Fabrication techniques

The amorphous magnetic wires for the GMI applications can be fabricated by a number of rapid quenching or solidification techniques. Melt spinning, in-water quenching, glass coating processes, electrodeposition, and melt extraction technology are important methods to be named. Among these, the melt extraction technology is a preferred choice for fabrication of amorphous metal alloys [182–184]. In this method, a metal alloy with a required metal composition is first molten and made to come in contact with a high-speed rotating wheel which has a sharp edge. The thin molten layers off the edges of the wheel are quickly extracted and the microwires with diameters ranging from 20-50µm are produced by rapidly quenching these layers. This method is known to offer following advantages over other production techniques: it has higher solidification rate (10⁵ −10⁶ K/s). This helps to form amorphous phase, in addition to imparting better soft ferromagnetic and mechanical properties to the wires.

2.2.4 Material properties

2.2.4.1 Domain structures of wires

Formation of particular domain structure in each amorphous material results from the complex interplay [185,186] of internal stresses generated during the rapid quenching process and what is known asmagnetostriction effect, a property of magnetic materials to change their dimension when subjected to magnetic field. A material constantλ_swith its sign and magnitude defines the type of magnetostriction that exists in a material. For GMI applications, materials with smallλsare required as the mechanical effects caused by magnetic field is low in this case. Due to the different quenching rates between inner and outer regions of the wire during the rapid quenching, domain structures with longitudinal, radial or circular magnetization directions are formed in the wire.

For amorphous magnetic wires with positive magnetostriction (λs >0), the internal stresses during the rapid quenching induce a longitudinal magnetization in the core and a radial magnetization in the outer shell of the wire. Examples of this type include Fe-based wires [187]. On the other hand, for wires with negative magnetostriction (λs <0), internal stresses during the quenching still yield a longitudinal magnetization in inner core but

(a) (b)

Figure 2.3:(a) Domain structure of negative magnetostriction amorphous wire. (b) Its typical hysteresis curve (schematic) showing linear magnetization (M) as a function of external field (H). A narrow hysteresis loop indicates negligible energy loss per cycle.

circular magnetization profiles in the outer shell (figure2.3a). These are also known as

‘bamboo’ domain structures. Typically Co-based wires come under this category [186].

The positive magnetostrictive amorphous wires are not favourable for the GMI ap-plications because of their radial magnetization in the outer shell domains. The radial domain structure does not result in the reorientation of the domains when an external fieldH_DC is applied, which will result in the low GMI effect. In contrast, in amorphous wires with negative and nearly vanishingλs, the magnetization and the anisotropy field H_kexist in circular direction in a plane perpendicular to the wire’s longitudinal axis¹. The H_DC acts to orient this transverse magnetization along its direction, thus decreasing the circular permeability,µφ. This results in the large GMI effect [188]. In general, materials with very small or zeroλ_sare preferred because there is no energy loss involved due to magnetoelastic response (unlike materials with large±λ_s) when theH_DC is applied. This aspect boosts the magnetic softness of the material as the material can be easily magnetized or demagnetized. Another decisive advantage of having materials with vanishingλ_sis that they are robust against certain drawback known as ‘magneto-impedance aftereffect’.

Materials with ‘magneto-impedance aftereffect’ tend to show degraded GMI properties over time and hence are not desirable for the applications which require reproducible results [177].

2.2.4.2 Hysteresis behavior

One of the main criteria for a material to show GMI effect is its magnetic softness.

Compared to hard magnetic materials, soft ferromagnetic materials, as a result of small coercive field (H_c), exhibit narrower hysteresis loop and the area enclosed within the loop is small. Hence the energy loss per magnetization cycle will be less. In addition, it is also necessary for the material to have a large saturation magnetization (M_s) as it enhances the interaction with the external magnetic field.

In materials with positiveλ_s, due to the above mentioned magnetic structure of the domains, the hysteresis loop is relatively large in area and has rectangular shape. In the

1Typically, theH_kvalues are nearly four orders of magnitude smaller than the saturation magnetization in Co-rich amorphous wires.

materials with negativeλ_s, as a result of easier re-orientation of the domains along the H_DC, theH_cis very small and the hysteresis loop is much narrower (figure2.3b).

2.2.4.3 Permeability

The relative magnetic permeability (µ_r) of soft magnetic materials is an important param-eter in dparam-etermining the suitability of the materials for the GMI applications. In general materials with largeµ_r are essential as they bring about large GMI effects upon the appli-cation of externalH_DC. The amorphous wires with very smallλ_sexhibit largest circular permeability (µ_φ) and hence are desired in applications, while wires with large positive or negativeλ_sshow smallerµ_φ.

Note that the equation2.10assumesµ_φto have a real (static) value. But to understand its dependence on frequency (ω) andH_DC, a simple phenomenological model has been proposed by Beachet al[164]. Here, theµφ is given as a complex term µφ(ω, Hdc) = µ⁰_φ+jµ^”_φwith,

µ⁰_φ= 1 + 4πχ₀(H_dc)

1 +ω²τ² ; µ^”_φ= 4πχ₀(H_dc)ωτ 1 +ω²τ²

Where,τ is relaxation time of the magnetization due to damped magnetic response of the domains,χ₀ is magnetic susceptibility atf=0. In the above equation forµ_φ, we see that permeability is a strong function of bothH_DC andω. At low frequencies,µ_φvaries rapidly with increasingHDC while flatten out at higherω. Whenωincreases, theµφwill decrease as the wire has less time to respond toH_DC and at GHz range theµ_φapproaches to unity.

2.2.4.4 Electrical properties

It is necessary to have amorphous materials with small resistivity as the smaller resistivity leads to large changes in theZand hence the GMI effect (see Eq.2.9). In general amorphous materials with room temperature resistivity in the range 100 µΩ.cm are chosen for the applications.

2.2.4.5 Effect of sample geometry

The geometrical dimensions like the length, radius play important role in the GMI effects.

The reference [189] observed that in certain Fe-based (having vanishingλ_s) wires showed an increase in the GMI effect when the length (l) of the wires increased. On the contrary Phan et al [190], reported rather diminishing GMI effect if the length (l) is increased in case of Co-based wires.

There exists an optimal thickness or diameter for obtaining the maximum GMI effects in the wires [191]. It is observed that as the diameter of the wire increased the GMI peak shifts towards the lower frequencies [192]. Because, as theµφvaries strongly withωat lower frequencies, the skin effect becomes stronger as the thickness of the wire increases.