3.1.1  Properties and Classification

Commonly, ferromagnetic or ferrimagnetic materials are considered as magnetic materials although other materials (diamagnetic and paramagnetic) also exhibit some magnetic properties, as discussed earlier. The magnetic materials can be further classified into two clearly separate categories: soft magnetic materials and hard magnetic materials. Coercivity is assumed as the main criterion, and IEC Standard 404-1 recommends the coercivity of 1000 A/m as a value to distinguish both groups. This border is rather symbolic because both classes are completely different. From soft magnetic materials, we require the coercivity to be as small as possible (usually much less than 100 A/m) while hard magnetic materials should have coercivity as high as possible (commonly above 100,000 A/m). There is also a subclass of hard magnetic materials called semi-hard magnetic materials (with coercivity between 1,000 and 100,000 A/m) Figure 3.1 presents magnetic materials taking into account their coercivity available Vacuumschemlze who is one of the main manufacturers.

Soft magnetic materials cover huge market of various products: about 7 × 10⁶ tons annually and about 10¹⁰ Euro (Moses 2003). We can divide these products taking onto account their magnetic performance, applications, cost, and other properties For example, grain-oriented silicon steel is mechanically much harder than the nonoriented, so the same punching die will wear off after producing smaller quantity of elements Even in the case of SiFe electrical steel, the best grade can be 10 times more expensive than ordinary grades of steel And between cheep ferrites and high-quality soft magnetic materials, these differences in cost can be much larger.

Therefore, selection of appropriate kind and quality of material for a given application is an important knowledge For example, the best quality steel after preparation of the product can be much more deteriorated than cheaper material that after the same technology can exhibit better performance (Schneider et al. 1998, Schoppa et al. 2000, Wilczynski et al. 2004) Figure 3.2 presents a comparison of the main parameters of typical soft magnetic materials including their cost.

It would be nice to be able to find the soft magnetic material with all excellent properties (high saturation polarization, small losses, small coercivity, small magnetostriction, good mechanical properties, etc ) even at much higher price. But such material simply does not exist. We have to accept always some compromises— high permeability at the cost of saturation polarization (Figure 3.3), small power loss at the cost of saturation polarization, better magnetic parameters at the cost of mechanical properties, etc Fortunately, there is a plethora of various magnetic materials and appropriate technology often helps to find desirable material (Fish 1990, Moses 1990, 1992, 2003, Pfützner 1992, Arai and Ishiyama 1994, McCurrie 1994, Kronmüller 1995, Stodolny 1995, Fiorillo 1996, Schneider et al. 1998, Goldman 1999, O’Handley 2000, Beckley 2000, 2002, Geoffroy and Porteseil 2005, Peuzin 2005, Degauque et al. 2006, De Wulf 2006, Lebourgeois and Guyot 2006, Waecklerle 2006, Waeckerle and Alves 2006a,b, Kazimierczuk 2009).

Taking into account the main applications of soft magnetic materials, it should be noted that this situation continues to change and develop For example, it was traditionally assumed that the main area of application of silicon steel is electric power industry But recently, more and more power electric and power electronics devices use higher frequency signals, up to MHz In high frequency range, electrical steel exhibits prohibitively high power loss and should be substituted by nanocrystalline and even ferrite materials (Figure 3.4). Consequently, in such applications, other accompanying devices, for example, measuring transformers, should be also made from high-frequency materials In turn, the progress in nanocrystalline/amorphous materials resulted in development of new classical electrical steel (e.g., thinner gauge of even 0.15 mm).

Taking into account the importance of various groups of soft magnetic materials, it should be noted that almost 80% of the market is occupied by SiFe electrical steel (Figure 3.5). With ferrites and permalloys (NIFe), it is more than 95% and we can see that other materials, including amorphous and nanocrystalline are marginal in value.

Depending on application, various properties are required In the case of electric power devices (power and distribution transformers, electric machines), the most important factors are low power loss and high saturation polarization If we would like to choose only between silicon steel and amorphous materials (neglecting other factors), we arrive at a contradiction— amorphous materials exhibit smaller power loss but also significantly smaller saturation polarization and vice versa Table 3.1 presents the comparison of parameters for the main soft magnetic materials.

If a material is used for magnetic shielding, then its losses are not as important as the permeability, and hence amorphous materials or permalloy is advisable In the case of high-frequency applications, apart from the losses, deterioration of magnetic properties (e.g., permeability) with frequency is important, so from Table 3.1 we can see that, in this case, the materials would be ordered as follows: SiFe, NiFe, amorphous/nanocrystalline, MnZn ferrite, NiZn ferrite (and in microwave range, garnets).

Especially important are the CoFe alloys because they exhibit high saturation polarization with the highest known value of 2.46 T. Table 3.2 presents the typical applications of soft magnetic materials.

Figure 3.6 presents a diversity of soft magnetic materials currently available commercially. The properties of such materials will discussed in more detail in the following sections.

3.1.2  Pure Iron

Pure iron has excellent magnetic properties: large saturation polarization J_S = 2.15 T, low coercivity H_c = 3–12 A/m, and high permeability μ_max = 280,000 (single crystal magnetically annealed even up to 1,400,000). But the main problem is that such performance is displayed only by pure iron: even small quantities of impurities cause significant deterioration of magnetic properties (Figure 3.7). In practice, such extremely pure material is expensive and possible to use only in laboratory.

Commercially available pure iron has much smaller permeability μ_max = 10,000–20,000 and larger coercivity H_c =20–100 A/m because impurities such as C, Mn, P, S, N, and O impede the domain wall motion. By annealing such material in hydrogen at 1200°C–1500°C, it is possible to remove most of these impurities but such process is also quite expensive.

Pure iron has low resistivityρ = 10 μΩ cm (in comparison with 45 μΩ cm of GO SiFe and 140 μΩ cm of amorphous material) Such good conductivity causes large eddy current loss and practically precludes pure iron from AC application.

Both problems—expensive manufacturing and limited frequency application—can be solved if we use the same material in form of a powder iron. This material is manufactured by grinding iron (or iron alloys*) into powder with dimension of particles 5–200μm and next by pressing this powder with insulating material Resistivity of such material is of the order ofρ = 10⁴ μΩ cm and therefore it can be used in high-frequency range to 100 kHz (specially prepared NiFe powder to 100 MHz) (Kazimierczuk 2009).

Instead of cheap pressing, most often sintering technology is used, which results in better magnetic performances of the powder materials (Table 3.3).

As a material for powder iron cores, most commonly, carbonyl iron is used. Technology of obtaining extra pure iron powder from iron pentacarbonyl, Fe(CO)₅, was developed in 1925 by BASF Company By thermal decomposition of iron pentacarbonyl, it is possible to produce 99.8% pure iron powder with spherical particles ranging from 1 to 8 μm.

Although the presence of carbon significantly deteriorate magnetic properties of iron (Figures 3.6 and (3).7), low-carbon steel is widely used as magnetic material mainly due to its low price (Figure 3.6) and good mechanical properties. As “low-carbon” steel it is assumed the material with following: C, 0.04%–0.06%; P, 0.05%–0.15%; Mn, 0.35%−0.8%; S, 0.006%–0.025%; and Si, 0.05%–0.25% Although the magnetic properties of low-carbon electrical steel are rather poor, they are acceptable for many cheap devices, like small motors, relays, or electromechanical mechanisms Figure 3.9 presents the part of phase diagram of Fe-C alloys.

Iron exists in two allotropic forms: α-Fe (ferrite Fe-C) ferromagnetic body-centered cubic and γ-Fe (austenite Fe-C) paramagnetic face-centered cubic Above 0.008% of C in ferrite appears as impurity cementite (iron carbide, Fe₃C) that above 210°C is nonmagnetic. Transition between α-Fe and γ-Fe is at 910°C,† but also ferrite is paramagnetic above Curie temperature 768°C.

Especially important are Fe-Co-based alloys Fe50Co50 (known as Permendur) that exhibit the largest possible saturation polarization J_S =2.46 T and very high Curie temperature (T_c = 930°C). To improve mechanical properties of FeCo alloy (and increase resistivity ρ = 40 μΩ cm), a small part of vanadium is added: Fe49Co49V2. The alloy Fe6Co94 has very high Curie temperature (T_c =950°C) (pure cobalt has T_c = 1130°C). Table 3.4 collects magnetic properties of iron and some of its alloys.

3.2.1  Conventional Grain-Oriented SiFe Steel

As presented in Figure 2.25, two inventions were ground breaking in history of improvement of electrical steels: addition of Si and Goss texture. The first invention was proposed by Robert Hadfield in 1902 (Barret et al. 1902) and patented in 1903 (Hadfield 1903). The second invention was patented by Norman Goss in 1934 (Goss 1934) and described in 1935 (Goss 1935).

As discussed earlier, one of the most important drawbacks of pure iron is its relatively low resistivity and hence large eddy current loss Figure 3.10 presents the resistivity of different iron alloys. We can see that good candidates for resistivity improvement are silicon and aluminum. Addition of silicon influences also saturation polarization and Curie temperature (both of which decrease with silicon content; see Figure 3.11).

From Figure 3.11, the best would be 6.5% content of Si because resistivity increases almost sevenfold and the material is non-magnetostrictive. Unfortunately, this material is very hard and brittle, what is disadvantageous in rolling process as well as in punching the final product In practice, punching can be carried out only for the steel with up to 3%–4% silicon content. Large content of Si causes also decrease of saturation polarization as well as the permeability. Therefore, the GO silicon steel is manufactured mostly often with 2.7%–3.3% of silicon although also 6.5% SiFe is offered in the market (in small volume and for higher price).

Figure 3.12 presents part of a phase diagram of iron-silicon. The transition between α-Fe and γ-Fe is at 911°C. For silicon content higher than 1.86%, this transition no longer takes place and it is possible to anneal the material to high temperatures for removal of parasitic impurities. The most unwanted components in SiFe steel are carbon, oxide, sulfur, and nitrogen because even small amounts of this element cause increase of hysteresis loss. Therefore, the starting material should be as pure as possible and after manufacturing, the content of these elements can be smaller than 10 ppm.

Figure 3.13 presents typical route of production of GO SiFe. The Goss invention is a method of developing of a grain texture By suitable combination of annealing and cold rolling, the grains having [001] direction in the rolling direction and (110) plane close to the sheet plane are privileged to grow In the meantime, the inhibitor manganese sulfide (MnS) suppresses the growth of other grains Figure 3.14 presents the example of grain structure of GO electrical steel.

In a grain-oriented steel, we profit from its aniso-tropic properties of the fact that the iron crystal have the best magnetic properties in “easy” [100] direction (Figure 2.14). Therefore, the main effort is made to obtain the best Goss texture with relatively large grains ordered in one direction Figure 3.15 presents dependence of flux density and loss on the tilt angle Surprisingly, the minimum of the loss occurs when the grain are slightly misoriented from the perfect direction. The best results are obtained for the grain orientation of about 2°.

The data from Figure 3.15 can be partially explained by results of domain investigations presented in Figures 3.16 and (3).1 Perfectly oriented grains (0°) have wider spacing of the 180° domain walls than for a tilt angle 2°. This domain width strongly influences excess loss (see Figure 2.118). The domain wall spacing can be significantly decreased by applying a stress, which is one of the methods known as a domain refinement.

After the first annealing in production process (Figure 3.13), the grain dimensions are only around 0.02 mm After second annealing (secondary recrystallization), the Goss-oriented grains grow through the thickness of the sheet to diameter 3–7 mm with average misorientation of around 6°.

Theoretically, as larger grains as better, but measurements of loss versus grain dimensions did not confirm such a simple relationship Indeed domain observations confirm that large grains have a wide domain spacing (Beckley 2000). This is why usually grain diameter in conventional GO steel does not exceed about 8 mm.

Excellent properties along rolling direction are advantageous when we can guarantee that magnetization is applied only in this direction But this advantage can be a problem when a part is magnetized not exactly in the rolling direction (e.g., corners of a square core) In such a case, we have to expect significant deterioration of the material performance Figure 3.18 presents the magnetization curve and losses determined for various directions of magnetization (Tumanski 2002).

Electrical GO steel is classified according to international standards based on the power loss European standard EN 10107 uses the following nomenclature for the steel grades:

• First letter M for electrical steel.
• Three digits after the first letter denote value of specific loss measured at 1.5 or 1.7T.
• Two further digits represent the thickness.
• Last letter describes type of material: N, normal (loss measured at 1.5 T), S, reduced loss (loss at 1.7T); P, high permeability (loss at 1.7T).

For example, M097-30N means electrical steel (M) of normal grade (N) with material thickness 0.3 mm (30) and power loss at 1.5T notexceeding 0.97 W/kg.* Table 3.5 presents examples of GO electrical steel according to EN Standard 10107.

Figure 3.19 presents parameters of a typical GO SiFe steel grade M089-27N and Table 3.6 presents an example of the measured results for a similar steel sample (as measured by Epstein method).

3.2.2  HiB Grain-Oriented Electrical Steel

The conventional GO SiFe steel has Goss texture [001] (110) with grain orientation dispersion (tilt angle) of about 6° In 1965, Nippon Steel Corporation developed new technology for production of improved GO SiFe steel (Taguchi and Sakakura 1964, 1969, Yamamoto et al. 1972) After addition of around 0.025% aluminum to the starting melt, the recrystallization process was enhanced due to aluminum nitride AlN acting as inhibitor. The production route was simplified; hot rolled material was initially annealed at 1100°C in N₂ and in one cycle cold rolled to final thickness. After that conventional procedure was performed, decarburization, batch annealing for recrystallization at 1200°C, and final annealing at 800°C are carried out.

As a result, a new class of material with more perfect texture was obtained: a tilt angle was on average 2°–3° and grain dimensions exceeding 10 mm. This material exhibits significantly lower losses at higher polarization (above 1.7 T), which in turn could be achieved at significantly lower magnetic field strength. This steel is known as high-permeability material (HiB) Figure 3.20 presents comparison of pole figures determined for HiB and conventional steel.

Similar new technology was introduced in 1973 by Kawasaki Steel with inhibitor MnSe + Sb and in 1975 by Allogheny Ludlum Steel Corporation used boron as inhibitor. The Kawasaki technology has two cycles of cold rolling (Goto et al. 1975, Fiedler 1977).

It should be noted that the better performance of the HiB steel is especially evident for high polarization (as the name suggests). For small polarization, the HiB steel does not really offer any advantages; sometimes this material can be comparable or even worse than a conventional steel Table 3.7 presents an example of the measurement results for HiB steel sample (by Epstein method) Figure 3.21 presents the typical parameters of HiB steel.

As discussed above in the previous section (see Figures 3.15 through 3.17), the effect of perfect grain orientation can be weakened by wide domain wall spacing. Therefore, the HiB steel is often produced with the support of the domain refinement tools: laser scratching, plasma jest irradiation, spark ablation, groove making, chemical treatment, or coating stress (Nozawa et al 1978, 1979, 1996, Fukuda et al. 1981, Iuchi et al. 1982, Ichijima et al. 1984, Krause et al. 1984, Beckley et al. 1985, Takahashi et al. 1986, Yabumoto et al. 1987, Sato et al. 1998) Recently, the most commonly used technique is laser scratching (sometimes supported by stress coating or chemical etching).

Figure 3.22 presents the effect of domain refinement on losses It is clearly visible that the most successful domain refinement occurs when the sample has grain orientation close to perfect. This corresponds with results of domain investigation presented in Figures 3.16 and (3).17. Therefore, domain refinement usually is used in the case of HiB steel.

Usually, the high-power laser beam focused into a 150 μm spot scribes a line transversely to the rolling direction with scratch distance of about 5 mm Figure 3.23 presents the example of result of laser scratching technique. After application of domain refinement, it is possible to obtain the core loss lower by 5%–10% than the untreated high-permeability steel It can be also deduced from Figure 3.23 that the domain refinement practically does not change the static hysteresis loss Because after laser scribing the dependence P/f=f(f) is more linear (thin straight lines shown for comparison), this means that the domain refinement mainly decreases excess loss (related to domain wall).

3.2.3  SiFe Non-Oriented Electrical Steel

As presented in Figure 3.18, grain-oriented SiFe steel is strongly anisotropic so magnetic properties in direction different than the rolling are poor. Thus if we cannot guarantee that direction of magnetic flux is the same as the rolling direction (e.g., in rotating machines), we can expect worst performance of the designed device as compared with the raw material In such a case, the non-oriented material is more advisable.

Figure 3.24 presents the magnetization curves of typical NO steel determined for various angles of magnetization It should be noted that this material is not purely isotropic but in comparison with grain-oriented steel, the change of properties with the change of direction of magnetization are acceptably small. That is why in rotating machines the NO material is much more often used than the grain-oriented steel (see Figure 3.5).

Figure 3.25 presents a collection of the main properties of typical non-oriented SiFe steel For comparison on the same scale, there are presented the same properties of conventional grain-oriented (CGO) steel We can see that generally the NO steel exhibits lower quality in comparison with the CGO But in many devices, such poor properties are acceptable mainly taking into account economic point of view: NO steel is much cheaper Moreover, because this SiFe steel contains less silicon (0%–3%), it is more ductile, which means that more parts can be punched with the same stamping tool.

NO steel is delivered in one of the two possible forms: fully finished or semifinished. In the case of semifinished steel, the customer has to anneal the material after stamping. Semifinished steel is only a partly decarbu-rized to obtain better punchability (final decarburization is obtained in final annealing). Because it is not necessary to perform 24 h annealing for recrystallization and grain growth, the production process is much simpler (faster and therefore cheaper) (Figure 3.26).

During annealing, care should be taken to not allow the extra grain growth For this reason, the duration of annealing and of cooling should be precisely controlled. The optimal grain size is around 100–200 μm (Figure 3.27).

In NO SiFe, the presence of impurities is directly related to the hysteresis loss, which constitutes almost 75% of the total loss Hence it is a crucial for magnetic performances is presence of impurities (Figure 3.28). Therefore, the starting material and technology of removing carbon (decarburization), oxide, sulfur, and nitride are very important In modern NO steel, these impurities do not exceed 10ppm. NO SiFe steel is manufactured with different contents of silicon (Table 3.8).

The influence of Si on steel parameters is described by following empirical rules:

NO SiFe steel is classified by international standards in a similar way as the GO SiFe steel, mainly according to the power loss.* Table 3.9 presents the classification according to European Standard EN 10106.

Standards determine maximum anisotropy of loss described as

where

• P ₁ is the loss in a sample cut perpendicular to the rolling direction.
• P ₂ is the loss in a sample cut parallel to the rolling direction.

Thus, the NO SiFe steel should be tested using two sets of samples Table 3.10 presents an example of the results of measurement for a typical NO SiFe steel.

NO SiFe steel is usually delivered in coated form Various coating materials, organic or inorganic, are used Coating plays important role because it is not only the insulating layer but also protects against oxidation, aids in punchability, and in certain cases it can introduce tensile stress to improve the quality Comprehensive review on this subject is presented in a review article of Coombs et al. (2001).

3.2.4  Unconventional Iron-Based Alloys

It can be concluded from data presented in Figure 3.11 that by increasing the contents of Si in the SiFe steel, we can obtain attractive material in comparison with 3% SiFe Although saturation polarization decreases with silicon content, the 6.5% SiFe exhibits almost two times higher resistivity, which makes it a good candidate for medium-frequency applications (due to significantly smaller eddy current losses) Moreover, the 6.5% SiFe exhibits very small magnetostriction.

The main problem is that steel with this amount of silicon is very hard and brittle and it is not possible to manufacture it by the conventional cold rolling. Therefore, several other manufacturing technologies of this material are proposed: by powder rolling processing (Yuan et al. 2008), by rapid solidification (Fiorillo 2004, Bolfarini et al. 2008), or chemical vapor deposition (CVD) (Crottier-Combe et al. 1996, Haiji et al. 1996).

The rapid solidification technology is used to avoid formation of FeSi (B₂) and Fe₃Si (DO₃) phases because they make the material brittle. The molten metal stream is ejected onto a rotating metallic drum. Thin (30–100 μm) ribbon is obtained as result with acceptable ductibility, coercivity lower than 10 A/m, and maximum permeability higher than 10,000. The average grain diameter is 5–10 μm and therefore sometimes this material is called as a microcrystalline material.

The magnetic properties can be improved by annealing and recrystallization to grain with average diameter of around 300 μm (Roy et al. 2009) But unfortunately annealing leads to poor mechanical properties.

The main advantage of microcrystalline 6.5% SiFe is much wider frequency bandwidth in comparison with conventional SiFe (Figure 3.29) From Figure 3.29, it is clear that 6.5% SiFe is superior in comparison with 3.2% SiFe above around 100 Hz.

More convenient for large volume manufacturing is CVD technology In this technology, conventional 3% SiFe is chemically polished and next is held at 1000°C for 1 h under a flowing gaseous mixture of SiCl₄ and argon (Figure 3.30) Fe₃Si forms near the surface of the sheet and the sheet loses Fe as a gaseous FeCl₂ During 13 h diffusion process at 1000°C, a homogeneous FeSi solution is obtained In this way, it is possible to manufacture various thickness grain-oriented or non-oriented 6.5% SiFe sheet.

As result of the CVD siliconization, a significant improvement of most of all frequency-dependent properties is observed Figure 3.31 presents the typical reduction of energy loss after the CVD process.

In 1993, NKK Corporation started a commercial scale production of 6.5% SiFe by CVD siliconizing process Several grades of 6.5% SiFe called NK E-core 0.05, 0.1, 0.2, and 0.3 mm thick were available. Table 3.11 presents properties of NKK 6.5% SiFe For medium frequency, this material is much better than conventional steel and can be an alternative for amorphous material.

From time to time, the idea of cubic texture is investigated Indeed, looking at the Goss texture (Figure 3.32), the positioning of crystals seems to be rather extravagant More natural order, like cobbles, seems to be the cube order (Figure 3.32) Moreover, in the Goss texture, there is just one easy direction and perpendicular to it is the hard direction: in cube texture, both directions are easy (see Figure 2.18). Such feature could be profitable in rotating machines.

First information about possibility of obtaining SiFe electrical steel with cube texture was published by Sixtus in 1935 (Sixtus 1935) In 1957, Assmus described condition of processing and annealing necessary for a cubic orientation (Assmus et. al. 1957) By applying this technology, Kohler confirmed it practically by applying annealing of 3% SiFe in slightly oxidizing atmosphere (Kohler 1960).

Since then, other technological possibilities were demonstrated, for example, by rolling the sheet two times in perpendicular directions In 1988, a patent was published describing technology where starting point to cubic texture was (114) [401] texture (Sakakura et al. 1988) In the 1970s, two manufacturers, Armco Steel and Vacuumschelze, offered electrical steel with cubic texture in laboratory scale.

But this material was not accepted by the market Cubic SiFe steel was expensive (due to very complex technology of producing), with large magnetostriction and therefore also recently is prepared only on the laboratory scale.

Other alternative to SiFe steel is iron-aluminum alloy As can be seen from Figure 3.10, that aluminum changes the resistivity similarly to the addition of silicon Indeed 16% Al-Fe exhibits large resistivity (p = 140 μΩm), almost four times larger than 3% SiFe Additionally, it exhibits reasonably small coercivity and high permeability (after annealing it can be up to 50,000). The drawback of AlFe steel is that this material is more susceptible to oxidation (Figure 3.33).

The other commercially available steel is 16% AlFe known as alperm (also as alfenol). Due to its high resistivity, it can be used for medium frequency applications (Adams 1962) Another alloy, 13% AlFe, known as alfer exhibits large magnetostriction and is used in magnetoelastic sensors.

In 1936, Masumoto developed new Fe-Si Al alloy known as sendust. This alloy (84.9 Fe–9.5 Si–5.6 Al) has very high permeability (even 140,000), low coercivity, and large resistivity (Masumoto 1936) Additionally, it exhibits a unique feature; simultaneous zero magnetostriction and zero magnetocrystalline anisotropy constant K ₁. It can be used in medium- or high-frequency applications as competitive to NiFe alloys Due to its hardness, it was used as material for magnetic reading heads Because it is very brittle, often it is manufactured as powder cores Table 3.12 present properties of main iron-aluminum alloys.

3.3.1  NiFe Alloys (Permalloy)

Permalloy* (NiFe alloy) was for many years the symbol of the highest quality soft magnetic material with extremely high permeability (μ_max = 1,000,000 in the case of Supermalloy) and small coercivity (H_c = 0.2 A/m in the case of Supermalloy) (Chin 1971, Pfeifer and Radeloff 1980, Couderchon et al. 1982) Superiority of permalloy illustrates impressive Figure 3.34 from Fiorillo book (Fiorillo 2004) Recently, the importance of NiFe alloys is shadowed by new stars: amorphous and nanocrystal-line materials having similar or better properties.

By an appropriate selection of the alloy composition (supported by additional elements like Mn, Cu, Cr, V) and annealing/cooling treatment, it is possible to obtain an alloy exhibiting various, often extraordinary properties, for example,

• Alloy with close to zero coefficient of thermal expansion (FeNi36 known as invar or Fe59Ni36Cr5 known as elinvar)
• Alloy with the coefficient of thermal expansion the same as glass (Fe53.5Ni29Co17Mn0.3Si0.2 known as kovar)
• Alloy with very high permeability (Fe16Ni79Mn4 known as supermalloy or Fe16Ni77Cu14 known as mumetal)
• Alloy with constant permeability (Fe55Ni36Cu9 known as isoperm)
• Alloy with permeability linearly dependent on temperature (Fe70Ni30 known as thermoperm or Ni67Fe2Cu30 known as thermalloy)
• Alloy with square hysteresis loop (Fe50Ni50 known as hipernik or permenorm)

By appropriate heat treatment, it is possible to obtain various types of texture, including isotropy Figure 3.35 demonstrates the possibility of change of the hysteresis loop by appropriate annealing: from square loop to linear.

Flexibility and versatility of NiFe as a function of temperature treatment and composition are advantageous but under some circumstances they could be a drawback. Their properties can be easily altered during operation of a given device and especially after cutting and stamping or mechanical shocks, it is necessary to anneal the material.

Figure 3.36 presents dependence of NiFe alloy properties on the nickel contents. There are three main areas of application:

• Close to 80% of Ni where the permeability is very high and coercivity is small.
• Close to 50% where the saturation polarization is the largest.
• Close to 36% where resistivity is large.

The anisotropy constant and magnetoelasticity constant are close to zero around 75%–91% Ni Unfortunately, it is not possible to obtain zero value of both parameters simultaneously (as it is the case with Sendust) but with small addition of other components (molybdenum, copper), it is possible to obtain nonmagnetostrictive material with zero anisotropy constant.

Table 3.13 presents the parameters of the main NiFe alloys In application of NiFe alloys, two types of alloys are important. The first is around 80% of Ni with high permeability, small coercivity, and close to zero magnetostriction. These alloys are most of all used as magnetic shields (mumetal) and for sensors (supermalloy). To obtain high permeability, the special heat treatment called permalloy treatment (or double treatment) is done. This annealing consists of heating for 1 h at 900°C–950°C and cooling not faster than 100°C/h to room temperature. Then, heating is continued to 600°C and the alloy is cooled in the open air to room temperature by placing on the copper plate.

High-permeability alloys have low resistivity and saturation polarization. Therefore, for other purposes (pulse transformers, audiofrequency transformers, null balance transformers, switches, chokes, etc ), alloys with around 50% Ni are used Figure 3.37 presents the dependence of core loss on a peak magnetic flux density.

As discussed earlier, NiFe alloys are very versatile in their performances Figure 3.38 presents the special purposes alloys of Vacuumschmelze. Thermoflux is an alloy with practically linear dependence of flux density on the temperature It can be used as a magnetic shunt to compensate temperature effects in permanent magnet systems Cryoperm is an alloy developed for low-temperature applications.

NiFe alloys are also available in form of the powder cores known as MPP (molybdenum permalloy powder, Ni81Fe17Mo2).

3.3.2  CoFe and CoFeNi Alloys (Permendur and Perminvar)

Alloys with around 50% Co is known as permen-dur—the alloy of the highest available saturation polarization—up to 2.46 T. Data and characteristics of such alloy are presented in Table 3.12 and Figure 3.39.

To improve the material properties, a small amount of vanadium (2%) is added In this way, resistivity and 10 A/m ductibility are improved partly at the cost of small decrease of saturation polarization. There is also a special kind of permendur alloy with carefully controlled purity and magnetically annealed known as supermendur It exhibits much lower coercivity around 10 A m and large permeability around 80,000.

CoFe alloys are used in applications where high saturation flux density is necessary, for example, as poles of electromagnets Mechanical force depends on the square of flux density, hence alloys with higher saturation flux density allow miniaturization of the cores. For this reason, the CoFe alloys are used when the weight is at premium, in the aerospace industry.

There is also the group of NiFeCo alloys, in which the most well known is perminvar Ni45Fe30Co25, the alloy with permeability constant over a wide range of applied field values.

3.4.1  Amorphous Soft Magnetic Materials (Metallic Glass)

Figure 3.40 illustrates technology of the amorphous ribbon production. The material in liquid state is rapidly cooled on a rotating copper drum. The speed of cooling should be fast enough not to allow the formation of crystal structure. To help in formation of the amorphous state, small addition of metalloid (mostly boron) is made in order to improve viscosity of the molten metal Since the ribbon should be cooled very quickly, it is thin with the thickness not exceeding 50 μm. Also the width of the ribbon is limited, usually not exceeding 20 cm.

Table 3.14 presents data of main amorphous ribbons Exceptional performances are exhibited by cobalt-based alloys: very high permeability, small coercivity, and possibility to obtain material with negligible magnetostriction But these alloys suffer from low polarization saturation and low Curie temperature On the other hand, iron-based alloys exhibit higher saturation but at the cost of permeability and coercivity. The highest polarization is possible to obtain by adding of about 20% of expensive cobalt to iron-based alloy Intermediate properties exhibit FeNi-Mo alloys that make them suitable for shielding purposes.

The magnetic parameters of amorphous ribbon can be improved by annealing (Figure 3.41), especially by annealing in longitudinal magnetic field. Because metallic glass is brittle, usually heat treatment is performed on the final form of the core (e.g., wound toroid). This way mechanical stress is removed, but this is also caused by winding of the toroid. The temperature should not exceed crystallization temperature of the amorphous state and is around 400°C for NiFe alloys, 480 for Fe alloys, and 550 for Co alloys.

The amorphous alloys have been introduced in 1970s by Allied Signals Inc Metglas Products Recently, market available products are offered by Metglas Inc Hitachi Metals and by Vaccumschmelze Table 3.15 presents data of commercially available soft magnetic amorphous materials. Typical thickness of the ribbon is around 25 μm, and its width does not exceed 20 cm.

The most versatile is Metglas SA1 with relatively large saturation flux density and permeability and low power loss Figure 3.42 presents the core power loss of this alloy.

It can be seen from Figures 3.42 and (3).43 that amorphous alloys can work in high-frequency bandwidth. It is the main application of this material—pulse transformers, high-frequency transformers, current transformers, and ground fault interrupters Indeed, as illustrated in Figure 3.44, amorphous materials are superior up to 1 MHz in comparison with other materials.

Another important application of amorphous materials is profiting on exceptionally high permeability: in Co-based alloy even 1,000,000 Such large permeability is recommended especially in shielding and sensors application Figure 3.45 presents typical magnetization curves of Co-base amorphous alloy.

The possibility of application of amorphous cores in power transformers is still under discussion (Moses 1994, Hasegawa and Azuma 2008) Indeed, a comparison of power loss at 1.3 T–0.64 W/kg in the case of silicon steel and 0.11 W/kg in the case of amorphous ribbon is rather impressive.

After introduction of amorphous alloys, it was expected that they should substitute conventional distribution transformer due to smaller loss and better efficiency. Up to 1990, around 20,000 amorphous metal distribution transformers (AMDTs) have been installed in the United States (in Japan about 32,000 units) (Moses 1994) Although amorphous material has much lower power loss in comparison with GO SiFe steel (due to smaller coercivity and larger resistivity), there are several practical obstacles in expansion of the AMDT units.

Amorphous ribbon is very thin (about 25 μm) and relatively narrow (10–20 cm), which makes difficult the design and manufacture large transformers Practically, only wound corers can be made In the case of one-phase distribution (dominant in the United States and Japan), the design of wound amorphous core transformer is relatively easy In the case of three-phase distribution (dominant in Europe), the design of AMDT unit is still a challenge.

The very significant obstacle is lower saturation flux density 1.56 T for most popular Metglas 2605 SA1 ribbon in comparison with 2.03 for GO SiFe. That is why Metglas Inc introduced a new-grade Metglas 2605 HB1 with improved properties: B_s = 1.64 T and H_c = 2.4 A/m (in the case of Metglas 2605 SA1 H_c = 3.4 A/m) (Hasegawa 2006). Table 3.16 presents performance of a 50 Hz three-phase 500 kVA transformer and Figure 3.46 the efficiency of distribution transformer.

It was estimated that in the United States the annual energy lost in transformer is around 140 TWh. Introduction of AMDT transformers resulted in saving of around 80 TWh, which corresponds with annual reduction of 60 tons of CO₂ * (Hasegawa and Azuma 2008) In 2009, ABB Corp introduced production of AMDT transformers in New Jersey.

Amorphous materials are described in detail in many review papers or books (Chen 1980, Luborsky et al. 1980, Hasegawa 1983, Egami 1984, Moorjani and Coey 1984, McHenry et al. 1999, Waeckerle et al. 2006) Lately, we observe that new papers on this subject are low in number Even introduction of the new grade Metglas HB1 is a rather cosmetic improvement Recently, more research papers are devoted to nanocrystalline materials and they can be considered as further development of amorphous materials (because as starting material often amorphous material is used for devitrification process).

3.4.2  Nanocrystalline Soft Magnetic Materials

In 1988, Yoshizawa et al. from Hitachi Metals Company proved that after appropriate annealing of Fe-based amorphous ribbon, it is possible to create very small grains of α-FeSi (average diameter around 10 nm) embedded in an amorphous matrix (see Figure 2.115) (Yoshizawa et al. 1988). This new material called FINEMET exhibited excellent magnetic properties, close to those possible to obtain in Co-based, much more expensive amorphous ribbon As the initial amorphous material Fe_73.5Cu₁Nb₃Si_13.5B₉ ribbon with thickness 20 μm was used (note that also expensive boron was used in smaller amount than in the typical amorphous material), copper was added to enhance the nucleation of α-Fe grains and niobium was used to lower the growth of the grains. The temperature of annealing for about 1 h was above the crystallization temperature, around 550°C. Moreover, the starting material had saturation magnetostriction λ _s = 20.10⁻⁶ but after annealing the nanocrystalline material exhibited close to zero magnetostriction. Thus, the paper of Yoshizawa was the starting point for the new class of soft magnetic materials known as a nanocrystalline material Figure 3.47 shows the properties of material presented in paper of Yoshizawa.

In nanocrystalline materials, the direction of anisot-ropy of the grains is randomized and therefore reduced in the overall performance. The properties of a nano-crystalline material are similar to the best grades of permalloy However, the NiFe alloys can be used in frequency only up to 100 kHz but the nanocrystalline materials can work correctly in the frequency bandwidth similar to best grades of ferrites.

After the initial information about FINEMET, many other publications about similar or other nanocrystali-line materials appeared. The most widely known are NANOPERM and HITPERM (see Figure 3.50). Team from Tohoku University in 1981 proposed to substitute Nb by other transition metal like zirconium (Zr) or hafnium (Hf) (Suzuki et al. 1991, Kawamura et al. 1994). Typical materials Fe₈₇Zr₇B₅Cu₁ or Fe₈₆Zr₇B₆Cu₁ are known as NANOPERM Such materials were obtained by rapid solidification of melting mixtures or by compaction of powder by hot-pressing machine (Kawamura et al. 1994) Figure 3.48 presents properties of NANOPERM.

Figure 3.49 presents changes of amorphous/nano-crystalline material during annealing.

From the data presented in Figure 3.48, it can be seen that the nanocrystalline NANOPERM has lower power loss and higher permeability in comparison with the Fe-based amorphous alloy In comparison with the FINEMET, this material exhibits higher saturation polarization (1.2 T for FINEMET compared to 1.5–1.8 T for NANOPERM). The main drawback of amorphous and nanocrystalline materials is their relatively small (compared to SiFe) polarization Similarly, as in the case of NiFe alloys, in order to obtain higher polarization, special alloys with an addition of cobalt known as HITPERM (Figure 3.50) were developed.

The FeCo nanocrystalline alloys with composition (FeCo)-M-B-Cu (where M—Zr, Hf, Nb, etc.) enable obtaining the saturation polarization close to the polarization of SiFe (Villard et al. 1999a,b). These alloys are known as HITPERM They can be used in elevated temperatures up to 650°C Table 3.17 presents the main features of nanocrystalline alloys.

The most commonly used nanocrystalline material is close to Fe_73.5Cu₁Nb₃Si_13.5B₉ alloy and is available under various trade names: Finemet, Vitroperm, Nanophy.

Usually nanocrystalline material is delivered as ready-to-use toroidal core, for example, choke or transformer because nanocrystalline material is very sensitive to annealing conditions Figure 3.51 presents the influence of the annealing temperature on coercivity and permeability Incorrect temperature of annealing leads to significant increase of coercivity due to overgrowth of grain diameter (coercivity strongly depends on grain diameter proportional roughly to D ⁶). Similarly small changes of alloy composition cause significant changes of parameters. Figure 3.52 presents the annealing temperature recommended for Finemet alloy.

By applying the magnetic field during annealing, it is also possible to change the magnetic parameters, for example, the shape of the hysteresis loop Figure 3.53 presents various types of hysteresis for the same Finemet type alloy annealed under various conditions.

Materials with high permeability are used in EMI filters, shielding sheets, current sensors, and magnetic sensors Materials with square hysteresis are used in pulsed power cores and surge absorbers Low magnetostriction is required for high-frequency applications such as transformers, filters, and chokes. Table 3.18 presents the properties of the main FINEMET materials.

Nanocrystalline materials are used mainly in high-frequency applications as competition to ferrites (see Figure 3.54 and Table 3.18).

3.5.1  MnZn and NiZn Ferrites

Ferrites are the ceramic ferrimagnetic materials with a spinel* structure. Investigating various possible compositions of ferrites, Snoek predicted that the two main classes of materials, MnZn and NiZn ferrites, should exhibit the best performances (Snoek 1936, Sugimoto 1999) And indeed although various soft ferrites compositions are being investigated (Stoppels 1996), only these two main mutually complementing families of materials are commercially available (Figure 3.55) Table 3.19 presents the main properties of both classes of soft ferrites MnZn ferrites exhibit higher permeability and saturation polarization but NiZn ferrites have much higher resistivity (close to electric insulators) and therefore can be used at higher frequencies (1–500 MHz while MnZn up to a few MHz).

The two classes of ferrites can be described by formulas Mn _x Zn_(1−x)Fe₂O₄ or Ni _x Zn_(1−x)Fe₂O₄. By changing the composition, it is possible to influence the properties of ferrite (Figure 3.56). There are three main groups of ferrites: with optimized permeability (for EMI filters, chokes and shield), with optimized saturation polarization (for signal processing), and with optimized loss (quality factor Q) for power application. Generally, magnetic properties of soft ferrites are poor in comparison with those of SiFe and additionally these parameters strongly depend on temperature But, there are a plethora of commercially available ferrite products due to their dominating performance in the high and very high frequency range Ordinary, inexpensive ferrites are also used in many applications where requirements are not high.

The manufacturing process of ferrites is not very complex. The raw materials (the oxides or carbonates of the constituent metals) in form of a powder are mixed Then this mixture is calcined (presintered at approximately 1000°C), where apart from other processes, calcination of carbonates MCO₃→MO + CO₂ occurs (in ordinary materials, sometimes this stage is omitted) After calcination, the material is milled to the powder with grains smaller than 2 μm Finally, the product is formed by pressing. The main process of sintering is performed at temperature between 1150°C and 1300°C Depending on the composition (including small addition of other elements), technology market offers a diversity of various ferrite materials (Figure 3.57).

In assessment of the quality of ferrites, slightly different parameters are used than it is in the case of low-frequency materials By considering permeability, both components (real and imaginary) are taken into account (Figure 3.58). The complex permeability

describes in a better way the energy dissipation represented by a phase shift δ between polarization J(t) and magnetic field H(t): The excess power loss is expressed as (Fiorillo 2004) For inductors used in filter applications, a quality factor Q = 1/tanδ often is used as the figure of merit. Another quality and performance indicator in form of the factor f. B _max for a fixed loss sometimes is used. The example of such dependence is presented in Figure 3.59.

Figure 3.60 presents the hysteresis loop of typical ferrite core and Table 3.20 presents properties of typical grades of commercially available ferrites.

3.5.2  Ferrites for Microwave Applications

New generations of electronic devices work at ever increasing frequencies. Therefore, there is a need for magnetic materials in the GHz range, up to 150 GHz In many microwave devices, magnetic part is very important, taking into account antennas, circulators, isolators, phase shifters, and filters. Fortunately, there are ferrites that work in the microwave range.

In the GHz frequency range, ferrites exhibit ferromagnetic resonance phenomenon (more exactly fer-rimagnetic resonance; see Section 2.7.4). Therefore, an important factor of a microwave material is ΔH, the

ferromagnetic resonance linewidth. The permeability of material is described by the Polder tensor where µ = µ₀(1 + ω₀ω _m /(ω² ₀-ω²)), k =µ₀ωω _m /(ω² ₀-ω²), ω₀ = γµ₀ H ₀, ω _m = γµ₀ M. and γ is ferromagnetic resonance (gyromagnetic) ratio, γ=g·017.6 [MHz/(kA/m)] and g is Landé factor (between 1.9 and 2.4 for various ferrite materials).

Thus, permeability depends on the frequency (ω), resonance frequency (ω₀), and internal bias magnetic field (H ₀).

In the microwave range, three most important materials can be used: garnets ferrite (in the range 1–10 GHz), spinnel ferrites (in the range 3–30 GHz), and hexagonal ferrites (in the range 1–100 GHz). Table 3.21 presents properties of the main microwave materials.

Microwave technique and microwave materials are described in many books and review papers (Dionne 1975, Nicolas 1980, Pardavi-Horvath 2000, Adam et al. 2002, Özgür et al. 2009).

3.6.1  General Remarks

Since the introduction of rare-earth metals such as neo-dymium and samarium in the production of permanent magnets (and after wider exploitation of deposits of the main minerals containing these elements—monazite, bastnäzite in China and Brasil), significant progress in the quality of permanent magnets is observed It is illustrated in Figure 3.61.

In the case of soft magnetic materials, we require as small as possible coercivity because hysteresis power loss strongly depends on this value Conversely, in the case of hard magnetic materials, we need to have as large as possible coercivity and remanence because stored magnetic energy approximately depends on the H_c ·B_r value (Figure 3.62).

Historically, as the first hard magnetic materials, simply different kinds of steel were used In 1917, in Japan, cobalt steel (Fe₅₅Co₃₅W₇Cr₂C_0.6) known as Honda alloy was developed In 1931, also in Japan, Mishima invented the Alnico alloy (Fe₅₈Ni₃₀Al₁₂), which gave better performance in comparison with steel Recently, cobalt steel has practically vanished from the market as a material for permanent magnets Table 3.22 presents parameters of the main hard magnetic materials and Figure 3.63 the market segmentation of permanent magnet materials.*

From the data presented in Figure 3.63, it can be seen that hard magnetic ferrites are still dominating the market (almost 60% of the market). The rare-earth-metal-based magnets overshadowed the earlier very popular Alnico and their applications are growing (Fastenau and van Loenen 1996).

For many years, the evaluation of magnetic materials was commonly based on the relationship B = f(H). Recently, this relation is commonly substituted by J = f(H) as more reliable and describing physics of the magnetic phenomena. ^† In the case of soft magnetic materials, both relations are very similar and differences are detectable only for extremely large H values. ^‡ In the case of hard magnetic materials, hysteresis B = f(H) is significantly different than J = f(H) (Figure 3.64) and therefore we need to distinguish between coercivity for the B(H) loop known as _BH_c and coercivity for the J(H) loop known as _JH_C. The coercivity _JH_C is usually larger than _BH_c and the difference is a measure of internal possibility of material to store the magnetic energy.

Another difference is that the soft magnetic materials are usually used in a form of a closed magnetic circuit But in the case of permanent magnets, we never use the hard magnetic materials in the form of a closed circuit (we are interested in generation of the external magnetic field between poles of the magnet). An example of a permanent magnet with a gap of the length l_g (and cross-section A_g ) is presented in Figure 3.65.

After opening of the closed circle, the remanence flux density B_r is decreased to the value B_m as result of the demagnetizing field. In the analysis of permanent magnets, we usually take into account only the second

quadrant of the hysteresis loop, known as demagnetization curve (Figure 3.65). The value of B_m is determined as the crossing point P of the hysteresis loop and the demagnetization line (or the load line) as where N_d is the demagnetizing coefficient depending on the geometry of the sample.

For the magnetic circuit presented in Figure 3.65, we can write the following relationships (neglecting the leakage magnetic field around the gap of the area A_g ):

From these equations, we obtain or

From Equation 3.11, we can conclude that

• The possibility of obtaining the magnetic field of the magnet depends directly on the (BH) value, called often as an energy product.
• For the assumed volume of an air gap V_g and assumed maximum energy BH _max of hard magnetic materials, we can determine the necessary volume of the magnet V_m (see Figure 3.61).
• We should design the dimensions of the magnet to ensure that the working point P (Figure 3.65) corresponds with the maximum of (BH) _max .

Figure 3.66 illustrates that we can obtain various BH(H) curves for the same values of B_r , H_c .

For a theoretical ideal magnet with square-shape hysteresis loop, the optimum working point P is in the middle of the line B_r – _BH_c and maximum energy product is

For NdFeB magnets, this theoretical limit is estimated as 485 kJ/m³. Usually, real magnets exhibit less than 60% of this theoretical value *.

Usually on the graph presenting the demagnetizing curve of a material, the lines B/μ₀ H representing 1/N value (Equation 3.7) as well as those representing the BH values (Figure 3.67) are also indicated. This way the designer of the permanent magnet can at once determine possible performances of the material and recommended geometry of the magnet.

The energy stored by the magnet also depends on the energy product BH and volume of the magnet V_m (Fiorillo 2004):

In many applications (e.g., in electric machines), the gap is not fixed; sometimes a magnet armature can move up to the state of closed magnetic circuit (full contact with the poles). The flux density does not return to the rema-nence B_r but to other point B_rc (Figure 3.68). Moreover, this movement creates a small hysteresis loop Because this loop is often very narrow, it is substituted by a line with a slope called the recoil permeability μ _r .

3.6.2  Alnico Alloys

Alnico was discovered in 1930 by Mishima and the first classical alloy contains 58% Fe, 30% Ni, and 12% Al It exhibited coercivity of over 30 kA/m, which was almost double of the best steel magnets then available Until introduction of the rare earth magnets in 1970s, Alnico was the main hard magnetic material Recently, its importance is reduced (see Figure 3.63); its main advantage is still high working temperature—up to 500°C. Alnico was evaluated with modified composition (addition of cobalt and titanium) known as Alnico 2, Alnico 3,…, Alnico 9 (Figure 3.69).

Various types of Alnico differ not only by the composition but also by heat treatment (including annealing in magnetic field); they are isotropic or anisotropic, non-oriented, or grain oriented. The properties of Alnico alloys are presented in Table 3.23.

Alnico are recognized as Alnico 2, …, Alnico 9 or by their various trade names: Alni, Alcomax, Hycomax, Ticonal In manufacturing of Alnico alloy heat treatment, often in presence of magnetic field is very important After the heat treatment, Alnico transforms to a composite material with rich iron and cobalt precipitates in a NiAl matrix Starting from Alnico 5, anisotropy is improved due to grain orientation—after heating in a presence of magnetic field and appropriate cooling the Fe-Co particles are long and ordered in one direction Starting from Alnico 6, titanium is added which increases the coercivity In Alnico 9, after appropriate heat treatment, a columnar crystallization is obtained Figure 3.70 presents a typical annealing process of Alnico material.

The Alnico material is hard and brittle hence it is usually cast or sintered into a final shape. Alnico 5 and higher versions contain cobalt and titanium and therefore this material is more expensive Figure 3.71 presents the demagnetization curves of the Alnico alloys.

3.6.3  Hard Magnetic Ferrites

Hard ferrites exhibit rather modest performance, especially relatively small saturation But because of their low price, they are commonly used in less demanding applications Hard ferrites are prepared as sintered from the powder but also composite, bonded materials are available. They are bonded with rubber, PVC, polyethylene, or polyester resins Although bonded materials are inferior in comparison with sintered (as result of reduction of magnetic part in the whole volume), they are popular due to flexibility and low price.

Almost exclusively, two types are manufactured as hard magnetic ferrites: barium ferrite (BaO · 6Fe₂O₃) and strontium ferrite (SrO · 6Fe₂O₃). Both groups of hard ferrites have similar properties although strontium ferrites have slightly better coercivity and saturation. The properties of these ferrites are presented in Figure 3.72 and Table 3.24.

Barium and strontium ferrites have exceptional properties due to two main reasons: they exhibit very large anisotropy and the powder grain is small (diameter around 1 m), so that every grain is close to a one-domain structure. The one-domain sample is magnetized by coherent rotation of magnetization and according to Stoner-Wohlfarth model, this leads to a rectangular hysteresis loop (see Figure 2.138).

The manufacturing process of hard ferrites includes calcination in a furnace at about 1200°C, formation of the powder, and then pressing and sintering at around 1200°C. The anisotropic properties are obtained by pressing the powder in the presence of magnetic field.

3.6.4  Rare Earth Hard Magnetic Materials

High anisotropy is a crucial for properties of hard magnetic materials Hence, many researchers looked for materials with exceptionally large magnetocrystal-line anisotropy In 1966, Hoffer and Strnat announced that they obtained material based on yttrium with very large anisotropy K₁ =5.7 MJ/m³ (Hoffer and Strnat 1966).

Later, other compositions—rare earth metal/ferromagnetic metals as Co or Fe were investigated. The most widely studied materials have the structure RECo₅, RECo₁₇, REFe₁₄B Light lanthanides were found to be most promising Indeed, these elements crystallized in complex hexagonal or rhombohedral structures exhibited not only high anisotropy but also large saturation polarization (Table 3.23) (Strnat et al. 1967, Strnat 1988, 1990, Buschow 1991, Kirchmayr 1996).

From data presented in Table 3.25, particularly interesting are SmCo₅ with exceptionally large anisot-ropy, Nd₂Fe₁₄B with high saturation, and Sm₂Co₁₇ with high Curie temperature. Indeed, in 1967, the first rare-earth permanent magnet material SmCo₅ was proposed as exhibiting the best properties and new era in magnet technology started (Strnat et al. 1967).

Rare-earth-based materials are prepared similarly to the ferrite materials: fine powder (diameter of grains to a few μm to obtain conditions close to one domain) is pressed (sometimes in a presence of magnetic field) and then sintered at about 1150°C for 3 h. Sometimes, this material is further heat-treated at a temperature of 850°C–900°C. There are also bonded materials with polymer or epoxy resin.

Both components of the SmCo₅ material are expensive. Therefore, other similar materials were tested One of them is MMCo5 or Sm_0.2MM_0.8Co₅ where samarium is substituted by mischmetal MM composed from various other lanthanides, for example, 55% Ce, 24% La, 16% Nd, 5% Pr, and 2% of additional lanthanide metal In another material known as Sm₂Co₁₇, there is less cobalt and samarium and other components (e.g., Fe, Mn, Cu, Cr) are added for the improvement of magnetic properties Figure 3.73 presents typical demagnetization characteristics of samarium-cobalt materials.

In 1984, two teams reported new hard magnetic material based on neodymium (Croat et al. 1984, Sagawa et al. 1984). The new material has much larger saturation polarization, larger coercivity, and therefore higher energy product (BH)_max (Figure 3.74) Moreover, the new material used less expensive components For this reason, recently the neodymium magnets slightly overshadowed the samarium-based materials.

First reported neodymium materials were obtained using classical technique (sintering) (Sagawa et al. 1984) but later also rapid solidification was employed (similar to the technology used in amorphous alloys) (Croat et al. 1984). Rapid solidification enables to obtain small grains of about 30 nm while in sintered materials they are around 3 μm. Theoretically (Kneller and Hawig 1991), small grains should result in higher coercivity but to date nanomaterials and nanocomposites exhibit worst parameters than sintered materials.

In other technology known as magnetquench, the alloy is rapidly quenched. After grinding, the flakes are bonded into an epoxy resin.

Figure 3.75 and Table 3.26 presents properties of typical rare-earth hard magnetic materials. The best performance is demonstrated by NdFeB material, but its Curie temperature is relatively low at 312°C. Therefore, samarium-based materials with Curie temperature 820°C are also commercially available.

Table 3.26 presents parameters of commercially available rare-earth hard magnetic materials, VACODYM (neodymium based) and VACOMAX (samarium based), the best grades of Vacuumschmelze Vacodym 722 with (BH)_max equal to 415 kJ/m³ is close to the theoretical limit (485 kJ/m³) (see Equation 3.12). Figure 3.76 presents characteristics of this material As can be seen, the temperature changes of the parameters are significant. This influence can be decreased by changing geometry of the magnet (compare movement of the working point with temperature for B/μ ₀ H = 1.0 and B/μ₀ H = 2.0).

3.7.1  Thin Magnetic Films

Thin film is a nanometer range layer deposited onto a substrate Such layer can be only a few atoms thick: fraction of a nanometer* or up to several hundred nanometer (typical thickness is several dozen of nanometers) Almost every material can be deposited, including soft and hard magnetic materials. Thin films are usually polycrystalline but they can be also amorphous or monocrystalline In electronics, the most important are, of course, semiconductor thin films. In this section of the book, mainly ferromagnetic thin films are described.

Up to 1970, ferromagnetic thin films were mainly the object of interest of physicists due to their unique features different than those of bulk materials In 1970, Hunt patented application of thin film magnetoresistor as a magnetic reading head (Hunt 1970) From that time, thin films gained rapid attention in computer industry as reading heads of discs. This development was crowned by a Nobel prize in 2007 (Fert and Grünberg) for GMR thin film for magnetoresistive effect (Fert 2008). Recently, thin ferromagnetic films are the object of interest in nanotechnology and a new scientific branch spintronics (Wolf et al. 2006, Bandyopadhyay and Cahay 2008).

One of unique features of thin ferromagnetic films (in comparison with a bulk material) is that they magnetize similarly to one domain Properties of one domain are described by Stoner-Wohlfarth model of hysteresis (see Section 2.11.3). Thin film exhibits uniaxial anisotropy induced in process of deposition In the initial state, a thin film is magnetized along the anisotropy axis called also easy axis of magnetization. Usually, we apply the magnetic field directed perpendicularly to anisotropy axis and the thin film is magnetized by coherent rotation of magnetization (hysteresis-free) up to the saturation (when the magnetic field reaches value equal to the anisotropy field H_k ). If we apply the magnetic field along the easy axis, but apposite to initial magnetization, the direction of magnetization changes suddenly when the magnetic field reaches value equal to anisotropy field H_k . Thus in the hard direction of magnetization, thin film is described by linear dependence M = f(H) while in the easy direction it is described by rectangular hysteresis (see Figure 2.138).

Theoretically one-domain sample cannot be demagnetized. The real thin films exhibit dispersion of anisotropy and therefore they are not in ideal one-domain state Dispersion of anisotropy means that the direction (angle dispersion of anisotropy) and magnitude (magnitude dispersion of anisotropy) can vary on the plane from one grain to another (not perfect texture).

Figure 3.77 presents comparison of theoretical and real hysteresis loops of a thin film element. We can see that also in hard direction of magnetization, there is a narrow hysteresis. But if magnetizing field is sufficiently small (H_X ≪H_k ), the magnetization is linear and hysteresis free (Figure 3.77c). This area is of particular interested for sensor applications (Tumanski 2001) because between direction of magnetization φ and value of external field H_X is the dependence close to linear (see Figure 2.39):

If external magnetic field is higher than the anisotropy field, the thin film can be demagnetized (see Figure 2.141). We can avoid such a situation by artificial increase of anisotropy—by additional biasing the film with the field H_B directed along the easy anisotropy axis: Thin film can be deposited with various technologies (Figure 3.78) such as by electroplating and chemical methods, but most commonly, sputtering technique or vacuum evaporation is used. In the evaporation method, the source of the material is heated by electron beam and the vapor of metal is transferred to the substrate in vacuum Glasses, oxidized silicon, or ceramic material can be used as the substrate To improve adhesion to the substrate, often predeposition of the buffer layer, for example, titanium or tantalum is used. The anisotropy of thin film is induced by deposition in presence of the magnetic field.

The evaporation technique is used mostly in laboratory In industry, often the sputtering technique is more efficient. The chamber of deposition is filled by a noble gas, for example, argon. Under the electrical field between the anode (attributed to the substrate) and the cathode (attributed to the source), the glow discharge appears. The ionized gas ejects the atoms of the material from the source and moves them into the substrate.

By changing sources, it is possible to deposit various materials and in this way form a multilayer structure.

In the thin film technology, molecular beam epitaxy (MBE) technique is very important (Figure 3.79) In this technique, it is possible to obtain almost perfect crystal structure because deposited film mimics the structure of substrate acting as a seed crystal Modern MBE apparatus is equipped with the testing method, for example, reflection high energy electron diffraction (RHEED). This enables to control the deposition process, crystal structure, and composition MBE method utilizes very high vacuum.

As a ferromagnetic thin film material, most commonly permalloy 81-19 is used Figure 3.80 presents the main properties of NiFe alloys. The main advantage of 81/19 alloy (permalloy) is that its magnetostriction coefficient (λ) is close to zero (non-magnetostrictrive material). Moreover, this material also exhibits relatively small anisotropy (H_k = 250 A/m), large magnetoresistance (Δρ/ρ = 2.2%), and small dispersion of anisotropy (α).

In GMR technology, thin film is created in a form of multilayer: typically two ferromagnetic layers separated by a conducting layer (spacer). This conducting layer should be very thin (less than a few nanometers) and therefore deposition of such thin layer without defects (especially pin-holes) is crucial for this technology Even more difficult is deposition of the spacer layer for a magnetic tunnel junction In this case, the intermediate layer should be an insulator; commonly, it is aluminum layer that is later oxidized.

After deposition, final shape of the thin film element is formed. This includes etching of the final form (most often a strip), leads or terminals, additional bias layers, additional planar coils, cover layer, etc. This process can change the properties of the thin film due the shape anisotropy (see Equation 2.214) It is not recommended to form a shape inclined at some angle with respect to anisotropy axis of material because the resultant anisot-ropy axis is then different than the axis of the material. The most critical case is when the strip is perpendicular to easy anisotropy axis because it causes significant increase of the dispersion of anisotropy.

The main application of thin magnetic films is the reading head for disk drives Such a head is a complex device in which a magnetoresistive reading head is usually merged with thin film writing head and both are inserted between thick film shields (Figure 3.81). Also the magnetoresistive element of the head is a complex multilayer design Figure 3.82 presents a surface view of a spin valve head. The GMR sensor is composed of four layers: two permalloy layers separated by a Cu layer and additional Co layer for improvement of the performances. This element is additionally magnetized by antiferromagnetic layer of NiO Sometimes, a magnet part for biasing the permalloy layer is added More information about spin-valve sensors is given later in the part devoted to magnetic sensors.

Progress in the density of information recording (due to miniaturization or writing/reading heads) forces further improvements in recording Materials should follow these improvements Previously as most commonly used recording material for tape recorders was γFe₂O₃ with coercivity of about 30 kA/m. Recently, hard disks composed of a few platters are used for data recording and storage Onto such platters quite complex multilayer structure is deposited by sputtering (Figure 3.83).

Typical recording media consist of six functional layers (Figure 3.83)—each of which can be composed from further several sub-layers, for example, two anti-ferromagnetic coupled layers separated by third layer as recording layer can be used as a recording layer Of course for quality of recording the recording layer is crucial—it is a polycrystalline layer Such material should exhibits high coercivity, high anisotropy, large saturation magnetization, and small grains (not coupled magnetically to each other) Recently, CoCrPt-oxide-based material is used commonly as magnetic recording medium. This material exhibits coercivity of about H_c ~300 kA/m and anisotropy H_k ~1000 kA/m. The average diameter of the grains is around 8 nm.

Typical hard disk platter is manufactured as follows A disk from aluminum with several additions (magnesium silicon, copper, and iron to improve mechanical properties) is used as a substrate and its thickness is 0.635, 0.8, 1.0, 1.27, 1.5, or 1.8 mm. This aluminum platter is carefully polished to decrease the roughness to below 0.1 nm. Then an adhesion layer (typically NiP) is deposited and followed by a magnetically soft underlayer (e.g., amorphous CoTaZr- or NiFe-based alloys) CoCrPt:SiO₂ layer is typically used as a recording layer.

Recently longitudinal recording practically reached limit of its possibilities. According to “superparamagnetic limit” KV > 40 kBT (K is magnetic anisotropy and V is volume of a grain), which means that the grain cannot be smaller than about 8 nm. Below this value, there is a risk of unstable reading with the temperature fluctuations. This limit for longitudinal recording is about 130 Gbit/in ² and this value is recently demonstrated Further improvement of density recording, up to about 500 Gbit/in ², is possible in slightly more complicated perpendicular recording In this recording, the reading head is a “monopole” instead of “ring” (Figure 3.84) Also the recording medium should be modified. The anisotropy of the grains should be directed perpendicularly to the surface Moreover, additional soft magnetic underlayer should be applied to close the magnetic flux beneath the recording layer. It is estimated that in order to achieve the density 500 Gbit/in ², the recording medium should exhibit coerciv-ity of about 500 kA/m and the grain diameters should be about 6 nm (Piramanayagam 2007).

3.7.2  Ferrofluids and Magnetorheological Liquids

Magnetic liquids consist of small ferromagnetic or fer-rimagnetic particles (most often γFe₂O₃, Fe₃O₄, or Co) suspended in a carrier liquid (usually mixture of water and oil). There are two classes of these materials: mag-netorheological liquid with particle dimensions at the order of μm and ferrofluid with much smaller particles, typically of dimension around 10 nm.

In both cases, viscosity depends on external magnetic field, what can be used in lubricants, dampers, shock absorbers, etc From magnetic point of view, the two materials differ; the magnetorheological liquid behaves like a fluid ferromagnetic material but the ferrofluid with very small particles suspended by Brownian thermal motion is closer to a paramagnetic state Although we can assume the nanometer range particles as one-domain particles (thus elementary magnets) due to thermal movements, they are distributed randomly. This effect is known as superparamagnetism In the absence of magnetic field, the average resultant magnetization of ferrofluid is not observed but in the presence of magnetic field, it can be polarized magnetically according to Langevin law with susceptibility much higher than in classical paramagnetic materials.

Ferrofluids are commonly known from their fantastic geometrical effects in the presence of magnetic field (Figure 3.85) and are used in art (there are readily available clips on YouTube). But due to their unique features, they are used in many applications: their birefringence effect is employed in light polarizers, telescopes, antiradar systems, in medicine for improvement contrast in NMR method of tumor detection, as domain and magnetic field viewers. The magnetorheological liquids are commonly used in mechatronics and robotic devices.

At the end of this chapter devoted to special magnetic materials it is worth to say several words about extraordinary magnetic material known as Heusler alloy. The curiosity of this alloy discovered in 1903 by Heusler (Heusler 1903, 1912, Webster 1969) is that it is a ferromagnetic material although it is composed of non-magnetic elements, for example Cu₂MnSn, Cu₂MnAl, Pd₂MnAl. The ferromagnetic features are obtained due to special crystal structure of these alloys with double-exchange mechanism between neighboring ions Many years these materials were studied mainly by physicians but recently application in spintronics elements is strongly reported (Ishikawa 2006).