values are small, but the dependence is highly nonlinear, with a maximum at a nucleus diameter of about 350 nm. In the case of nearly zero magnetostrictive wires, the domain wall mobility values are significantly larger (about two orders of magnitude), and there is a monotonic increase in mobility with the diameter, with a tendency of saturation for diameters larger than 600 nm.

Let us discuss first the case of the Co_68.15Fe_4.35Si_12.5B₁₅ nearly zero magnetostrictive nanowires and submicron wires. Because of the very small magnetostriction constant (λ ≅ − 1 × 10^− 7), the magnetoelastic anisotropy K_me, which is proportional to the product between λ and the preponderant component of the internal stress tensor σ (Velázquez et al., 1996), is expected to be negligible compared with the shape anisotropy. This assumption is well supported by the small propagation fields when compared with the case of highly magnetostrictive wires and by the much larger values of the domain wall mobility. Therefore, one can assume that the monotonic increase in domain wall mobility with the wire diameter is an indication of a preponderant shape anisotropy, the strength of which decreases monotonically with an increase in the wire diameter. In brief, a positive slope in the mobility (S) versus wire diameter (Φ) curve indicates a preponderant magnetic shape anisotropy.

In the case of Fe_77.5Si_7.5B₁₅ amorphous glass-coated nanowires and submicron wires with large and positive magnetostriction (λ = 25 × 10^− 6), the S versus Φ curve also exhibits a region with a positive slope. This region corresponds to the smallest diameters, that is, nanowires with Φ < 350 nm. This indicates that shape anisotropy is more important at smaller diameters, which is very likely. Nevertheless, the situation is not so straightforward in the sense that large values of the applied field are still required to propagate the domain walls, and therefore the magnetomechanical coupling between internal stresses and magnetostriction cannot be dismissed altogether. It plays an important role in the pinning of the domain walls in highly magnetostrictive amorphous nanowires and submicron wires. Thus, a positive slope of the S(Φ) curve and large values of S show a domain wall propagation controlled mostly by shape anisotropy, with a negligible effect of magnetoelastic anisotropy—as in Co_68.15Fe_4.35Si_12.5B₁₅ wires—whereas a positive slope and small values of S seem to indicate domain wall displacement controlled by shape anisotropy but pinning that is determined by the magnetomechanical coupling, as in the case of Fe_77.5Si_7.5B₁₅ nanowires with diameters < 350 nm.

For Fe_77.5Si_7.5B₁₅ samples with diameters larger than 350 nm, the slope of the S versus Φ dependence is negative, and the values of the mobility are small. On the other hand, one would expect in this case an increased role of magnetoelastic anisotropy, enhanced by the reduction of shape anisotropy as the diameter increases and by the large frozen-in stresses. Obviously, domain wall pinning remains controlled by the magnetoelastic term. The important role of magnetoelastic anisotropy in highly magnetostrictive Fe_77.5Si_7.5B₁₅ amorphous submicron wires is supported by the results of FMR investigations. Thus, Figure 7.21 illustrates the FMR spectra of a glass-coated Fe_77.5Si_7.5B₁₅ amorphous submicron wire with a nucleus diameter of 500 nm at three frequencies: 8.5, 9.5, and 10.5 GHz. Irrespective of the working frequency, one can observe a small split of the resonance curves, indicating a slightly different anisotropy direction in the near-surface region of the wire. This is consistent with the effect of the magnetoelastic term, since it is the only possible cause of magnetization misalignment with respect to the wire axis. It is clearly not a well-defined domain in the sense of the radial outer shell encountered in microwires with the same composition; it is more likely a magnetization ripple, which nevertheless produces visible effects on the FMR spectra (Chiriac et al., 2011b). To summarize, domain wall mobility is a good indicator of the type of preponderant magnetic anisotropy and of the nature of the pinning of preexistent end domain walls.

7.3.3 Shape of the propagating domain walls

The combined MOKE and Sixtus–Tonks method allowed the shape of the moving domain walls within glass-coated amorphous submicron wires and nanowires prepared by means of rapid solidification to be analyzed. The main idea is that there is a delay Δt between the simultaneously recorded MOKE and Sixtus–Tonks signals generated by a moving magnetic domain wall. It is important to emphasize that the MOKE signal comes from the surface layer of the wall, within the near-surface region of the samples, whereas the Sixtus–Tonks signal is determined by the entire volume of the moving domain wall. Therefore, the synchronization of the two signals under various circumstances is key in interpreting the results.

Figure 7.22 sums up the results obtained through the simultaneous MOKE–Sixtus–Tonks method in Fe_77.5Si_7.5B₁₅ amorphous submicron wires and nanowires. For these samples, the inductive peaks of the Sixtus–Tonks signal precede the Kerr transition, which means that the edges of the moving domain wall follow the bulk of the wall in its movement. Thus the wall is not planar but most likely has a parabolic or conical shape. The delay Δt is actually the delay between the top of the wall and its edges form the near-surface region of the wires. As the diameter of the sample decreases, so does Δt, until it vanishes completely for the thinnest wires (< 300 nm for Fe_77.5Si_7.5B₁₅). Hence, the wall becomes planar only for very thin nanowires.

For Co_68.15Fe_4.35Si_12.5B₁₅ wires, the situation is exactly the opposite: the Kerr transition precedes the Sixtus–Tonks signal. Again, Δt vanishes for very thin nanowires (< 400 nm in this case). In summary, highly magnetostrictive submicron wires and nanowires exhibit domain walls shaped as positive parabolas, whereas nearly zero magnetostrictive ones display walls shaped as negative parabolas. The shape of the propagating walls is linked to the preponderant type of magnetic anisotropy in a way that is more or less similar to the link between anisotropy and domain wall mobility. The delay of the surface for highly magnetostrictive wires is most likely the result of the magnetization misalignment caused by the above-mentioned magnetization ripple. On the other hand, the surface mobility is enhanced in nearly zero magnetostrictive samples, in which no such ripple caused by the magnetoelastic term has been emphasized.