Ferrite Materials

Chapter 4

Ferrite Materials: Nano to Spintronics Regime R.K. Kotnala* and Jyoti Shah CSIR-National Physical Laboratory, New Delhi, India *Corresponding author: E-mail: [email protected], [email protected]

Chapter Outline 1. Introduction 1.1 Soft Ferrites 1.2 Hard Ferrites 2. Classification of Magnetic Materials 2.1 Susceptibility 2.2 Diamagnetism 2.3 Paramagnetism 2.4 Ferromagnetism 2.5 Antiferromagnetism 2.6 Ferrimagnetism 3. Magnetic Properties 3.1 Magnetic Moment 3.2 Domain Wall Energy 3.3 Magnetostatic or Demagnetization Energy 3.4 Magnetocrystalline Anisotropy 3.5 Coercivity 4. Types of Ferrite 4.1 Structure of Spinel Ferrites 4.2 Site Preference of Ions in Spinel Ferrites 4.3 Magnetic Interactions 4.4 Exchange Interactions

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5. Electrical Properties of Ferrite 5.1 Dielectric Properties 5.2 Resistivity of Ferrites 5.3 Power Loss in Ferrites 5.4 Electromagnetic Interference Shielding 5.5 Shielding Effectiveness 5.6 Absorption Loss 5.7 Reflection Loss 5.8 Multiple Reflections 6. Nanomagnetism 6.1 Single-Domain Theory: Superparamagnetism 6.2 Surface and Interface Effects 7. Spintronic Regime 7.1 Spin Dynamics 7.2 Ferromagnetic Resonance 7.3 Hall Effect 7.4 Anomalous Hall Effect 7.5 Spin Hall Effect 7.6 Multiferroics (Magnetoelectric) 8. Ferrites as Humidity/Gas Sensor

Handbook of Magnetic Materials, Volume 23. http://dx.doi.org/10.1016/B978-0-444-63528-0.00004-8 Copyright © 2015 Elsevier B.V. All rights reserved.

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292 Handbook of Magnetic Materials 9. Nanoparticles Synthesis Methods 9.1 SoleGel Method 9.2 Citrate-Gel (Modified SoleGel) Method 9.3 Coprecipitation Method 9.4 Microemulsion Method 9.5 Controlled Synthesis of Magnetic Nanocrystals in Shape and Size 10. Ferrite as Shielding Material 10.1 Barium Ferrite 10.2 Manganese Zinc Ferrite 10.3 Lithium Ferrite 10.4 Effect of Substituent and Additives on the Properties of Lithium Ferrite 10.4.1 Zinc, CadmiumSubstituted Lithium Ferrite 10.4.2 Aluminium, TitaniumSubstituted Lithium Ferrite 10.4.3 ManganeseSubstituted Lithium Ferrite 10.4.4 NickelSubstituted Lithium Ferrite 10.4.5 CobaltSubstituted Lithium Ferrite 10.5 Modification in Dielectric, Magnetic

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and Power Loss of Lithium Ferrite 10.6 Influence of Additives on the Properties of Lithium Ferrite 10.7 Influence of Nano-SiO2 on Li-Cd Ferrite 11. Magnesium Ferrite as Humidity Sensor 11.1 Linear Humidity Sensing by Ceria-Added MgFe2O4 11.2 Lithium-Substituted Magnesium Ferrite for Humidity Sensing 11.3 Significant Increase in Humidity Sensing of MgFe2O4 by Praseodymium Doping 11.4 Humidity Sensing Mechanism Exploration on Magnesium Ferrite by Heat Equation 11.5 Magnesium Ferrite Thin Films 11.6 CHR by Ceria-Added Magnesium Ferrite Thin Film by Pulsed Laser Deposition 12. Pervoskite Ferrite as Multiferroics 12.1 Bismuth Ferrite 12.2 Gadolinium Ferrite 13. Spin Pumping Induced SHE Acknowledgments References

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1. INTRODUCTION Ferrites are basically ferromagnetic oxide materials possessing high resistivity and permeability. Although the saturation magnetization of ferrite is less than half of ferromagnetic alloys, but they have advantages such as applicability at higher frequency, high resistivity, lower price, greater heat resistance, and higher corrosion resistance. Commercial application of ferrites boosted after 1950 in radio, television, carrier telephony, computer circuitry, and microwave devices. Despite of its huge application as a bulk material the origin of magnetism is a nanoscale phenomenon (Beringer and Heald, 1954). The development of magnetic nanocrystalline materials is a subject of concern, both for the scientific value of understanding the unique functional properties of materials and for the technological significance in enhancing the performance of existing materials (Arico` et al., 2005; Banerjee and Tyagi, 2011). To meet the demand of high-performance devices an important step is to synthesize ferrites in nanoscale form. Below the critical size these nanocrystals exist in a single-domain state so that the domain wall resonance is avoided and the material can work at higher frequencies (Rao et al., 2006). The growing interest is due to their chemical stability, biological compatibility, relative ease of preparation, and numerous applications associated with them. These ranges from thermal and mechanical applications as sealants, lubricants, coolants, microwave absorber, and magnetic data storage. Recent developments of bioconjugated magnetic nanoparticles have been demonstrated in a multitude of biomedical applications. For example, superparamagnetic iron oxide nanoparticles are coated with polymer as blood-pool contrast enhancement agents (Lee et al., 2006). Another common approach to biomodification of superparamagnetic iron oxide nanoparticles is to coat nanoparticles with dextran to increase the cell uptake (endocytosis) of nanoparticles and consequently enhance the cell imaging (Moore et al., 1997). A remarkable result of application of iron oxide nanoparticles in cancer diagnosis has been recently reported, in which the size of prostate cancer as small as 2 mm can be distinguishably identified in MRI scan by using superparamagnetic iron oxides as contrast enhancers compared with conventional MRI (Harisinghani et al., 2003). In addition, various other methods have also been reported in cancer and tumor diagnosis, gene expression, T-cell migration, DNA and cell purification, and sorting (Berry and Curtis, 2003; Chatterjee et al., 2001; Dodd et al., 2001; Gupta and Kotnala, 2012; Hoegemann et al., 2002; Pankhurst et al., 2003). A further application of magnetic nanoparticles is based on hyperthermia, which a medical treatment depends on locally heating tissue over 42
C for a short period of time to destroy the tissue, especially tumors. In hyperthermia, the heat is produced by the hysteresis of magnetic materials. For superparamagnetic particles, the hysteresis is typically lagging on the timescale of magnetic measurements. However, in a relatively high-frequency ac magnetic field, the magnetization lags behind the

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magnetic field, giving rise to a complex susceptibility. Thus, the magnetic energy will be dissipated as heat as a result of the out of phase and loss susceptibility (Rosensweig, 2002). Superparamagnetic particles with higher saturation magnetization and lower anisotropy would be an ideal hyperthermia system, if considering the limitations of injection dose and ac magnetic field strength that can be applied in hyperthermia treatments (Che et al., 2004; Dennis et al., 2009; Hashimoto and Hisano, 2011; Lee et al., 2007; Liu et al., 2008; Moser et al., 2002; Nacev et al., 2011). Particularly magnetite and maghemite (g-Fe2O3) nanoparticles are used for these applications as they are more biocompatible and more amenable to the buffered aqueous solution present in biological systems (Rastogi et al., 2011). The main reason behind ferrite applicability is the ease with which they can be detected and manipulated by the application of an external magnetic field. Magnetic response times are dependent on size strongly, thus introducing the possibility of synthesizing particles to yield application tailored response times. There are numerous applications for hard ferrite as well both at radio and microwave frequencies. On account of high initial permeability coupled with high saturation magnetization, ferrite finds an extensive application in radio communication and television industry in the radio frequency range. These ferrites have been used in deflection yoke core in CRT picture tube, antenna cores, also used as inductors, memory, switching devices, and transformers, and so on. At microwave frequency they are extensively used as isolators, circulators, gyrators, and phase shifters. Garnets like as Gd3Fe5O12, Yttrium Iron Garnet, and cubic ferrites MnZn ferrite, NiZn ferrite are used in microwave and other high-frequency devices (Gairola et al., 2010a,b). Now the era of multifunctional materials are gaining acceleration. An electric field-controlled magnetization that exhibit ferromagnetic and ferroelectric properties at the same time called multiferroic materials. The designation of multiferroics depends on nanoscale effects causing switchable domains. Multiferroics are an important topic of current research as multiferroic devices may be employed in future random access memories that combine the advantages of magnetic and ferroelectric random access memories. The only room temperature existing ferroelectric and antiferromagnetic compound is bismuth ferrite. However, it exhibits a high leakage current that has been suppressed by forming its composite with other ferroelectric compound (Bhattacharjee et al., 2009; Singh et al., 2008a,c; Verma and Kotnala, 2011). Its homogeneous atomic level mixing with ferroelectric compound by chemical synthesis leads to atomic origin of magneto electric coupling in nanocomposite (Gupta et al., 2013; Singh et al., 2008b, 2011). In composite multiferroic with ferroelectric compound, spinel ferrite has been the unanimous choice. From a technological point of view, electric fields are easy to implement on even very small length scales, power efficient, and fully switchable. The ability to reversibly switch the magnetization orientation by an electric field is thus considered a milestone on the way to new functional spintronic devices.

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Recent interest of researcher in the bulk ferrite is diminishing in the scenario of futuristic advanced material developments. Recently traditional magnetism of spinel ferrite ultimately leads to frontier area of spintronics. Ferrites like MnFe2O4, CoFe2O4 have been investigated as spin filter (Lukashev et al., 2013; Matzen et al., 2013). Even complicated magnetic structures of garnet ferrite have enormous potential in spin-based device applications (Uchida et al., 2013). Apart from magnetic property of ferrite, its nanoporous and microporous microstructure plays a key role in gas and humidity sensing properties. Microporosity increases the surface area and reactivity of the particles with vapors/gas molecules. MgFe2O4, ZnFe2O4, Fe3O4 are commonly used ferrites for gas sensing. Recently a colossal change in humidity sensing by MgFe2O4 thin film has been observed (Kotnala et al., 2013). The most important ferromagnetic substances apart from metals, iron, cobalt, nickel, and their alloys are metallic oxides of the spinel-type ferrites. 2 The basic formula of spinel ferrites is M2þFe3þ 2 O4 , where M is divalent 2þ 2þ 2þ 2þ 2þ metal ion such as Mn , Cd , Ni , Zn , Mg , Fe2þ, and so on. It is also possible for M to represent two types of unequal number, one trivalent, the other monovalent; or it may be represented by a mixture of trivalent ions and vacant sites (a defect structure), for example, lithium ferrite 2þ 2 ions, one can (Li1þFe3þ)1/2ðFe3þ 2 ÞO4 . By mixing two or more kinds of M formulate mixed ferrites to modify its physical properties according to desired applications. Lithium ferrite is a magnetic material of immense scientific and technological interest due to its relative high Curie temperature (Tc), high saturation magnetization (Ms), and low magnetic losses at higher frequencies besides its excellent chemical stability and high resistivity. In particular, mixed lithium ferrites are of much interest because of their application in microwave devices such as isolators, circulators, gyrators, and phase shifter. For broad technological applications, if further requires improvement, in its dielectric value, magnetic loss, resistivity, density, etc. Magnetic and electrical properties of ferrites are strongly dependent on material processing steps. Small amount of additives drastically affect the properties of ferrites (Gonchar et al., 2000). The magnetic properties of ferrites in general are determined by chemical composition, porosity, and grain size. Some of dopants can affect the grain boundary energy and therefore act as driving force for grain growth which in turn improves the microstructure. Among the different measurements of microstructure, grain size is one of the most important parameter affecting the magnetic properties of ferrites (Yan et al., 2007). Ferrites can be categorized into two classes on the basis of their magnetic coercivity: soft ferrites and hard ferrites.

1.1 Soft Ferrites Ferrites having low coercivity and low hysteresis losses are called as soft ferrites and a typical hysteresis curve is shown in Figure 4.1(a). Because of

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(b)

(a) M

M

H

H FIGURE 4.1 Typical M-H curves of (a) soft ferrite and (b) hard ferrite.

their comparatively low losses at high frequencies and high magnetization, they are extensively used in the cores of switched-mode power supply, RF transformers, and inductors (Bellad, 1999; Bellad et al., 1998; Radha and Ravinder, 1995). Manganese ferrite (MnFe2O4), Zinc ferrite (ZnFe2O4), Nickel ferrite (NiFe2O4), Copper ferrite (CuFe2O4), Lithium ferrite (Li0.5Fe2.5O4) are the some examples of soft ferrite.

1.2 Hard Ferrites The ferrites having comparatively high coercivity (2 kOe or higher) are called as hard ferrites. They are used in loudspeaker, automotive system, and so on, as permanent magnets (Charanjeet et al., 2008; Yang et al., 2009). Figure 4.1(b) shows a representative M-H loops of soft and hard ferrites. Barium ferrite (BaFe12O19) and cobalt ferrite (CoFe2O4) are some typical examples of hard ferrite.

2. CLASSIFICATION OF MAGNETIC MATERIALS 2.1 Susceptibility Susceptibility of a material is the extent to which any material is magnetized by applying magnetic field. The equation of susceptibility is defined as MfH

(4.1)

M ¼ cH

(4.2)

where M is the magnetization of the material, H is the applied magnetic field, and c is the susceptibility of the material. The behavior of inverse susceptibility with temperature for different magnetic materials has been shown in Figure 4.2.

2.2 Diamagnetism Materials which lack permanent magnetic dipole moment are called diamagnetic. It is induced by a change in the orbital motion of electrons with applied magnetic field. Diamagnetic material exposed to an external magnetic field, magnetic moment is induced in a direction opposite to that of an applied

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FIGURE 4.2 The inverse susceptibility varies with T for (a) paramagnetic, (b) ferromagnetic, (c) ferrimagnetic, and (d) antiferromagnetic materials, respectively.

H=0

H>0

FIGURE 4.3 The atomic dipole configuration for a diamagnetic material without and with applied magnetic field (H).

magnetic field. The magnitude of induced magnetic moment is extremely small. Since a negative magnetization is produced and thus the material characterized by a negative susceptibility (Lines and Glass, 1997). Figure 4.3 shows the schematic arrangement of magnetic nature of a diamagnetic material. Overall diamagnetism is the fundamental property of the materials, and it is found in all the materials; but it is so weak that it can be observed only when other types of magnetism are totally absent.

2.3 Paramagnetism Paramagnetic materials possess a permanent magnetic dipole moment due to incomplete cancellation of electron spin and orbital magnetic moment. In absence of applied field the dipole moments are oriented randomly and therefore the material has no net macroscopic magnetization. Figure 4.4 shows the schematic diagram of atomic dipole configuration for a paramagnetic material. In paramagnetic materials, localized magnetic moments are present but they do not exhibit net microscopic magnetization in the absence of applied field. There are two types of paramagnetism. In one, the magnetic moments are present at sufficiently low concentration so that they are well separated from each other, and their spins do not interact. In other one,

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H=0

H>0

FIGURE 4.4 The atomic dipole configuration for a paramagnetic material without and with applied magnetic field (H).

paramagnetism can also exist when there are interactions between the magnetic moment, but these interactions are so weak that there is no net magnetization when the applied field is zero. This type of paramagnetism occurs in ferromagnetic materials above their critical temperature (Hook and Hall, 1991). At low temperature, many paramagnetic materials possess a finite magnetization in absence of an applied field. This spontaneous magnetization is due to the alignment of permanent dipole moments below a critical temperature. The interaction between dipoles results in what is known as magnetic ordering. Paramagnetism is characterized by a positive susceptibility and its variation with temperature is shown in Figure 4.2.

2.4 Ferromagnetism In case of ferromagnetic materials, the dipolar interactions promote a parallel alignment of the magnetic dipole vectors, resulting in a material that has a net magnetization in the absence of an external magnetic field. Figure 4.5(a) shows the schematic diagram of atomic dipole configuration for ferromagnetic material. The total energy of a ferromagnetic material is the sum of contributions from exchange, magnetostatic, anisotropy, and Zeeman energy terms.

FIGURE 4.5 Varieties of magnetic orderings (a) ferromagnetic, (b) antiferromagnetic, and (c) ferrimagnetic.

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In a ferromagnetic material, quantum mechanical exchange interactions make the magnetic moments of neighboring atoms parallel, even in the absence of an external magnetic field. This coupling of the atomic moments allows material to have a large magnetization, or moment per unit volume. If the temperature is increased until the thermal energy is comparable with the exchange energy, long-range ferromagnetic ordering is lost. The temperature at which the spontaneous magnetization drops to zero is known as the Curie temperature of the material and follows the relation. c¼

C  Tc T

(4.3)

where “C ” is the Curie constant and Tc the Curie temperature of the material. The Curie temperature measurement of a material is used to determine the exchange stiffness (A) of the material (Koch, 2007): Aa (4.4) k where “a” is the nearest-neighbor separation between spins, and k is the Boltzmann constant. Short-range (<1 nm) exchange interactions dominate the nearest-neighbor couplings, but long-range magnetostatic interactions between moments in different locations within the ferromagnetic material are also important. In a ferromagnetic material, the overall energy is minimized by magnetic domain formation. While neighboring atomic moments are nearly parallel, the moments in general beyond 100 nm away are distributed randomly. The magnetostatic energy reduction through the formation of flux closure pathways exceeds the increase in energy due to domain walls, where neighboring atomic moments are not exactly parallel. The formation of the magnetic domains is energetically unfavorable below a critical size (nanoscale), which is different for each material. In this case, a material is classified as a single domain. In absence of an applied field, the direction of the moment is determined by anisotropy (k). At low temperature the moment would lie along a particular crystallographic direction called the easy axis. The magnitude of k is determined by the energy required to rotate magnetic moment away from the easy axis. Magnetocrystalline effects due to spineorbit coupling, as well as shape and stress contribute to the overall value of k. Orbital motion is highly dependent on orbital shape which is influenced by crystal field interaction. Cubic crystal structures tend to have lower values of magnetocrystalline anisotropy than those with tetragonal or hexagonal lattices, where the moment must rotate 180
between easy axis directions. The latter materials are said to be uniaxial, and are important for applications with a stable magnetization, such as permanent magnets or magnetic recording media. The behavior of a ferromagnetic material is often reported in terms of three technical parameters. The saturation magnetization (MS) is the magnetic moment per unit volume when all atomic moments are aligned parallel to an external applied field. After material Tc z

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saturation, if the field is reduced to zero there will be a remanent magnetization (Mr). To reduce the magnetization to zero, an applied field in the opposite direction equal to the coercivity (HC) must be applied. Together, these three parameters describe the basic features of a hysteresis loop, which is a plot of the magnetization between positive and negative saturation, and back again shown in Figure 4.6.

FIGURE 4.6 Typical hysteresis loops for ferromagnetic, paramagnetic, diamagnetic, and superparamagnetic materials illustrating saturation magnetization (Ms), remanent magnetization (Mr), and coercivity (Hc).

2.5 Antiferromagnetism It is a phenomenon exhibited by some materials in which complete magnetic moment cancellation occurs as a result of antiparallel coupling of adjacent atoms or ions. Figure 4.5(b) shows the schematic diagram of atomic dipole configuration for antiferromagnetic material. In a simple antiferromagnetic material, the atoms can be divided into two sublattices, where magnetic dipole moments are aligned antiparallel and is the cause of small magnetic susceptibility in these materials. A kind of ferrimagnetic behavior may be displayed in the antiferromagnetic phase, with the absolute value in one of the sublattice magnetizations differing from that of the other sublattice, resulting in a nonzero net magnetization. Antiferromagnetic substances are characterized by having a small positive susceptibility at all temperatures, but their susceptibilities vary in a peculiar way with temperature. As the temperature decreases, c increases and goes through a maximum at a critical temperature called the Neel temperature TN. The substance is paramagnetic above TN and antiferromagnetic below it (Cullity and Graham, 2009). The variation of inverse susceptibility as a function of temperature is shown in Figure 4.2.

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2.6 Ferrimagnetism A ferrimagnetic material is defined as one in which the magnetic dipole of the atoms on different sublattices are opposed as in antiferromagnetism but in ferrimagnetic materials, opposing moments are unequal and a spontaneous net magnetization remains. Figure 4.5(c) shows the schematic diagram of atomic dipole configuration for a ferrimagnetic material. The magnetic dipole moments in a ferrimagnetic material are divided into sublattices and are classified as subset of antiferromagnetic materials. Each sublattice can be treated as ferromagnetic material and the difference between the magnetic dipole moments for the sublattices results in the net magnetization for the ferrimagnetic materials. This happens when the sublattices consist of different materials or ions such as M2þ and M3þ in ferrites. Ferrimagnetic materials are like ferromagnets in that they hold a spontaneous magnetization below the Curie temperature, and show no magnetic order above this temperature that means showing paramagnetism. However, there is sometimes a temperature below the Curie temperature at which the two sublattices have equal moments, resulting in a net magnetic moment zero; this is called the magnetization compensation point. This compensation point is observed easily in garnets and rare earth-transition metal alloys. Furthermore, ferrimagnets may also exhibit an angular momentum compensation point at which the angular momentum of the magnetic sublattices is compensated. This compensation point is a decisive point for achieving highspeed magnetization reversal in magnetic memory devices (Stanciu et al., 2006). Below the magnetization compensation point, ferrimagnetic material is magnetic. At the compensation point, the magnetic components cancel each other and the total magnetic moment is zero. Ferrimagnetic materials have high resistivity and have anisotropic properties. The anisotropy is actually induced by an external applied magnetic field. When this applied field aligns with the magnetic dipoles it causes a net magnetic dipole moment and causes the magnetic dipoles to precess at a frequency controlled by the applied field, called Larmor precession frequency. The variation of inverse susceptibility as a function of temperature is shown in Figure 4.2.

3. MAGNETIC PROPERTIES 3.1 Magnetic Moment The magnetic properties of a matter are due to the electrons in atoms, which have a magnetic moment by means of electron motion. At the atomic level, there are fundamentally two types of electron motion, spin, and orbital with an associated a magnetic moment with it. The orbital motion of an electron around the nucleus can be equated to a current in a loop of wire having no resistance. The magnetic moment of an electron, due to this motion, is as mo ¼ ðarea of loopÞðcurrent in emuÞ

(4.5)

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According to Bohr’s theory (1913) of atom the electron moves with velocity v in the circular orbit of radius r. If e is the charge on the electron in esu and c the velocity of light, then e/c is the charge in emu. The current or charge passing a given point per unit time is then (e/c)(v/2pr). The orbital magnetic moment m0 is given.
ev  m0 ¼ spr 2 ¼ evr=2c (4.6) 2prc Since the angular momentum of electron must be integral multiple of h/2p, where h is Plank’s constant, hence mvr ¼ nh=2p

(4.7)

m0 ¼ eh=4pmc

(4.8)

combining the above relations

Similarly the spin contribution of electron gives the spin magnetic moment of electron. ms ¼ eh=4pmc

(4.9)

The magnetic moment due to spin and that due to motion in the Bohr orbit are exactly equal and thus magnetic moment is expressed in terms of Bohr magneton (mB) as   mB ¼ eh 4pmc ¼ 0:927  1020 erg Oe or 0:927  1024 Am2 (4.10) When a magnetic material is subjected to an external magnetic field (H) it gets magnetized. The magnetization (M) of a material is defined as the magnetic moment per unit volume (V). M ¼ m=V

(4.11)

The magnetic susceptibility (c) of a material is defined as c ¼ M=H

(4.12)

The magnetic induction (B) is related to the field intensity (H) as B ¼ mH

(4.13)

where m is characteristic of a medium and is known as magnetic permeability. The relative permeability is defined by the ratio of magnetic permeability to that of free space (Dekker, 1959). (4.14) mr ¼ m=m0 There are various forms of magnetism that arise depending on how the dipoles interact with each other on the application of an external magnetic field.

3.2 Domain Wall Energy The spontaneous magnetization of magnetic material produces demagnetization magnetic field due to dipole alignment at the edge. To minimize the

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demagnetization field magnetic domain are formed in the magnetic material. The spontaneous magnetization of each domain is opposite to the domain separated by high-energy domain walls. The energy of domain wall depends on increase or decrease in the width of the domain walls due to the growth or shrinkage of domains. The domain wall energy is equal to sum of the exchange and anisotropy energies and is given by sWall ¼ sex þ sK ¼

Zf h

i Aðdf=dxÞ2 þ gðfÞ dx

(4.15)

f

where g(f) ¼ Kusin2f for uniaxial anisotropy and g(f) ¼ K1sin2fcos2f for cubic anisotropy with magnetization confined to [100] direction and A ¼ nJS2/a is called the exchange stiffness or the exchange constant. Here n is the number of atoms per unit cell, and “a” is the lattice parameter. The exchange stiffness A has units of J/m or erg/cm, and is regarded as a macroscopic equivalent of the exchange energy J. The quantity represents the rate at which the direction of local magnetization rotates with position in the wall (Cullity and Graham, 2009).

3.3 Magnetostatic or Demagnetization Energy The magnetized material behaves like a magnet, with a surrounding magnetic field. This field acts to magnetize the material in the direction opposite from its own magnetization, causing a magnetostatic energy which depends on the shape of the material. This magnetostatic energy can be reduced by reducing the net external field through the formation of domains inside a material. The magnetostatic energy of the single-domain crystal per unit volume is given by 1 Ems ¼ Nd Ms2 2

(4.16)

where Nd is the demagnetizing factor. The value of Nd for a cubic crystal in a direction parallel to an edge is 4p/3 (cgs) or 1/3 (SI). Substituting these values in the above equation, the magnetostatic energy of the cubic crystal per unit area of its top surface is 2 1 Ems ¼ pMs2 L ðcgsÞ or Ms2 L ðSIÞ 3 6

(4.17)

where L is the thickness of domains in vertical direction. The magnetostatic energy of the multidomain cubic crystal, per unit area of the top surface is given by (Chikazumi, 1997) Ems ¼ 0:85MS2 D

(4.18)

where D is the thickness of the slab-like domains in horizontal direction, provided that D is small compared with L.

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The total energy is the sum of the magnetostatic and domain wall energies: E ¼ Ems þ EWall E¼

0:85MS2 D

L þs D

(4.19) (4.20)

where s is the domain wall energy per unit area of wall and is the domain wall area per unit volume of the top surface of the crystal. The minimum energy occurs when sL ¼0 D2 pffiffiffiffiffiffiffiffiffi E ¼ 2MS 0:85sL 0:85MS2 

(4.21) (4.22)

A further reduction in magnetostatic energy will result if the unlike poles on each end of the crystal are mixed more intimately.

3.4 Magnetocrystalline Anisotropy The magnitude of energy required to rotate the magnetic moment away from easy axis of magnetization is known as magnetic anisotropy. Permanent magnets need a high magnetic anisotropy to keep the magnetization in a desired direction. Soft magnets are characterized by a very low anisotropy, whereas materials with intermediate anisotropies are used as magnetic recording media. The simplest anisotropy energy expression in terms of q and f, for a magnet of volume V is expressed as Ea ¼ k1 VSin2 q ¼ k1 Cos2 q ¼ k1 s2z

(4.23)

This anisotropy is known as lowest order or second-order uniaxial anisotropy and k1 is the first uniaxial anisotropy constant. For k1 > 0 the easy magnetic direction is along the z-axis, which is called easy axis anisotropy, whereas k1 < 0 leads to easy plane anisotropy while easy magnetic direction is anywhere in the xey plane. For very low symmetry crystals, the first-order anisotropy energy is   (4.24) Ea ¼ k1 VSin2 q þ k10 VSin2 qCos 2f where k1 and k0 1 in general are of comparable magnitude. This expression is used for magnets having a low symmetry shape, such as ellipsoids with three unequal principal axes and for a variety of surface anisotropies, such as that of bcc (011) surfaces (Sander et al., 1996). By definition, there are only even-order anisotropy terms. Odd-order anisotropies may be caused by relativistic MoriyaeDzialoshinskii interactions, exchange biasing, or particular micromagnetic regimes (Moorjani and Coey, 1984; Skomski et al., 1998). This refers in particular to unidirectional anisotropies of the type kudCosq and is observed as a shift of the hysteresis loop.

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It is necessary to distinguish between magnetostatic effects and magnetocrystalline anisotropy with respect to the physical origin of anisotropy. It has been observed that magnetostatic interactions give rise to shape anisotropy. For homogeneously magnetized ellipsoids of revolution, the shape anisotropy is given by k1;sh ¼

m0 ð1  3DÞMs2 4

(4.25)

where D is the ellipsoid’s demagnetizing factor (D ¼ 0 for long cylinders, D ¼ 1/3 for spheres, and D ¼ 1 for plates). In noncubic crystals there is also a magnetostatic contribution associated with dipole interactions between neighboring atoms; such contribution is independent of the macroscopic shape of the magnet. The anisotropy of most of the materials reflects competition between electrostatic crystal field interaction and spineorbit coupling ll$s, where s and l are the spin and angular momentum operators, respectively, and l is the spineorbit coupling constant. This anisotropy contribution was first considered by Bloch and Gentile (1931) and is known as magnetocrystalline anisotropy. The crystal field reflects local symmetry of the crystal or surface and acts on the orbits of the inner shell d and f electrons. The shape and orientation of the charge density depends on the crystal field via spineorbit coupling on the spin orientation of the central atom. Changing the spin direction modifies the electron cloud of the central atom and changes the crystal field energy. This is the source of magnetocrystalline anisotropy. The magnitude of the anisotropy depends on the ratio of crystal field energy and spineorbit coupling. The spineorbit coupling is a relativistic effect, so that l is largest for inner electrons in heavy elements. In the case of 3d atoms, the spineorbit coupling l z 50 meV is much smaller than the crystal field energy E0  1 eV and the magnetic anisotropy can be obtained perturbatively. For uniaxial symmetry we have k1 z

l2 E0

(4.26) 2

Whereas the anisotropy of cubic materials scales as El 0 . In 3d oxides, E0 is essentially equal to the electrostatic crystal field splitting (Bloch and Gentile, 1931), whereas in itinerant magnets it is roughly given by the width of the d band. Rare earth 4f electrons are close to the atomic core and exhibit a strong spineorbit interaction. This leads to a rigid coupling between spin and orbital moment and magnetocrystalline anisotropy which is given by the comparatively small electrostatic interaction of unquenched 4f charge clouds with crystal field (Herbst, 1991). However, due to absence of quenching effects, the interaction with the crystal field is very effective and rare earth single-ion anisotropies are much larger than typical for the 3d case. It is exploited in advanced rare earth permanent magnets.

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A variant of magnetocrystalline anisotropy is magnetoelastic anisotropy, where crystal field contributions are changed or created by mechanical strain. The magnetoelastic contribution to the first anisotropy constant is 3ls s (4.27) 2 where s is uniaxial stress and ls is saturation magnetostriction. Another source of magnetocrystalline anisotropy is surfaces and interfaces of the material (Bland and Heinrich, 1994; Millev et al., 1998). The anisotropy is also observed to be dependent on temperature as Ea/kBT. The realization of room temperature anisotropy requires support of the interatomic exchange field which suppresses the switching of individual atomic spins into states with reduced anisotropy. k1;me ¼

3.5 Coercivity Coercivity value determines stability of the remanent state and gives rise to the classification of magnets into hard magnetic materials (permanent magnets), semi-hard materials (storage media), and soft magnetic materials. The coercivity of magnetic samples has a striking dependence on their grain size. As the grain size decreases, the coercivity increases to maximum and then decreases. The change in coercivity is attributed to its change from the multidomain nature to single-domain superparamagnetic state by further decrease in grain size results in an unstable state where spin fluctuations dominates. In the multidomain region where magnetization changes by domain wall motion, the variation of coercivity with grain size is expressed as HC ¼ a þ

b D

(4.28)

where “a” and “b” are constants and “D” is the diameter of the particle. Hence in the multidomain region the coercivity decreases as the particle diameter increases. Below the critical diameter DS, where magnetization changes by spin rotation, the coercivity decrease is attributed to thermal effects. As the grain size decreases HC decreases below a critical grain size as governed by the equation HC ¼ g þ

h D3=2

(4.29)

where “g” and “h” are constants. Below a critical diameter Dp the coercivity is zero. This is attributed again to thermal effects, which are now strong enough to spontaneously demagnetize a previously saturated assembly of particles. Such particles exhibit superparamagnetic behavior. A material will spontaneously break up into a number of domains to reduce the large magnetization energy if it is a single domain. The ratio of the energies before and after division into domains varied as OD, where D is the particle diameter. Thus for

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small D, the energy reduction takes place and it is obvious that for very small D, the material prefers to remain in the single-domain state.

4. TYPES OF FERRITE Ferrites crystallize into four crystal types: spinel, garnet, magnetoplumbite, and orthoferrites. The first two have a cubic structure; the magnetoplumbite has a hexagonal structure, while orthoferrites have pervoskite structure. Classification of different ferrites have been shown in Table 4.1. Spinel ferrites are a class of magnetic materials with ferric ions as the main component having formula M2þFe3þ 2 O4, where M is divalent metal ion such as Mn2þ, Ni2þ, Zn2þ, Cd2þ, Mg2þ, Fe2þ, and so on. By mixing two or more kinds of M2þ ions, one can formulate mixed ferrites to modify its physical properties according to the required applications. The most important characteristics of these materials possess very good magnetic properties, and very high D.C. resistivity (Laughton and Warne, 2002) unlike ferromagnetic metal and magnetic alloys (Rossiter, 1991). The spinel ferrites are applicable in a megahertz range due to their Snoek limitation. Although the bandwidth for hexaferrites is narrow, they could work very well in a gigahertz (GHz) range (Matsumoto and Miyata, 1996). Nanocomposites of exchange coupled soft and hard ferrite have been utilized for high-energy products for microwave absorption (Shen et al., 2012). That is why they are extensively used as core

TABLE 4.1 Classification of Ferrites Ferrites

Crystal Structure

Spinel

Cubic

M2þFe3þ 2 O4 M2þ ¼ Ni2þ, Mn2þ, Zn2þ, Mg2þ,Cu2þ ions or a combination of these ions

Garnet

Cubic

R3þFe3þ 5 O12 R ¼ Y3þ, Gd3þ

Hexaferrite

Hexagonal magnetoplumbite

AFe12O19 M-type W-type AM2Fe16O27 X-type AM2Fe23O46 A2M2Fe16O27 Y-type A3M2Fe24O41 Z-type A4M2Fe36O60 U-type M2þ ¼ Fe2þ, Ni2þ, Mn2þ, Zn2þ, Mg2þ ions or a combination of these ions

Orthoferrite

Orthorhombic perovskite

R3þFe3þO3 R3þ ¼ Gd3þ, Y3þ, Nd3þ, Sm3þ, Lu3þ

Composition

308 Handbook of Magnetic Materials

materials for inductances and transformers in telecommunication industry, audio and video recording heads, memory devices, digital systems, tapes, magnetic memory and spintronic devices, and so on.

4.1 Structure of Spinel Ferrites Spinel ferrites have a crystal structure that has the space group, Fd3m, consists of the eight formula units having 56 atoms; 32 are oxygen anions assuming a close-packed cubic structure and the remainders are metal cations residing on 8 of the 64 available tetrahedral (A) sites and 16 of the 32 available octahedral (B) sites. Figure 4.7 shows the unit cell of a spinel structure. The ionic positions are different in two octants sharing a face or a corner and the same in two octants sharing an edge. Thus, to give a complete picture, it is necessary only to show the positions of the ions in two adjacent octants. Here each octant contains four oxygen ions (large spheres) on the body diagonals and lying at the corners of a tetrahedron. The right-hand octant contains in the center a metal ion (small sphere, not shaded) surrounded by the tetrahedral of oxygen ions, this ion is said to occupy an A-site. The left-hand octant shows four metal ions (small shaded spheres) surrounded by an octahedron (one of which is shown) formed by six oxygen ions. There ions are said to occupy B-sites. Ferrites having M2þ in A-site (Tetrahedral) and Fe3þ in B-site (Octahedral) referred as normal spinel structure. Ferrites in which the divalent ions are on B-site and the trivalent ions are equally divided between A- and B-sites are

FIGURE 4.7 Crystal structure of a cubic ferrite.

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known as inverse spinel structure. The cation distributions on A- and B-sites in general are represented by  2þ 3þ  2þ 3þ 2 (4.30) Md Fe1d A M1d Fe1þd B O4 . where d ¼ 1 for normal spinel ferrites, d ¼ 0 for inverse spinel ferrites, and 1 < d > 0 for mixed spinel ferrites. The size and valence of the cation species determines the filling of these sites which in turn strongly influences the materials magnetic and electronic properties.

4.2 Site Preference of Ions in Spinel Ferrites The preference of sites by different ions in spinel ferrites basically depends mainly on the ionic radii of the specific ions, size of the interstices, and sintering temperature. The most important factor for site preference is relative size of the ion compared with the size of the lattice site. Generally, divalent ions are larger than the trivalent ions because the larger charge produces greater electrostatic attraction and so pulls the outer orbit inward. Hence in an inverse spinel structure the octahedral site is also larger than the tetrahedral site (Azadmanjiri, 2007; Fu, 2006) and vice versa in case of normal spinel structure. Most of the ferrite systems fall in the category of inverse spinel structure, therefore, it would be reasonable that the divalent ions would go into the octahedral site and trivalent ions would go into tetrahedral site. Two exceptions, viz. Zn and Cd, prefer tetrahedral sites because the electronic configuration is favourable for tetrahedral bonding to the oxygen ions (Ajmal and Maqsood, 2008; Yue, 2003) and these are classified as normal spinel structure. Distribution of divalent and trivalent ions between tetrahedral site and octahedral sites in spinel structure has been shown in Table 4.2.

4.3 Magnetic Interactions To study the origin of the magnetic behavior associated with spinel ferrites, mainly three types of magnetic interactions are possible between the metal ions at A- and B-sites through the intermediate O2 ion, that is, superexchange interaction. These are the jAeB, jBeB, and jAeA interactions. Figure 4.8 shows the schematic representation of superexchange interactions between two metal ions via an oxygen ion. The interactions between the moments of the two metal ions on different sites depend on the distances between these ions and oxygen ion that link them and also on the angle subtended (f) by the two metal ions at oxygen site. The direct exchange interaction between the two ions is negligible because of large distance between the ions. It has been established experimentally that these interaction energies are negative and hence induce an antiferromagnetic orientation when the d orbital of the metal ions are half filled or more than half filled, while a positive interaction accompanied by ferrimagnetism results when d orbital is less than half filled.

Magnetic Moment per Molecule in (mB)

Ferrites

Tetrahedral Site

Octahedral Site

Magnetic Moment of Tetrahedral Ions in (mB)

Fe3O4

Fe3þ

Fe2þ þ Fe3þ

5

4þ5

4

4.1

NiFe2O4

Fe3þ

Fe3þ þ Ni2þ

5

5þ2

2

2.3

Li0.5Fe2.5O4

Fe3þ

þ Fe3þ 1:5 þ Li0:5

5

7.5 þ 0

2.5

2.6

MgFe2O4

Fe3þ

Fe3þ þ Mg2þ

5

0þ5

0

1.1

CoFe2O4

Fe3þ

Fe3þ þ Co2þ

5

3þ5

3

3.7

Ionic Distribution

MnFe2O4 CuFe2O4 CdFe2O4 ZnFe2O4

3þ

Fe

3þ

Fe

2þ

Cd Zn

2þ

Magnetic Moment of Octahedral Ions in (mB)

Theoretical

Experimental

3þ

þ Mn

5

5þ5

5

4.6

3þ

þ Cu

5

1þ5

1

1.3

3þ

þ Fe

0

55

0

1

3þ

þ Fe

0

55

0

1

Fe Fe Fe Fe

2þ

2þ

3þ 3þ

310 Handbook of Magnetic Materials

TABLE 4.2 Structural Ionic Distribution and Magnetic Moment of Some Ferrites

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FIGURE 4.8 Schematic of representation of super exchange interaction of A and B sublattice cations via oxygen.




The exchange energy is having its maximum value at an angle of 180 and it decreases rapidly with increasing bond distance. Experiments have shown that the values of bond length are smaller and the values of bond angle are
fairly high (w180 ) for AeB interaction, which makes it the strongest interaction among the three interactions. The BeB interaction (bond length is too large for the effective interaction) is weak interaction as compared with the AeB interaction, while the AeA interaction is the weakest of all the in
teractions for which f w 80 (Gorter, 1954; Nakamura and Miyamoto, 2003). Since, in case of inverse spinel ferrites the metal ions in the sublattice A are antiparallel with respect to metal ions in the sublattice B. The net magnetic moment of the material is the difference in magnetic moments of sublattices A and B, it explains why the magnetic moment per formula unit was lower than the expected value. To explain the magnetic properties of spinel ferrites quantitatively, it is necessary to know what sort of ions are involved and which ion occupies which site.

4.4 Exchange Interactions The magnetic moment and the spontaneous magnetization are realized by the exchange interaction between electrons. In a simple two-electron picture, exchange gives rise to [[ (ferromagnetic) or [Y (antiferromagnetic) coupling between spins. There are two main types of exchange interactions. First, atomic moments are determined by intraatomic exchange interactions. For example, ferric iron has six 3d electrons and intraatomic exchange interaction yields the schematic spin states [[[[[Y. Second, there is an interatomic exchange interaction between neighboring magnetic atoms. Interatomic exchange interaction yields, for example, the long-range magnetic order observed in ferromagnets, ensures finite temperature magnetocrystalline anisotropy, and is of importance in micromagnetism. Exchange interaction is an electrostatic many-body effect, caused by 1/ jrer0 j Coulomb interactions between electrons located at r and r0. Physically,

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[Y electron pairs in an atomic orbital are allowed by the Pauli principle but unfavorable from the point of view of Coulomb repulsion. Parallel spin alignment ([[) means that the two electrons are in different orbitals, which is electrostatically favorable. However, the corresponding gain in Coulomb energy competes against an increase in one-electron energies: only one electron benefits from the low ground-state energy and the second electron must occupy an excited one electron level. In agreement with Hund’s rule, intratomic exchange favors parallel spin alignment. The sign of the interatomic exchange is more difficult to predict. In case of two electrons and two atomic sites, lowest order perturbation theory yields (Skomski and Coey, 1999).   (4.31) Jeff ¼ JD þ U 4  OT 2 U 2 16 where U is the energy necessary to add a second electron into an atomic orbital (Coulomb energy), T denotes the interatomic hopping integral, and JD is the direct exchange integral. The direct exchange integral is always positive, but for typical solid-state interatomic distances it is not larger than about 0.1 eV, that is smaller than U by at least one order of magnitude. On the other hand, hopping reduces the effective exchange interaction, making Jeff less ferromagnetic. In oxides, T << U and hence  Jeff ¼ JD  2T 2 U (4.32) Due to the smallness of the direct exchange interactions, oxides are often antiferromagnets. A widely used approach to discuss interatomic exchange is s 1 and b s2, the Heisenberg interactiondJbs $bs between neighboring spins b 1 2 where J is some effective exchange integral. The indirect exchange is described in a theory by RudermaneKitteleKasuyaeYosida (RKKY) which s 2 is given by finds that the coupling between b s 1 and b
.  2 s 1 $b s2 (4.33) 2mkF4 p3 F0 ð2kF R12 Þb J12 ¼ Jsd where F0(x) ¼ cos(x)/x3 þ sin(x)/x4, and Jsd is the indirect exchange coupling constant, m is the electron mass, kF is the Fermi-wave vector, R12 is the distance s 2 (Ashcroft and Mermin, 1976). The between the localized spins b s 1 and b function F0(x) shows that for short distances the coupling is ferromagnetic, however it reverses sign and oscillates as the distance increases. These RKKY oscillations in the exchange coupling are important for the magnetic properties of surfaces and small particles. Interatomic exchange competes not only with finite temperature disorder but also with micromagnetic magnetization inhomogenities, like in domains. On a continuum level, the Heisenberg exchange translates into the energy density Ad VM 2 =Ms2, where Ad is the exchange stiffness. For typical ferromagnets Ad is of the order of 1011 J/m. The macroscopic behavior of a magnetic material also depends on the spatial direction in which it is measured. Such a phenomenon is called

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magnetic anisotropy. The brief descriptions of various types of magnetic anisotropies responsible for the magnetic properties of magnetic nanomaterials are outlined here.

5. ELECTRICAL PROPERTIES OF FERRITE 5.1 Dielectric Properties Most ionic solids and molecular solids are insulators because of the negligible concentration of conduction electrons or holes. Electrical insulators are also known as dielectrics. Consider two conductor plates connected to the two ends of a battery of voltage V as shown in Figure 4.9. Assuming the potential between the two metal plates is V and the medium between the plates is a vacuum. There are a lot of conduction electrons in the metal plates and metal wires. The positive end of the battery attracts conduction electrons, making the left plate positively charged. The negative end of the battery repels conduction electrons rendering the right plate negatively charged. Let the area of each plate be A. The magnitude of charge per unit area of each plate is known as the charge density (D0). D0 ¼ Q=A

(4.34)

The electric field E between the plates is given by E ¼ V=d

(4.35)

where d is the separation between the plates. When E ¼ 0, D0 ¼ 0. In fact, D is proportional to E. Let the proportionality constant be ε0. Then D 0 ¼ ε0 E ε0 is called the permittivity of free space (8.854  10 equation represents the Gauss law.

(4.36) 12

F/m) and this

FIGURE 4.9 A pair of positively and negatively charged conductor plates in vacuum.

314 Handbook of Magnetic Materials

Just as D0 is proportional to E, Q is proportional to V. The plot of Q versus V is a straight line through the origin as shown in Figure 4.10, with Slope ¼ C0 ¼

Q ε0 EA ¼ ¼ ε0 A=d V Ed

(4.37)

C0 is known as the capacitance in Coulomb/Volt or Farad (F). Consider that the medium between the two plates is not a vacuum, but an insulator whose center of positive charge and center of negative charge coincide at zero voltage. But, when V > 0, the center of positive charge is shifted toward the negative plate and the center of negative charge is shifted toward the positive plate. Such displacement of the centers of positive and negative charges is known as polarization. In case of a molecular solid with polarized molecules the polarization in the molecular solid is due to the preferred orientation of each molecule such that the positive end of the molecule is closer to the negative plate. In case of an ionic solid, the polarization is due to slight movement of the cations toward the negative plate and that of the anions toward positive plate. For an atomic solid the polarization is due to the skewing of electron clouds toward positive plate. When polarization occurs the center of positive charge attracts more electrons toward the negative plate causing charge on the negative plate to be εrQ, where εr > 1. Similarly, the center of negative charge repels more electrons away from the positive plate causing the charge on the positive plate to be εrQ. εr is a unit-less number called the relative dielectric constant. When an insulator is kept between the plates, the charge density is given by Dm ¼ εr D0 ¼ εr Q=A

(4.38)

Dm ¼ εr ε0 E ¼ εE

(4.39)

or where ε ¼ εrε0 is known as dielectric constant. When an insulator is kept between the plates, capacitance is given by Cm ¼

εr Q εr ε0 EA εr ε0 A ¼ ¼ ¼ εr C 0 V Ed d

(4.40)

From this equation capacitance is inversely proportional to d, so capacitance measurement provides a way to detect changes in d, that is, to sense strain.

FIGURE 4.10 Plot of charge Q versus potential V.

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Ferrites are the materials having properties like mechanical, magnetic, dielectric, and optical properties that need consideration. The dielectric properties of ferrites are equally important as magnetic properties due to duality of complex permeability and complex permittivity. There are many studies regarding the magnetic properties of ferrites, but their studies on dielectric properties are rare. Dielectric materials usually exhibit a very high resistance. Dielectric material is distinctly different from the electrical conductor which provides the path for free charges moving inside its body with applied voltage or field. However, dielectric materials do not provide path for electrical charges to pass through, when an electric field is applied on it. But a phenomenon called Polarization will occur inside the body in which bonded charge particles align with applied electric field (Batoo et al., 2009; Dekker, 1959). This alignment of the bonded charge particles will produce additional electric field to compensate the applied electric field. The fundamental basis of phenomena is interaction of dielectric material with applied electric field and this interaction could be characterized by dielectric constant. When a ferrite material is subjected to an applied electric field there are not many free carriers and ferrite behaves as an insulator with high resistance. Since there are six electrons in the 3d shell of Fe2þ and among them one may transfer to the “s” orbit of the next shell and hence become free electron that contributes toward conduction. These moving free carriers will contribute to the leakage current and consume the electric energy which can be termed as loss tangent of power consumption. For ideal capacitor when an alternative electric field is applied the electrical energy is stored as potential energy through charge accumulation at the surface in positive half cycle and charge accumulated is discharged to give off energy in the negative half cycle, hence no energy dissipated within the dielectric materials. While an electric field is applied to the ferrites, there are few phenomena happen from atomic to the macroscopic level. At the atomic level, through atomic polarization, the center of positive nuclei and negative electron clouds are away from the original position with a small displacement. In ferrites, the ionic polarization occurs at the molecular level that will displace the cation and anion sublattices. The ferrite crystal may polarize and become bipolar under an electric field. The polarized charges or some free charges accumulate at the boundary and restrict movement of the charges moving inside the grains. All these phenomena contribute toward the dielectric properties of the ferrites. The ability of a dielectric to withstand electric fields without losing its insulating properties (a point known as dielectric breakdown) is its dielectric strength. A good dielectric must return a large percentage of the energy stored in it when the field is reversed. Dielectrics exhibiting high dielectric constants at high frequencies, high dielectric strengths, and with low loss tangents are desirable for many applications (Ravinder and Reddy, 2003). The dielectric constant and loss tangent may have different characteristics at different

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frequency, which could be characterized by the impedance spectroscopy. Impedance spectroscopy is a classical method for studying the frequency response of dielectric materials. Since, it is difficult to construct a model to describe the dielectric properties of ferrites at all levels. Impedance spectroscopy is ideal for investigating the electrical response of dielectric materials as a function of frequency. It can be used to study impedance behavior of a material and be analyzed based on an idealized circuit model with discrete electrical components. The analysis is mainly accomplished by fitting the impedance data to an equivalent circuit which is representative of the material under investigation. The impedance analysis allows separation of several contributions of total impedance arising from the bulk conductance and interfacial phenomenon, viz. grain, grain boundary, and other electrode interface effects (Kingery et al., 1976).

5.2 Resistivity of Ferrites The resistivity of ferrites is very important in technology aspects. Ferrite materials resistivity usually depends on the composition, microstructure, preparation method, and sintering conditions. Ferrites are known to have semiconducting properties though their conduction mechanism is different. Electrical conduction in ferrites, in general, can be explained by the Verwey mechanism of electron hopping between cations with two different valence states distributed randomly on equivalent lattice sites (Verwey and De Boer, 1936). According to this model, ferrites are known to form a close-packed oxygen lattice with metal ions situated at the tetrahedral sites (A-sites) and octahedral sites (B-sites). These cations can be well treated as isolated from each other, to a first approximation. The conduction is due to electronic exchange between the Fe2þ and Fe3þ ions occupying the B-sites (Kothari et al., 1990). The formation of Fe2þ ions during sintering at high temperature preferably occupies the B-sites (Devi et al., 2000). AeA electronic hopping does not take place. Since AeB distance is larger than the BeB distance, the dominant mode of conduction therefore is the BeB electronic hopping between Fe2þ and Fe3þ ions. Ferrites as semiconductors, their resistivity decreases with increasing temperature according to the relation r ¼ r0 eEa =kT

(4.41)

Taking natural logarithms on both sides we have lnr ¼ lnr0 þ Ea =kT

(4.42)

where r is resistivity, k is Boltzmann constant, T is absolute temperature, and Ea is activation energy required for hopping of an electron from one lattice site to another. In case of ferrites, the activation energy is often associated with the mobility of charge carriers rather than their concentration. The charge carriers

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are considered as localized at the ions or vacant sites and conduction occurs via hopping-type process, which implies a thermally activated electronic mobility. According to the band theory, the temperature dependence of conductivity is mainly due to variation in charge carrier concentration with temperature, while in the hopping model, change in their mobility with temperature is considered to lead the conduction current by jumping or hopping from one iron ion to the next. Thus conduction in ferrites increases with temperature and consequently the resistivity falls with increasing temperature. Resistivity of ferrites at room temperature can vary from 102 to higher than 1010 U-cm (Hendricks et al., 1991). To obtain samples with a high resistivity it is necessary to ensure that there are no ferrous ions in the stoichiometric ferrite. The change in the resistivity is brought about by substitution of some appropriate metal ions in the metal site. Another way of increasing the resistivity is to use SiO2, Bi2O3, and CaO, and so on, additives that diffuse toward grain boundaries during the cooling part of the sintering process and create a high-resistive insulating layer in the grain boundary region (Liu and He, 2008).

5.3 Power Loss in Ferrites The demand is increasing for smaller and more efficient switching power supplies in keeping with the advancement of more compact and more power saving electronic equipments. Now, the driving frequency of power supplies has been raised from kHz to about 1 MHz and thus, there is an urgent need for the reduction of power losses of ferrites in this high-frequency range (Beatrice et al., 2006; Jeong et al., 2002). Power loss (PC) as a function of frequency (f) and magnetic flux density (B) can be expressed as PC ¼ kBx f y

(4.43)

where x and y are called Steinmetz coefficients (Snelling, 1988). Theoretically, the power loss in ferrites is generally split up into three contributions with quite different physical origins (Inoue et al., 1993; Stoppels, 1996):  (4.44) PC ¼ Ph þ Pe þ Pr ¼ CH B3 f þ CE B2 f 2 r þ Pr where PC is the total power loss, Ph, Pe, and Pr are the hysteresis loss, eddy current loss, and residual loss, respectively. CH and CE are constants, B is magnetic flux density, f is frequency, and r is electrical resistivity (Stoppels, 1996; van der Zaag, 1999). The relative importance of the different loss contributions to the total loss PC depends on frequency and on induction level. Pc corresponds to the dissipation already present in the DC measurement and is considered to be caused by hindrances in domain wall movement when irreversible jumps of domain walls occur between pinning points, such as grain boundaries, internal pores, or inclusions. Hysteresis losses can be minimized, if one reduces

318 Handbook of Magnetic Materials

hindrances to domain wall movements by reducing their concentration and their individual influence. This requires a low-volume fraction of pores, impurities, and dislocations, and also a low level of stresses, small magnetocrystalline anisotropy, small magnetostriction, and high saturation magnetization are also necessary. Uniform grain growth and low porosity are also desired properties to reduce hysteresis loss. Hence, hysteresis loss can be minimized by selecting an appropriate composition and modifying the microstructure of the ferrite. In ferrites, the magnetocrystalline anisotropy can be described as the sum of two contributions, one from Fe2þ ion with a large positive contribution and the other from the host with a negative one. It is characterized by the compensation temperature Tmin, at which anisotropy passes through zero. It coincides with the secondary maximum temperature of the magnetic permeability versus temperature and also with the temperature where power losses exhibit a minimum. In addition, compositions having a low magnetostriction constant are usually taken. As per the microstructure is concerned, the inner part of the grains should be homogeneous and free of impurities, pores, and other defects. The eddy current loss (Pe) becomes an important factor as the ferrite is used at higher frequencies. Eddy current losses become too high at higher frequencies reducing the performance considerably. It can be reduced by providing a high electrical resistivity. The resistivity of polycrystalline ferrites can be increased by increasing the grain boundary resistivity either by careful control of the processing conditions or by adding glass phase forming dopants and to increase the resistivity inside the grains. The electrical conductivity in ferrite has been attributed to electron hopping between the two valence states of iron, at crystallographically equivalent sites. Maintaining the þ3 valence state of octahedral Fe ions is thus a prerequisite for achieving high resistivity. There are types of additions increasing the electrical resistivity of grain boundary and multivalent ions can increase grain resistivity. At higher frequencies, perhaps the most widely practiced method of suppressing Pe is the use of composite CaOeSiO2 additives that diffuse toward the grain boundaries and create a high-resistive insulating layer in the grain boundary region. A way to increase resistivity inside the grains is to substitute multivalent ions in spinel lattice of the ferrite. They may form pairs with Fe2þ ions and thus may reduce electron hopping. Residual loss (Pr) plays an important role in reducing power loss in the MHz range as it claims over 80% of the total core loss at frequencies above 500 kHz (Otobe et al., 1999). Residual loss (Pr) is associated with magnetic relaxations and resonances in the ferrite. Magnetic relaxations contributing to these losses are due to domain wall excitations by the driving ac magnetic field. Magnetic resonance may occur in two ways, viz. as rotational resonance and as domain wall resonance. To reduce Pr, the complex permeability has to be made to peak at the frequency as high as possible, and this can be

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achieved by using fine-grained ferrites (Shokrollahi, 2008) Small grains can be realized by using finer powders, enabling sintering at lower temperatures during shorter periods. Also applying sinter acids, such as Bi2O3, may lower the sintering temperature and thus yield small grains. Because of their low melting point, these oxides melt at grain boundaries and initially act as a grain growth inhibitor, but special attention should then be paid to homogeneous distribution of the additives, otherwise secondary grain growth may deteriorate the ferrite.

5.4 Electromagnetic Interference Shielding Electromagnetic interference (EMI) shielding refers to the reflection and adsorption of electromagnetic radiation by a material that acts as a shield against its penetration. Therefore, it limits the amount of electromagnetic radiation from the external environment that can penetrate the circuit and contrary, it influences how much EMI energy generated by the circuit can escape into the external environment. As we know that electromagnetic radiation consists of coupled electric and magnetic fields. As the electric field is applied to the surface of an ideal conductor, displacement of charge inside the conductor takes place due to the induced current that cancels the applied field inside, at which point the current stops (Bridges, 1988; Shokrollahi, 2008). In the same way magnetic fields generate eddy currents that act to cancel the applied magnetic field (Duffin, 1968). The result is that electromagnetic radiation is reflected from the surface of the conductor and hence internal fields reside inside and external fields reside outside. The effectiveness of a shield as being the ratio of the magnitude of the electric or magnetic field that is incident on the barrier to the magnitude of the electric or magnetic field that is transmitted through the barrier.

5.5 Shielding Effectiveness The effectiveness of a shield and its resulting EMI attenuation are based on the frequency, the distance of shield from the source, the thickness of the shield, and the shield material. Shielding effectiveness (SE) is normally expressed in decibels (dB) as a function of the logarithm of the ratio of the incident and transmitted electric (E), magnetic (H), or plane-wave field (F) intensities as SE (dB) ¼ 20logEi/Et or SE (dB) ¼ 20logHi/Ht or SE (dB) ¼ 20logFi/Ft, respectively. With any kind of EMI, there are three mechanisms contributing to the effectiveness of a shield. Part of the incident radiation is reflected from the front surface of the shield, part is absorbed within the shield material, and part is reflected from the shield near surface to the front where it can aid or hinder the effectiveness of the shield depending on its phase relationship with the incident wave as shown in Figure 4.11.

320 Handbook of Magnetic Materials

FIGURE 4.11 Graphical representation of electromagnetic interference (EMI) shielding.

Hence, the total SE of a shielding material equals the sum of the absorption loss (SEA), the reflection factor (SER), and the correction factor to account for multiple reflections (SEM) in thin shields. SE ¼ SEA þ SER þ SEM

(4.45)

The multiple reflection factor (SEM) can be neglected if the absorption loss (SEA) is greater than 10 dB (Ohlan et al., 2010; Ott, 1988; Paul, 2004; Schulz et al., 1988).

5.6 Absorption Loss SEA is a function of the physical characteristics of the shield and is independent of the type of source field. The amplitude of an electromagnetic wave decreases exponentially when it passes through a medium. This decay or absorption loss occurs because currents induced in the medium produce Ohmic losses and material heating (Singh et al., 2010). The SEA in decibel is given by the expression



 pffiffiffiffiffiffiffiffi t t log e ¼ 8:69 ¼ 131:t f ms (4.46) SEA ¼ 20 d d where t is thickness of the shield in mm, f is frequency in MHz, m is relative permeability, s is conductivity relative to copper, and d is skin depth of the material. Skin effect is especially important at low frequencies, where the fields experienced are more likely to be predominantly magnetic with lower wave impedance. From the absorption loss point of view, a good material for a shield should have high conductivity and permeability and sufficient thickness to achieve the required number of skin depths at the lowest frequency of concern. Thus from the above it is clear that absorption loss is highly dependent on the thickness and magnetic properties of the shield.

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5.7 Reflection Loss Energy reflection occurs when electromagnetic waves encounters a material. Reflection can occur from both the front and back surfaces and within the material which is independent of the material thickness. The reflection loss is related to the relative mismatch between the incident wave and the surface impedance of the shield. The reflection loss for electric, magnetic, and plane waves are given by the expressions    (4.47) RE ¼ K1 10 log s f 3 r 2 m  2   (4.48) RH ¼ K2 10 log fr s m RP ¼ K3 10 logðf m=sÞ

(4.49)

where RE, RH, and RP are reflection losses for the electric, magnetic, and plane wave fields, respectively, s is the conductivity relative to copper, f is the frequency in MHz, m is the relative permeability, and r is the distance from the source to the shield in meter.

5.8 Multiple Reflections The multiple reflection factor (SEM) can be either positive or negative and becomes insignificant when the absorption loss SEA > 10 dB. It is important when the frequency applied are low (i.e., approximately below 20 kHz) and metals used are thin. The multiple reflection factor (SEM) is given by the expression
 (4.50) SEM ¼ 20 log 1  e2t=d

6. NANOMAGNETISM For a long time, focus has been on naturally occurring magnetic materials, such as iron and magnetite. In the past few decades, there has been a revolution in the development of magnetic materials. On one hand, atomic scale quantum-mechanical and relativistic effects have been exploited to create high-performance magnetic materials, such as the alloys, which are used to produce permanent magnets. On the other hand, geometrically well-defined nanostructures such as multilayers, particle arrays, and bulk composites are now actively explored and used to fabricate magnetic materials for a wide range of applications (Baibich et al., 1988; Comstock, 1999; Sellmyer et al., 2002; Skomski and Coey, 1993; Weller et al., 2000; Wood, 2000). When an object becomes so small that the number of surface atoms is a sizable fraction of the total number of atoms then obviously surface effects will be important. In general, a property will depend on the size of an object if its size is

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comparable with a dimension which is relevant to that property. In the simplest case above, the parameter is the ratio of the atomic radius to the size of the object (which approximately equals to the surface to bulk atomic ratio). However there are many other length scales that are relevant depending on the physical property under investigation. In magnetism, for example, a typical size of a magnetic domain is of the order of 1 mm and particles much smaller than that will be single domain. Another scale involves exchange coupling effects, which affects the magnetic polarization of neighboring ferromagnetic particles in nonmagnetic hosts, have a range of the order of several nanometers (Barbara, 1996; Hernando, 1993) It is important to realize that the “nano” in magnetism is not uniquely defined. For researcher active in nanomagnetism, nano does not signify nanometer scale, but rather submicron or merely small. Bulk magnetic materials arrange in magnetic domains which are of this small size scale and consequently all magnetic systems can be considered to be “nanostructured”. While interest in many systems on the nanoscopic scale is academic to a great extent, small magnetic particles have been of industrial importance since the 1950s primarily stimulated by the recording industry’s desire for ever denser and more reliable recording media. The quest for smaller particles which can be used for recording purposes (Mee, 1994) continues since a smaller particle implies higher data storage densities (Lambeth et al., 1996). There are of course material limits to how small a magnetic particle can be and still be useful. For example, not only should the particle be ferromagnetic but it should retain its magnetic orientation in ordinary conditions for many years. New magnetic materials are also used for reading and recording magnetically encoded information. Recently, it has been found that nanocomposites composed of ferromagnetic particles embedded in noble metal matrices exhibit giant magnetoresistance effects related to those found in magnetic/ nonmagnetic super lattices (Meservey and Tedtrow, 1994). These new materials are important for magnetic sensors: giant magnetoresistance reading heads are used to read magnetically stored data. Magnetic nanostructures are also important class of materials of investigations for basic materials research. Magnetic systems have complex electronic structures (Crangle, 1991; Mattis, 1985) and consequently it is a computational challenge to determine even the ground state of the smallest of ferromagnetic particles (i.e., clusters of only a few atoms) from first principles. The complications mainly arise because the electronic spin (which is the carrier of the magnetic moment) clearly cannot be ignored as it can be in more simple metallic systems (de-Heer, 1993). To bypass these complications, numerous approximations have been devised which highlight specific aspect of magnetic response; however, approximations usually compromise predictive power (Crangle, 1991). Many interesting magnetic properties are related to the dynamics of the spin system (Crangle, 1991; Mattis, 1985). At low temperatures, the magnetic moment (or total electronic spin) of the system may spontaneously change

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direction in a quantum tunneling process (Sangregorio et al., 1997). At higher temperatures, the spin direction will fluctuate due to thermal agitation (Bean and Livingston, 1958). At the same time the magnitude of the magnetic moment will reduce, and eventually vanish at high enough temperatures (at the Curie temperature). These processes are well known and reasonably well understood; however spin dynamics in magnetic systems is still a topic of great theoretical interest and controversy (Crangle, 1991; Mattis, 1985). Owing to the extremely small dimensions of nanostructure materials, a major portion of the atoms lie at the grain boundaries, this in turn is responsible for superior magnetic, dielectric, and mechanical properties in these materials compared with their conventional coarse-grained counterparts. Nanometer magnetic particles exhibit specific properties such as superparamagnetism and spin-glass like behavior, generally attributed to the cation disorder and surface effects (Nathani and Misra, 2004). A better understanding of magnetism in such particles is crucial not only for basic physics but also because of the technological applications in information storage and medicine. Superparamagnetism can improve the efficiency of systems that are subjected to rapidly alternating ac magnetic fields like transformers and rotating electrical machinery. In a traditional magnet, exposed to an ac magnetic field, the magnetic field cycles through its hysteresis loop often causing a loss of efficiency and a rise in temperature. This rise in temperature is due to the frictional heating that occurs when magnetic domains are varying their orientation. The amount of energy loss in each cycle is proportional to the area enclosed by the loop, so a small or nonexistent coercivity is desirable. It has also been shown that particle size has a large effect on microwave absorption. Particles of nanometer size greatly improve the absorptive efficiency and broaden the bandwidth (Kittle, 1996).

6.1 Single-Domain Theory: Superparamagnetism The concept of a magnetic domain was first postulated by Frenkel and Dorfman (1930). It is well known that a bulk magnetic material is composed of magnetic domains. The magnetization inside each domain is uniform, but varies from domain to domain as they are separated by an interfacial layer known as the domain wall. Below a critical size, it is not energetically favorable to form a domain wall and the particle is said to be monodomain. The maximum monodomain size Rcr is predicted using the relation . 1 (4.51) Rcr ¼ 72ðAkÞ2 Ms2 In spherical particles, it ranges from w20 nm to several hundred nanometers. As particles are reduced in size relative to the bulk, the coercivity increases reaching the maximum value at Rcr (Luborsky, 1961) and then further decreases. There have been numerous studies of size-dependent magnetic properties in monodomain particles (DaSilva et al., 2011;

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Farrell et al., 2003; Kachkachi et al., 2000; Kumar et al., 2010a,b,c; Sivakumar et al., 2006; Thakur et al., 2009a,b). In the absence of an applied magnetic field a bulk ferromagnet may have no net magnetization, since the contributions from different domains will cancel. However, a monodomain particle will always act as a giant moment. In the StonereWohlfarth model for an ellipsoidal monodomain particle of a uniaxial material, all spins within the particle are aligned and magnetization reversal occurs by coherent rotation (Stoner and Wohlfarth, 1948; Kneller, 1969). Here the atomic spins remain parallel as they rotate to a new magnetic moment direction. The energy of an isolated monodomain particle with volume V is the sum of the anisotropy and Zeeman energy terms as   (4.52) Ept ¼ kVSin2 q  Ms HVCos f  q Here q is the angle between the particle magnetic moment, which has a magnitude and the easy axis and f is the angle between the easy axis and the applied field H. When the particles are free to rotate, the anisotropy and Zeeman terms can be minimized simultaneously and for fixed size particles, the moment direction is determined by the competition between the interactions and by the significance of thermal fluctuations. The net magnetization of an ensemble of identical, noninteracting, uniaxial particles can be predicted in terms of an energy barrier model. Suppose the field is applied parallel to the easy axis direction, so that f ¼ 0. Figure 4.12 shows that the energy minima occur when q ¼ 0
and 180
and that there is an energy maximum in between. When an external field is applied, one minimum is lower in energy. Classically, the rate of particles reversing their magnetization depends on the barrier height relative to the thermal energy (Neel, 1959). It also depends on the attempt frequency which is comparable with the Larmor

FIGURE 4.12 Schematic diagram of StonereWohlfarth anisotropy energy barrier for magnetization reversal.

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precession frequency of the moment and the particles to reverse their magnetization directions with a rate    (4.53) s1 ¼ s1 0 exp DE kT where the barrier height is given by DE ¼ kV½1  Ms H=2kB 2

(4.54)

DE ¼ kV½1  H=Hk 2

(4.55)

or

Hk is known as the anisotropy field and it represents the highest possible switching field for a material. As applied field is increased, magnitude of the energy barrier is reduced. The coercivity of a material depends on the measurement time (Sharrock, 1990) smeas and is given by h i Hc ¼ Hk 1  flnðsmeas =s0 ÞkT=kB Vg1=2 (4.56) When the measurement time smeas is much greater than the characteristic relaxation time s the sample shall approach equilibrium and no coercivity shall be observed. The rate of magnetic relaxation is also very sensitive to the temperature. If kBT << DE, a nonequilibrium magnetization is measured and this gives rise to hysteresis. While for kBT >> DE, thermal fluctuations will tend to demagnetize the sample. If coercivity is zero due to thermal fluctuations the sample is said to be superparamagnetic. The threshold temperature for superparamagnetism is called the blocking temperature (TB). The blocking temperature is defined as the temperature at which the magnetic moment relaxation time is equal to the measurement time or the temperature where the moment is able to overcome the energy barrier into the superparamagnetic state at a certain measurement time, which is given by TB ¼ kVlnðsmeas =s0 Þ=kB

(4.57)

Below this temperature the particle spins are said to be blocked. The blocking temperature depends on measurement time and therefore on the type of experimental technique. With DC magnetometry TB is often determined by measuring zero field-cooled (ZFC) and field-cooled (FC) magnetization as a function of temperature. The ZFC curve measured by cooling the sample in zero field, applying field at low temperature and then measuring the magnetization while increasing temperature. It exhibits a maximum magnetization at a temperature commonly referred as blocking temperature (TB) of the sample. At temperatures above TB, the thermal energy, characterized by kBT, is larger than the magnetic energy barrier and thus the materials become superparamagnetic following the CurieeWeiss law. The field-cooled magnetization MFC is measured initially by applying a small field at room temperature. As the sample is cooled, the magnetization rises due to less as thermal fluctuations. Unlike MZFC, the field-cooled

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magnetization saturates at low temperature. TB is known as the temperature at which the magnetic anisotropy energy barriers of magnetic single-domain particles are overcome by thermal activation energy leading to the variation of the magnetization direction. In the Neel’s model for the rate of equilibration of the magnetization, the magnetization relative to its value at zero temperature is a Langevin function (Neel, 1949) M 1 ¼ LðxÞ ¼ CothðxÞ  Mð0Þ x

(4.58)

where x ¼ mH/kT. Because the Langevin function depends on the ratio H/T, data collected at different temperatures will scale to a universal curve (Bean and Livingston, 1959). The magnetization curve can be fitted to extract values for the average particle moment m (McHenry et al., 1994) and if the magnetization of the material is assumed to be constant it can be used to determine the particle size distribution (Chantrell et al., 1978). An ensemble of identical and noninteracting particles will have a magnetization that decays exponentially with time (Wernsdorfer, 2001) and is given by MðtÞ ¼ M0 expð t=sÞ

(4.59)

where M0 is the magnetization at zero time, t0 (Brown, 1963). However, if there is a distribution of energy barriers due to variations in the particle size, crystallographic orientation or anisotropy or to magnetostatic interactions among the particles, then there will be a range of values for s and the contributions must be integrated. Street and Woolley have shown that a flat distribution of finite width yields a magnetization that decays logarithmically in time MðtÞ ¼ M0  Slnðt=t0 Þ

(4.60)

where S is the magnetic viscosity (Street and Woolley, 1949). While this distribution is a crude approximation in a wide variety of nanoparticle systems, logarithmic decay is observed over the timescale ranging from 102 to 105 s. At shorter timescale deviations are evident (Chamberlin and Scheinfein, 1993) but the viscosity model is useful for predicting long-time behavior, such as the thermal demagnetization of magnetic recording media. For submicrosecond timescales the precession of a magnetic moment about an applied field cannot be ignored. With only a Zeeman energy term in equilibrium a magnetic moment will be parallel to the applied field. When the field is first applied, however, the moment will precess counter clockwise around it at the Larmor precession frequency circling around and gradually decaying inward.

6.2 Surface and Interface Effects In ideal monodomain particles in which all of the atomic spins are parallel, the StonereWohlfarth model yields an exact solution in which it ignores more complex interactions within and between the particles. Within a single particle, the

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atomic moments at the surface will be exchange coupled to fewer nearest neighbors than those within the particle core. The surface spins of these nanoparticles have resulted in reduction of their exchange energies. At the same time symmetry is broken at a surface and nanoparticles of cubic compounds shall show enhanced surface anisotropy (Arrott et al., 1993). Because the core and surface spins are still exchange coupled this leads to increased effective values of k and higher switching fields. Open hysteresis loops have been observed in ferrite nanoparticles even at high applied fields and this result has been interpreted in terms of spin canting at the nanoparticle surface (Kodama and Berkowitz, 1996). Large surface anisotropies in nanoparticles have been reported by many groups (De Biasi et al., 2002; Pankhurst et al., 2004; Wilcoxon et al., 2004). Coreeshell nanoparticles of two different materials, usually a metallic core and metal oxide shell, made via partial oxidation show many related effects. The strong exchange coupling between the nanoparticle core and oxide shell leads to a shift in the field-cooled hysteresis loop (Meiklejohn and Bean, 1957). The higher reversal field for antiferromagnetic CoO prevents the exchange-coupled Co from switching at lower fields. The effect is asymmetric because the direction of the applied field during cooling selects an easy magnetization direction. This phenomenon is considered to as pinning in thin film multilayers. Small-angle neutron scattering (SANS) studies of Fe/FeO nanoparticles showed that at moderate fields the spins in the ferromagnetic shell had a net perpendicular magnetization (Ijiri et al., 2005). This is similar to the behavior of an antiferromagnet or ferrimagnet in a spin flop phase, except that it is stabilized at fields up to 5 T presumably due to higher surface anisotropy. Coreeshell nanoparticles have been proposed as a possible solution to the superparamagnetic limit problem in magnetic data storage (Givord et al., 2005; Skumryev et al., 2003). Coreeshell nanoparticles with passivating surfaces have additional interest because they enable particles to have higher magnetic moments than pure oxides. This attribute would be useful in ferrofluids for MRI contrast agents and also for high-frequency nanocomposite inductors (Ohnuma et al., 2000). There has been a report of true epitaxial oxide coating on nanoparticles prepared by high-temperature gas phase methods and then slowly oxidized (Kwok et al., 2000).

7. SPINTRONIC REGIME 7.1 Spin Dynamics When magnetic material is placed in applied DC magnetic field its magnetic moment presses around the applied field. The vectorial representation of torque on precessing spin is shown in Figure 4.13. The magnetic field will produce a precession torque sp on the magnetic moment as sp ¼ M  Hdc

(4.61)

where M is the magnetization of the material, Hdc is the applied magnetic field.

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FIGURE 4.13 Vectorial representation of precession torque perpendicular to magnetic moment and applied magnetic field.

7.2 Ferromagnetic Resonance Magnetic material placed in an applied DC magnetic field begins to precess about the applied magnetic field. The equation of motion of magnetization state in presence of damping force is given as (Slichter, 1990) dM ¼ gM  Hdc dt

(4.62)

where M is the magnetization, g is the gyromagnetic ratio, and Hdc is the DC magnetic field. When microwave frequency is applied perpendicular to static field, power absorption is when precession frequency is same with applied frequency. This behavior is called ferromagnetic magnetic resonance (FMR). The condition of Larmor ferromagnetic resonance (Kittel, 1947) is written as u ¼ gðBHdc  4pMs Þ

(4.63)

where u is the angular frequency of microwave, Hdc is the DC magnetic field, g is the gyromagnetic ratio, B is the magnetic induction of the material, and Ms is the saturation magnetization. The equation of motion was modified by Landau and Lifshitz (2002) considering the Gilbert damping effect to conserve the magnitude and to obtain a phenomenological LandaueLifshitzeGilbert equation of the spin dynamics as dM g ag ðM  Heff Þ  M  ðM  Heff Þ ¼ dt 1 þ a2 ð1 þ a2 ÞMs

(4.64)

where a is the damping constant due to relaxation mechanism, Heff is the effective magnetic field.

7.3 Hall Effect Hall Effect refers to the accumulation of charges of opposite signs at sample boundaries by the application of Lorentz Force F in presence of magnetic field perpendicular to both current and Hall voltage. Hall voltage is calculated by V¼

IB net

(4.65)

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where I is the applied current, B is external magnetic field, n is carrier concentration, and e is charge of electron and t is the thickness of the sample rH ¼ RH B

(4.66)

RH is ordinary Hall coefficient.

7.4 Anomalous Hall Effect Hall effect in ferromagnetic materials exhibit much larger resistivity than nonmagnetic semiconductor/metal thus named Anomalous Hall effect (AHE). In ferromagnetic materials or in magnetic semiconductors the Hall resistivity has two contributions, the ordinary Hall resistivity and the anomalous Hall resistivity. AHE is one such phenomenon, arising due to spineorbit interaction, however, it may have both extrinsic and intrinsic contributions, arising respectively from asymmetric impurity scattering, or finite effective magnetic flux, associated with the Berry phase of itinerant charge carriers with different spin polarization (Sinova et al., 2010). The Anomalous Hall resistivity is rH ¼ R H B þ Rs M

(4.67)

where RH is the ordinary Hall coefficient, Rs is anomalous Hall coefficient, and M is the saturation magnetization of magnetic material.

7.5 Spin Hall Effect In 1971 Spin Hall effect (SHE) was predicted by Dyakonov and Perel (1971). Later it was introduced by Hirsch (1999). Spin current generates magnetic field (relativistic field generated by moving spin electrons) which interacts with spin resulting in to spineorbit coupling. Such spineorbit coupling leads to asymmetric scattering (opposite spins move in opposite direction) and spin up and spin down electrons are deflected toward the same edge of metal mediated through magnons. Due to this spin current yields a charge imbalance measured as spin Hall voltage. SHE involves two mechanismsdExtrinsic and Intrinsic Rashba (1960) effect (Dong et al., 2013). Extrinsic mechanism is responsible for SHE in normal metal/semiconductor due to spin orbit interaction, skew scattering, and side jump (Vignale, 2010). In nonmagnetic metals charge current produces spin current as Js ¼ g H s  J c

(4.68)

where Js is spin current in metal, gH is spin Hall angle, s is spin polarization, and Jc is the charge current. The spin Hall voltage has been enhanced in bilayer ferromagnetic/metal thin films involving spin pumping and spin torque effects (Ralph and Stiles, 2008; Rojas-Sa´nchez et al., 2014). At resonance condition electrons spin in ferromagnetic layer begins to precess with microwave frequency. At this stage

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damping effects on electrons can be taken as cancelled. This is a state of effective excited ferromagnet acts as a spin pump which transfers angular momentum between the ferromagnetic (FM) and nonmagnetic material (NM). The transfer is mediated by magnons (low energy-quantized spin waves) which through the conservation of angular momentum are responsible for spin flips of electrons directions leading to spin current free of charge transfer. Due to strong spineorbit coupling in platinum the pumped spins from ferromagnetic layer produces charge current (DC voltage) perpendicular to spin current. Thus maximum spin Hall voltage can be obtained at FMR condition in bilayer thin films through inverse SHE on metallic layer. The mechanism of SHE in bilayer has been illustrated in Figure 4.14.

7.6 Multiferroics (Magnetoelectric) The coexistence of ferroelectricity, ferroelasticity, and ferromagnetism in a single compound or composite is known as multiferroic materials (Bibes, 2012; Eerenstein et al., 2006; Khomskii, 2009; Spaldin et al., 2010; Spaldin and Fiebig, 2005). For the spintronic devices, high magnetoelectric-coupled materials are desirable in which magnetic dipole and electric dipole are mutually coupled. Magnetoelectrically coupled materials are promising candidates for low energy-consumed miniature devices as polarization/magnetization of the material can be externally controlled by applied magnetic/electric field (Nan et al., 2008; Srinivasan, 2010). One of the compound to induce magntoelectric coupling should be either antiferromagnetic/ferromagnetic or

FIGURE 4.14 Spin hall effect by ferromagnetic resonance.

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ferroelectric. Accordingly, doping/substitution of ferroelectric or ferromagnetic elements are incorporated in the basic compound to achieve magnetoelectric coupling. Yet, room temperature high ME coupling has not been observed in single-phase compound except bismuth ferrite (Ma et al., 2011). A schematic diagram to exhibit multiferrocity is depicted in Figure 4.15. The increase in polarization due to magnetoelectric coupling between electric and magnetic domain interaction which is estimated by expansion of Landau’s free energy for a magnetoelectric system: 1 1 FðE; HÞ ¼ F0  Psi Ei  Mis Hi  ε0 εij Ei Ej  m0 mij  aij Ei Hj 2 2 gijk bijk E i Hj Hk  H i E j Ek  /  2 2

(4.69)

where F0 is ground state free energy, subscript (i, j, k) refer to three components of a variable in spatial coordinates, Ei and Hj the components of the electric field E and magnetic field H, ε0 and m0 is dielectric and magnetic susceptibility of vacuum, εij and mij is second-order tensor of dielectric and magnetic susceptibility. aij, bijk, and gijk are the component of tensors which are designated as the linear, quadratic, and higher order magnetoelectric coupling coefficients (Fiebig, 2005). The induced electric polarization and magnetization are given by Pi ðE; HÞ ¼ 

bijk vF Hj Hk þ / ¼ Psi þ ε0 εij Ei þ aij Hj þ 2 vEi

(4.70)

and m0 Mi ðE; HÞ ¼ 

gji vF ¼ aji Ej þ Ej Ek þ / 2 vHi

FIGURE 4.15 Multifuctional multiferroic compound.

(4.71)

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Rivera has given experimental realization of linear “a” and quadratic “b” magnetoelectric coupling coefficients for multiferroic compounds (Rivera, 1994). The linear magnetoelectric coupling coefficient “a” is determined experimentally by fixing DC magnetic field along with simultaneous sweeping of AC magnetic field. Quadratic coefficient has been measured experimentally by fixing AC magnetic field while sweeping DC magnetic field (Kumar et al., 1998b; Park et al., 2007; Rivera, 2009). The ME coefficient in terms of voltage equation was given by Rivera. Dynamic method is successful even in detecting quadratic MEB coefficient. The linear “a” and quadratic “b” coupling coefficients obtained from material’s output voltage as a¼

dE 1 dV Vout ¼ ¼ dH d dH h0 d

(4.72)

Vout h20 d

(4.73)

b¼

where Vout, H, h0, and d are induced output voltage, DC-biased magnetic field, AC magnetic field magnitude, and sample thickness, respectively.

8. FERRITES AS HUMIDITY/GAS SENSOR Ferrites are decorated as strategic material ranging from permanent magnets audio/video magnetic memory applications, microwave components, shielding material, multiferroics, and finally as humidity/gas sensor material. Ferrites exhibit a number of special characteristics which make them particularly attractive for sensor applications apart from magnetic material wherein its magnetic character is not utilized but oxygen deficient and porous nature is exploited (Reddy et al., 2000). Transition metal ferrites are a family of oxides that play an important role in a wide variety of fields. The basis for this wide range of applications is related to the variety of transition metal cations that can be incorporated into the lattice of the parent magnetite (Fe2þFe3þ 2 O4) structure. Apart from their technological importance as magnetic materials, ferrites have also been well studied for their catalytic behavior especially in some industrially important reactions. In the case where these ferrites are used for catalytic (Rennard and Kehl, 1971; Zhihao and Lide, 1998), magnetic, or electrical applications (Dube and Darshane, 1993) high-density materials are prepared by high-temperature solid-state reactions between the finely dispersed and wellground constituent powders. Most of these above-mentioned applications demand ferrites in the form of ceramic materials with very high density. On the other hand, like in application as materials for humidity/gas sensors, lower density and higher surface area materials are preferred. Some of the earlier reports of ferrites as gas sensing materials include the work of Arai and Seiyama (1991) on nickel ferrite which was used as a highly reproducible humidity

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sensor with a fairly good linearity with humidity. There is also a report on semiconducting cadmium ferrite that has been used as a high-performance ethanol sensor (Liu et al., 1998; Zhang et al., 1999). In earlier reports it has been shown that nickel ferrite is a promising candidate as a chlorine sensor (Reddy et al., 1999). The relationship between the microstructure and the electrical properties of MgAl2O4 and MgFe2O4 spinel porous compacts has also been explored by the others (Gusmano et al., 1991, 1992, 1993a,b). Semiconducting zinc ferrite was also explored for gas sensing properties (Chu et al., 1999). Use of ferrites as temperature sensors is well known. Seki et al. (1988) has reported use of temperature-sensitive ferrites as humidity sensors. Change in impedance by humidity sensing of magnesium ferrite thin film prepared by RF sputtering has been reported earlier (Kotnala et al., 2011). Bulk magnesium ferrite shows good sensitivity toward humidity by sensing decrease in resistance due to dangling bond produced by oxygen vacancies (Misra et al., 2003). The improvement in resistance change with humidity can be achieved by adding foreign elements. Particularly, ceria as additive showed pronounced effect due to its catalytic and reducing properties (Bernal et al., 1993; Fang et al., 2000; Jiang et al., 2010; Mi et al., 2012). High gas sensitivity response has been observed by low concentration of ceria-added films than the undoped thin film. Humidity-dependent properties of ferrites are shown to be enhanced by dopingcontrolled percentages of alkali ions (Okanoto et al., 1986). One more advantage of using ferrites is that, they can be porous and porosity is the basic need of a humidity sensor. Humidity-dependent properties of ZnCu ferrite doped with CaC12 and LiCl are reported (Vaingankar et al., 1997). The response of Ni ferrite for different reducing gases (Kapsea et al., 2009) and for LPG sensing (Rezlescu et al., 2005; Satyanarayana et al., 2003) was investigated. Recently lithium ferrite was also investigated for alcohol vapor sensing (Rezlescu et al., 2008). For the first time colossal change in resistance performance with humidity of PLD grown pure and ceria-added magnesium ferrite thin films have been reported. Humidity sensing mechanism in magnesium ferrite thin film is shown in Figure 4.16. It shows change in resistance of the order of six termed as Colossal Humidoresistance (CHR). FIGURE 4.16 Humidity sensing mechanism on magnesium ferrite thin film resulting into colossal humidoresistance.

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9. NANOPARTICLES SYNTHESIS METHODS 9.1 SoleGel Method The solegel method is a versatile solution-based process for making ceramic and glassy materials. The solegel process in general involves the formation of a sol (colloidal suspension) and subsequent cross-linking to form a viscous gel. The most common starting materials or precursors used in the preparation of the sol are water-sensitive metal alkoxide complexes {M(OR)x, where R ¼ alkyl group}. The nature of the metal and associated R groups may be altered to affect the rate and properties of the ultimate oxide material. During the solegel process, the molecular weight of the oxide product continuously increases, eventually forming a highly viscous three-dimensional network by step growth polymerization called condensation. The most widely used metal alkoxides are Si(OR)4 compounds such as tetramethoxysilane (TMOS) and tetraethoxysilane (TEOS). However, alkoxides of Al, Ti, and B are also commonly used in the solegel process, often mixed with TEOS. Aluminum silicates may be generated through hydrolysis and condensation of siloxides, which proceed through an intermediate AleOeAl network known as alumoxanes.      AlðOSiR3 Þ3 þ H2 O/ Al O ðOHÞx  ðOSiR3 Þ1x n gel /ðAl2 O3 Þm ðSiO2 Þn (4.74) The typical steps involved in solegel synthesis are graphically represented in Figure 4.17.

9.2 Citrate-Gel (Modified SoleGel) Method Pechini in 1967 developed a modified solegel method that is not suitable for traditional solegel-type reactions due to their unfavorable hydrolysis equilibria (Pechini, 1967). The Pechini method is based on the formation of complexes of metals and even nonmetals with bi- and tri-dendate organic chelating agents such as citric acid. A polyalcohol such as ethylene glycol is added to establish linkages between the chelates by a polyesterification reaction resulting in gelation of the reaction mixture. Schematic representation of this process is shown in Figure 4.18. The advantage of the Pechini method lies in the elimination of the requirement that the metals involved form suitable hydroxocomplexes. Chelating agents tend to form stable complexes with a variety of metals over a wide range of pH, allowing relatively the easy synthesis of oxides of considerable complexity. In addition to citric acid there are numerous alternative chelating agents resulting in the variation of Pechini method. Ethylenediaminetetraacetic acid (EDTA) is occasionally substituted for citric acid (Xu et al., 2001) and is widely used as a complexing agent for quantitative complex-metric titrations

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FIGURE 4.17 Illustration of the products obtained through solegel processing.

FIGURE 4.18 Schematic representation of condensation in the Pechini method.

due to its ability to bind almost any cation. The four carboxylate groups allow the molecule to behave as a bi-, tri-, tetra-, penta-, or hexa-dendate ligand, depending on the pH of its solution. The polymer is simply combined with the metal cations in solution to form a precursor that is subsequently calcined to pyrolyze the organic species. These reactions are sometimes referred to as polymer combustion synthesis. Similar to the Pechini method there are a number of synthesis process reported in the literature, in which carboxylic acid-based chelating agents are used and pyrolysis of the resulting precursors are done by the use of a polyol or similar reagent to induce polymerization

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(Hui and Michele, 2002). It has been noted that the products of such reactions tend to exhibit relatively large crystallite sizes with irregular morphologies (Anderton and Sale, 1979).

9.3 Coprecipitation Method Many of the earliest synthesis of nanoparticles were achieved by the coprecipitation of sparingly soluble products from aqueous solutions followed by thermal decomposition of these products to oxides. Coprecipitation reactions involve the simultaneous occurrence of nucleation, growth, coarsening, and agglomeration processes. Due to the difficulties in isolating each process for independent study, the fundamental mechanisms of coprecipitation are still not thoroughly understood. Chemical reactions that result in products with low solubility are chosen generally, so that the solution quickly reaches a supersaturated condition. The chemical reactions used to induce coprecipitation can take numerous forms. Inducing precipitation of a compound, however, does not guarantee that the product will be monodispersed and nanoparticulate. The processes of nucleation and growth govern the particle size and morphology of products in precipitation reactions. When precipitation begins, numerous small crystals initially form called nucleation, but they tend to quickly aggregate together to form larger, more thermodynamically stable particles called the growth followed the phenomenon, “Coarsening” by means of which smaller particles are essentially consumed by larger particles during the growth process. Kinetic factors compete with the thermodynamics of the system in a growth process (Lagally, 1993). Factors such as reaction rate, transport rate of reactants, accommodation, removal and redistribution of matter compete with influences of thermodynamics in particle growth. The growth process of the precipitated particles can be either diffusion limited or reaction limited. The interface-controlled growth of a small particle in solution becomes diffusion controlled after the particle exceeds a critical size (Turnbull, 1953). The reaction and transport rates are affected by concentration of reactants, temperature, pH, and order of introduction of and degree of mixing of reagents. The structure and crystallinity of particles may be influenced by reaction rates and impurities. Factors such as supersaturation, nucleation and growth rates, colloidal stability, recrystallization, and aging processes have effects on the particle size and morphology. At low supersaturation, the particles are small, compact, and well formed and the shape depends on crystal structure and surface energies. At high supersaturation, large and dendritic particles form. At even higher supersaturation, smaller but compacted and agglomerated particles form (Walton, 1979) which mean supersaturation shows predominant influence on the morphology of the precipitate.

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9.4 Microemulsion Method Hoar and Schulman in 1943 noted that certain combinations of water, oil, surfactant, and an alcohol or amine-based cosurfactant produced clear, apparently homogeneous solutions that Schulman termed microemulsions (Hoar and Schulman, 1943). Presently now microemulsions have found a wide range of applications, from oil recovery to synthesis of nanoparticles (Chhabra et al., 1997). Microemulsions are isotropic, macroscopically homogeneous, and thermodynamically stable solutions containing at least three components, namely a polar phase, a nonpolar phase, and a surfactant. Surfactants are commonly used to stabilize nanoparticles or colloids against aggregation in solution. They can adsorb on the surface or form an envelope around the particle to provide either electrostatic or steric repulsion. Surfactants may also be used in post-synthesis processing to disperse the agglomerated particles. Deagglomeration is accomplished by breaking the agglomerates by milling or ultrasonication in a suitable solvent and surfactant (Shanefield, 1996). Surfactants, as self-assembled structures, can be used as a reactor to synthesize nanoparticles (Shchukin and Sukhorukov, 2004). In an appropriate solution, for example, an aqueous medium surfactant molecules orient themselves so that contact of the nonpolar tails of the molecules with the solvent is minimized. The polar headgroups of the molecules are attracted to water by electrostatic and hydrogen bond interactions. These interactions allow the molecules to self-assemble into membrane structures with minimum energy configuration. Self-assembly has been used to form monolayer films, LangmuireBlodgett films, micelles, reversed micelles, vesicles, and tubules. Membrane structures such as reverse micelles and vesicles can be used as nanoreactors to synthesize nanoparticles of metals, oxides, ceramics, and several other materials (Lopez-Quintela, 2003) inside the hollow compartments of these membrane structures. A schematic representation of different steps involved in reverse microemulsion synthesis is shown in Figure 4.19. The particles are encapsulated inside these membranes and are prevented from agglomeration with other particles by the membrane which acts as a barrier. Since it is possible to incorporate functional groups on vesicle surfaces, nanoparticles may be carried inside these functionalized membranes for targeted applications. Reverse micelles (W/O microemulsions) are a single layer of surfactant molecules entrapping solubilized water pools in a hydrocarbon solvent. The size of the water pool depends on the amount of water entrapped at a given surfactant concentration (water/surfactant ratio). Nanoscale colloids of metal (Chen and Chen, 2002) semiconductors (Simmons et al., 2002) are made using the reverse micelle method. Monodisperse spherical silica particles containing homogeneously dispersed Ag quantum dots are synthesized via a controlled photochemical reduction of silver ions during hydrolysis of tetraethoxysilane in a microemulsion (Wang and Asher, 2001). Ternary and quaternary nanostructured mixed oxides are also

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FIGURE 4.19 Schematic representation of various steps involved during reverse microemulsion synthesis.

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synthesized in microemulsions (Herrig and Hempelmann, 1997). Vesicles are closed bilayer membrane assemblies and their size can be controlled either by sonication or extrusion. Extrusion, however, is limited to the preparation of only a small quantity of vesicles which are more stable than micelles. Nanoscale oxide particles may be synthesized using the vesicle-mediated approach. Metal ions and lipid mixtures form vesicles upon sonication. After removal of exogenous ions, anions are added and allowed to diffuse through the membrane layers and intravesicular precipitation occurs. Due to preferential anion diffusion across the membrane, generally oxides have been prepared by this approach (Bhandarkar and Bose, 1990). Dispersed nanocrystalline metal particles can be prepared using polymerized phospholipid vesicles (Markowitz et al., 1994). The noncrosslinked polymerization of vesicles results in many individual polymer chains in the membrane structure. This enhances the structural integrity of vesicles and provides breaks in the polymer network through which both anions and cations can diffuse across the polymerized membranes thus removing the restriction to only oxide synthesis as in the case of nonpolymerized vesicles. To explain the variation of the particle size with the precursor concentration and with the size of the aqueous droplets two models have been proposed. The first is based on the LaMer diagram Figure 4.20 (La-Mer and Dinegam, 1950) which has been proposed to explain the precipitation in an aqueous medium and thus is not specific to the microemulsion. This diagram illustrates the variation of the concentration with time during a precipitation reaction and is based on the principle that the nucleation is the limiting step in the precipitation reaction. In the first step the concentration increases continuously with increasing time. As the concentration reaches the critical supersaturation value nucleation occurs, which leads to the decrease of concentration. Between the concentrations Cmax and Cmin the nucleation occurs. Later the

FIGURE 4.20 Stages of nucleation and growth for the preparation of monodisperse nanoparticles in the framework of La Mer model.

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decrease of the concentration is due to the growth of the particles by diffusion and this growth occurs until the concentration reaches the solubility value. The second model is based on the thermodynamic stabilization of the particles in which the particles are thermodynamically stabilized by the surfactant. The size of the particles stays constant with the precursor concentration and the size of the aqueous droplets vary. The nucleation occurs continuously during the nanoparticle formation.

9.5 Controlled Synthesis of Magnetic Nanocrystals in Shape and Size The performance and properties of a material depends on atomic structure, composition, microstructure, defects, and interfaces which are controlled by thermodynamics and kinetics of the processing methodology. Nanostructured materials, often characterized by a physical dimension such as grain size of less than 100nm, attract much interest because of their unique properties compared with conventional materials. In general, the synthesis of nanomaterials has been classified into topedown and bottomeup methodologies. Current advances in synthesizing and processing of functional materials for high technology emphasize the bottomeup approach to assemble atoms, molecules, and particles from the atomic or molecular scale to the macroscopic scale. Increasing recent interests have been found in chemical synthesis and processing of nanostructured materials (Hrianka and Malaescu, 1995; Klabunde and Richards, 2009; Komarneni et al., 1988; Rao et al., 2006; Wang et al., 1998). Chemical synthesis of materials may be conducted in solid, liquid, or gaseous state. The traditional solid-state approach involves grinding and mixing of solid precursors, followed by heat treatment at high temperatures to facilitate diffusion-controlled chemical reactions to obtain the final products. Mixing and grinding steps are usually repeated throughout the heating cycle with special efforts to mix materials at the nanoscale and provide fresh surfaces for further chemical reactions. Grain growth, if not prevented, occurs at elevated temperatures resulting in undesirable large grain size. Material diffusion in liquid or gas is advantageously many orders of magnitude larger than in the solid phase allowing the synthesis of nanostructures at lower temperatures. Reduced reaction temperature prevents detrimental grain growth. The reactants may be solids, liquids, or gases in any combination in the form of single elements or multielement compounds. A multielement compound often acts as a precursor where the components of the final product are in a mixture with atomic scale mixing. Many precursors may be prepared by precipitation, in which the mixing of two or more reactant solutions leads to formation of an insoluble precipitate or a gelatinous precipitate. Size-selective precipitation or size sorting has become a practical procedure and is frequently used to narrow the size distribution of as-synthesized nanocrystals to monodispersity. Special procedures may be required to remove any impurities from

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the products and to avoid postsynthesis contamination. Parameters such as solvent, temperature, pH, reactant concentration, and time ideally should be correlated with factors such as supersaturation, nucleation, and growth rates, surface energy and diffusion coefficients to ensure the reproducibility of reactions. Chemistry is based on the manipulation of atoms, molecules, and indeed has a very long history in the synthesis of materials comprising nanostructures. The recent popularity of nanoscience not only revisited the use of many old chemical methods, but also motivated many new and modified ones to be developed for the synthesis of nanostructured materials. The wide scope of chemical processing of nanostructured materials spans structural, optical, electronic, magnetic, biological, catalytic, and biomedical materials. The synthesis of monodisperse nanoparticles is emphasized due to the importance of size-dependent properties and feasibility of particle organization to form two-dimensional and three-dimensional superlattices. Remarkable progress in synthesis of ferrite nanocrystals has been made over the few years (Hashim et al., 2013a,b,c, 2012; Kumar et al., 2012, 2010a; Sharma et al., 2011). However, Kotnala’s group has synthesized different ferrites particle size of the order of 3e5 nm with a narrow size distribution by reverse microemulsions method (Dar et al., 2012; Kumar et al., 2010b,c). For most of shape-controlled synthesis of colloidal semiconductor nanocrystals, the growth mechanism on shape evolution has been investigated by Peng (2003) based on the semiconductor nanocrystals. A monomer concentration dependence model has been proposed to account for the mechanism of shape evolutions of semiconductor nanocrystals (Liu et al., 2008; Nacev et al., 2011). In the case of metal and metal oxides nanocrystals; no general shape evolution mechanism has been established so far. However, it has been demonstrated in many cases that the surfactant plays a key role on the shape evolutions, because the binding of a surfactant on a specific facet of crystal will vary the surface energy and consequently change the growth rate from one facet to another. An effective strategy on shape control involves the application of a pair of surfactants, whereby one coordinates tightly on the nanocrystal surface slowing the growth rate and the other binds weakly allowing rapid growth. By adjusting the ratio of these surfactants, the growth rate and therefore the shape of nanocrystals can be controlled. To establish the correlation of size and shape effects with the variation in magnetic properties, it is critical to develop a general synthetic method that allows for control over both the size and shape of nanoparticles and produces nanoparticles with a narrow size distribution. Recent advances on the synthesis of colloidal semiconductor nanocrystals have demonstrated that size- and shape-controlled synthesis of nanocrystals can be achieved by thermal decomposition of molecular precursors in high-temperature organic solvents in the presence of proper surfactants. The size and shape of nanocrystals can be precisely controlled by manipulating reaction variables such as molecular precursors, concentration, temperature, growth rate, type of surfactant, and solvent.

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10. FERRITE AS SHIELDING MATERIAL 10.1 Barium Ferrite Hexagonal barium ferrite is used as good microwave absorber due to high resistivity, large permeability, high magnetization value, and good dielectric properties at microwave frequency. Barium ferrite exhibits magnetoplumbite structure in which the iron ions are coordinated tetrahedrallly (FeO4), trigonal bipyramidally (Fe2O5), and octahedrally (FeO6) by oxygen ions. A unit cell contains two formula units. Barium ferrite thin films exhibit large magneto-optic rotation thus has high potential to be used as the next generation magnetooptical (MO) disk material (Das et al., 1993; Dhara et al., 1992; Kotnala, 1992; Kotnala and Das, 1994). In thin films form it exhibits high perpendicular magnetic anisotropy due to large magneto-crystalline anisotropy along C-axis. Such oxide materials exhibit high corrosion resistance to attain high reliability to magnetic data storage. By using focused laser beam bits density can be made with much narrower track widths than the conventional magnetic recording of the order of 108 /cm2. Using magneto-optic media such optical recording technology could be made erasable and have all the features of present-day magnetic recording as well as the high bit densities of optical recording.

10.2 Manganese Zinc Ferrite The development of magnetic nanocrystalline materials is a subject of concern, both for the scientific value of understanding the unique properties of materials and for the technological significance of enhancing the performance of existing materials. To meet the demand of high-performance devices an important step is to synthesize ferrites in nanoscale form. Below the critical size these nanocrystals exist in a single-domain state so that the domain wall resonance is avoided and the material can work at higher frequencies. Verma and Joy (2005) studied the magnetic properties of superparamagnetic lithium ferrite nanoparticles synthesized by low-temperature autocombustion method. Several workers have also synthesized Ni-Zn nanoferrites for different applications (Gubbala et al., 2004; Lu et al., 2011; Thakur et al., 2009). Sertkol et al. (2010) synthesized supermagnetic NieZn nanoparticles by microwaveassisted combustion route. Kumar et al. (2010c) have synthesized nanocrystalline NieZn ferrite and observed that they show superparamagnetism at room temperature. Rath et al. (1999, 2000, 2002) have synthesized superparamagnetic MneZn nano ferrites by using hydrothermal route. They have reported increase in Curie temperature in MneZn ferrite nanoparticles prepared using chemical methods. Jeyadevan et al. (2003) used chemical coprecipitation method to control over particle size to achieve better magnetic properties. Thakur et al. (2007) investigated the dielectric behaviour of MneZn ferrites and found an enhancement in resistivity of nano samples as compared with bulk one.

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With the advancement of electric and electronic industry, the use of electronic products and telecommunication equipment have increased due to which the problem of EMI has attracted serious consideration, as it reduces the lifetime, competence of the instruments, and also affect the safety operation of many electronic devices. To avoid these problems, all electronic equipments must be fortified against electromagnetic destruction. Most of the research groups have studied Fe3O4/polyaniline (PANI) nanocomposites (Xiao et al., 2007); however, a very few reports have dealt with multicomponent ferrite/ polyaniline nanocomposites. Gairola et al. (2010) have explored the microwave absorption properties of Mn-Zn/PANI nanocomposites prepared by mechanical blending. Also Jiang et al. (2009) have explored the synthesis of Mn-Zn/PANI nanocomposite by reverse microemulsion method and explored their magnetic properties at different temperatures. An enhancement in the magnetic loss of polyurethane/Mn-Zn composite and hybrid polymer composite/Mn-Zn composites have been reported by Moucka et al. (2007).

10.3 Lithium Ferrite Lithium ferrite is one of the most versatile magnetic materials. It is generally useful for microwave devices, memory core, power transformers in electronics, antennas, read/write heads for high-speed digital tapes, and so on, because of its high resistivity, low electric losses, high Curie temperature. In particular, mixed lithium ferrites are of much interest because of their application in microwave devices such as isolators, circulators, gyrators, and phase shifter.

10.4 Effect of Substituent and Additives on the Properties of Lithium Ferrite The changes in the magnetic, electrical, dielectric, and microstructure, and so on, as a result of substitution and addition of foreign atoms in lithium ferrite are briefly discussed which follows as:

10.4.1 Zinc, Cadmium-Substituted Lithium Ferrite Zn and Cd ions are often included in the basic composition of lithium ferrite (Li0.5Fe2.5O4) for enhancing the saturation magnetization value in lithium ferrites (w65 emu/g), as Zn and Cd enters predominantly on the tetrahedral site (Bellad et al., 2000). The formula of lithium ferrite with M ¼ Zn/Cd substitution is represented by Li0.5x/2MxFe2.5x/2O4 whereas cation distribution is described by [MxFe1x]Tetra[Li0.5Fe1.5þx/2]OctaO4. Saturation magnetization increases (<80 emu/g) for x ¼ 0.3 concentration of Zn or Cd in Li0.5x/2ZnxFe2.5x/2O4 and begin to decrease with further substitution. Zn substitution is also very effective in controlling several other properties. It promotes the grain growth and densification during sintering which ultimately

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lowers the anisotropy. All such results in resonance line width decrease and coercive force.

10.4.2 Aluminium, Titanium-Substituted Lithium Ferrite Magnetic, electric, dielectric, and thermoelectric power properties of lithium ferrites are strongly affected by the aluminium and titanium substitutions. Al3þ substitution results in increase of anisotropy but it decreases the saturation magnetization and Curie temperature (Fu et al., 2006; Ravinder et al., 2000). The titanium-substituted lithium ferrites show higher dielectric constant while higher concentration of Ti3þ in lithium ferrites decreases Curie temperature and saturation magnetization (Gruskova et al., 2006). 10.4.3 Manganese-Substituted Lithium Ferrite A very essential requirement for microwave ferrites is their low conductivity and dielectric loss tangent (tan d). Manganese substitution is a wellestablished practice being adopted for inhibiting the formation of Fe2þ in spinel ferrites for achieving the low conductivity (Fu and Hsu, 2005). The role of Mn ions is described by the well-known buffering reactiond Mn3þ þ Fe2þ 4 Fe3þ þ Mn2þ. The reaction is favored in forward direction. Another notable effect of Mn ions is to enhance the permeability and lowering the stress sensitivity of materials (Fu and Hsu, 2005, Qi et al., 2003). 10.4.4 Nickel-Substituted Lithium Ferrite A small amount of Ni is also often included in the composition of ferrites as it has been found useful in enhancing the remanence ratio. It is attributed to lowering of magnetostriction (Kumar et al., 2008; Lima et al., 2008). 10.4.5 Cobalt-Substituted Lithium Ferrite The loss of microwave power in ferrite devices is found to increase nonlinearly beyond some critical incident power level. Such losses can be minimized by substituting cobalt in lithium ferrite. A small substitution of cobalt in lithium ferrite can improve its magnetic, electrical, and dielectric properties (Gupta et al., 2005; Venudhar and Mohan, 2002). For high power devices the ferrites capable of handling desired power levels are designed. To achieve this, incorporation of divalent Co ions in very small quantity is very effective.

10.5 Modification in Dielectric, Magnetic and Power Loss of Lithium Ferrite Dielectric properties of ferrite materials strongly depend on the composition. Small amount of substituent can greatly affect the properties of dielectric materials. Main criterions of the substituted ions are ions valence and solubility with respect to host ferrite. Dielectric properties of large number of

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mixed ferrites like Li-Mn (Ravinder et al., 2001), Li-Ni (Trivedi et al., 2000), Li-Co (Baldha et al., 2002), Li-Ge (Ravinder and Reddy, 2003), Li-Ti (Mazen et al., 1997) have been reported. Hankare et al. (2010) reported that the chromium plays an important role in changing dielectric properties of lithium ferrites. Small amount of Ce ¼ 0.06 in Li0.5CexFe2.5xO4 produce uniform grain structure and highest dielectric constant (w3.5  104) at a frequency of 1 KHz has been reported (Verma et al., 2008a). There is a remarkable increase in dielectric constant with Ti4þ and Zn2þ doping of lithium ferrites; it shows a maximum value of 1.5  105 for the x ¼ 0.25 doped ferrite as shown in Figure 4.21. There is also decay in loss tangent values by substitution of Ti and Zn in Li0.5ZnxTixMn0.05Fe2.452xO4 (Verma et al., 2009a). Dielectric properties of nano-sized pure and Al-doped lithium ferrite have been studied (Dar et al., 2010). It was observed that dielectric increase with increasing Al3þ doping up to x ¼ 0.1 (Li0.5AlxFe2.5xO4), thereafter, this parameter decreases with further doping. It is explained on the basis that Li ferrite possesses an inverse spinel structure and the degree of inversion depends upon the heat treatment. Al3þ ions prefer to occupy B-site, while magnetic Fe ions occupy both tetrahedral and octahedral sites. It can be seen that a significant improvement in the electrical conductivity of Al-doped Li0.5AlxFe2.5xO4 observed at higher as well as lower frequencies, the conductivity increases with increasing addition of Al ions up to x ¼ 0.1, thereafter it decreases with Al doping. It is explained on the basis that in most of the ferrites Fe3þ ions are usually reduced to Fe2þ ions due to sintering process at elevated temperature. Increase in ac conductivity up to x ¼ 0.1 is explained on doping basis of Al ions force Fe3þ ions to migrate from tetrahedral site to octahedral site.

FIGURE 4.21 Variation of dielectric constant with frequency for Li0.5ZnxTixMn0.05Fe2.452xO4 at room temperature.

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The increase in the number of Fe2þ and Fe3þ ions at the octahedral site and Al doping has increased the value of sac. When the Al concentration goes beyond x ¼ 0.1, the addition of Al results in the migration of Fe3þ ions from octahedral site to tetrahedral site, thereby decreasing the number of Fe3þ/Fe2þ ions at B-site which are responsible for conduction in ferrites. Hyun and Kim (2007) have investigated magnetic properties of high-temperature thermal decomposition and solegel-synthesized Li ferrites. They observed saturation magnetizations (Ms) for the sample prepared by high-temperature thermal decomposition method at room temperature is 55 emu/g and those for the samples annealed at 700
C and quenched at 1000
C prepared by solegel method are 59 and 62 emu/g, respectively. In contrast, the coercivity (Hc) values of each sample are 4.1, 93.7, and 9.1 Oe, respectively. Fu and Lin (2009) have investigated magnetic properties of nano-sized Li0.5Fe2.5xMgxO4 ferrite. They observed the saturation magnetization of 71.1 emu/g was found for Li0.5Fe2.5O4 specimen. As increased Mg content, the saturation magnetization and remanent magnetization (Mr) decreased significantly. This is ascribed to the fact that as Mg content increases, AeOeB interactions become weak, and consequently BeOeB interaction becomes stronger and hence resulted in the decrease of magnetization. Magnetic and dielectric properties of the solegel prepared Li0.5Fe2.5O4 fine particles have been explored by George et al. (2006). They observed that the value of coercivity increases with the size of grains, reaches a maximum, and then decreases. It could be due to transition from a multidomain to a single-domain structure. Magnetization measurements show deviation in saturation magnetization values with respect to its bulk counterparts. Such variation in the magnetization values is partly attributed to the formation of a-Fe2O3 because of the volatization of Li0.5Fe2.5O4. However the large discrepancy in the magnetization value in asprepared ultrafine particle samples has been interpreted from the contribution from aligned surface spins. The electrical parameters, namely, dielectric permittivity and ac conductivity were evaluated for all the samples and studied as a function of frequency, temperature and size of the particles. Both dielectric permittivity and ac conductivity decrease as grain size of the ferrite particles increases. The comparatively lower value of resistivity or higher value of permittivity in samples sintered at lower temperatures are possibly due to the presence of a localized state in the forbidden energy gap, which arises due to lattice imperfections. The presence of these states effectively lowers the energy barriers to flow of electrons. Verma and Joy (2005) have investigated magnetic properties of superparamagnetic lithium ferrite nanoparticles synthesized by an autocombustion method with particle size in the range of 4e50 nm. They observed a superparamagnetic blocking temperature of 225 K of lithium ferrite particles of 4 nm in size. This blocking temperature is extremely large value when compared with that observed for other spinel ferrite nanoparticles, indicating large contributions from magnetic dipolar interactions. The blocking

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temperature varies with applied field following the de AlmeidaeThouless formalism usually observed for a spin-glass system. An unusual behavior, similar to the Hopkinson effect where a peak is observed near the Curie temperature for bulk material measured under a very small magnetic fields in superparamagnetic particles of lithium ferrite. This is associated with a sharp fall of the magnetization at the Curie temperature of lithium ferrite. This anomaly is explained in terms of the combined effect of the decreasing anisotropy with increasing temperature, increasing magnetization due to particle growth during the heating run, and decreasing anisotropy due to the increasing particle size. Hayashi et al. (2008) have synthesized highly transparent lithium ferrite nanoparticle/ethyl (hydroxyethyl) cellulose (EHEC) hybrid via in situ hydrolysis of prepolymerized iron(III) 3-allylacetylacetonate (IAA) and lithium acrylate (LA) in the presence of EHEC below 100
C. The hybrid film was flexible and self-standing exhibiting high transmittance in the visible region. The hybrid was superparamagnetic with a blocking temperature of 13 K. The absorption edge of the hybrid film was blue shifted compared with bulk lithium ferrite. The blue shift increased with decreasing crystallite size, which was controlled by the amount of EHEC. The self-standing film exhibited a Faraday rotation depending upon the magnetic field. The figure of merit of the hybrid film was about 3.5 at 700 nm, which was higher compared with those of reported ferrite composite at shorter wavelengths, due to its high transparency. Saafan et al. (2010) have studied the magnetic properties of nano-structured and bulk LieNieZn ferrite samples. They observed a reduction in saturation magnetization of nanosamples in comparison to their bulk counterparts attributed to large surface-to-volume ratio, crystal imperfection on the surface layer, reduction in superexchange interactions, and noncollinear magnetic structure in these nanosamples. There is a significant enhancement in permeability with Ti- and Zn-doped lithium ferrite and showed a maximum value of 106 for x ¼ 0.20 (Verma et al., 2009) as shown in Table 4.3, which is very important feature for power applications of ferrites. Grain growth mechanism is also one of the important features in Zn- and Ti-doped lithium ferrites. The grain size 3.9 mm for x ¼ 0.0 sample increases to 7.8 mm for x ¼ 0.20 sample with Ti, Zn concentration in Li0.5ZnxTixMn0.05Fe2.452xO4 as shown in Figure 4.22. This has been observed that there is a reduction in power losses in Ti- and Zn-substituted lithium ferrite. The variation of power loss (Pcv) with flux density (Bm) at 50 kHz of Li0.5ZnxTixMn0.05Fe2.452xO4 samples has been shown in Figure 4.23. The variation of power loss increases with flux density for all samples. However, decrease in power loss with the substitution of Zn and Ti in lithium ferrite exhibits a minimum loss for x ¼ 0.25 sample of Li0.5ZnxTixMn0.05Fe2.45-2xO4. Frequency-dependent power loss (Pcv) for the samples at exciting condition of Bm ¼ 10 mT is shown in Figure 4.23. It is evident from Figure 4.24 that the power loss reduces with the concentration of

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TABLE 4.3 Microstructure and Magnetic Properties of Li0.5ZnxTixMn0.05 Fe2.45-2xO4 Samples Composition Li0.5ZnxTixMn0.05 Fe2.452xO4

Lattice Constant (A˚)

x ¼ 0.00

8.321

x ¼ 0.05

Permeability (m) at frequency 1 MHz

Saturation Magnetization (emu/g)

Grain Size (mm)

27.9

58.5

3.9

8.342

46.5

56.2

6.1

x ¼ 0.10

8.347

64.4

55.9

6.4

x ¼ 0.15

8.358

59.8

51.9

7.0

x ¼ 0.20

8.357

105.5

52.6

7.8

x ¼ 0.25

8.348

51.4

54.5

6.2

x ¼ 0.30

8.340

45.5

40.9

5.1

FIGURE 4.22 SEM micrographs of Li0.5ZnxTixMn0.05Fe2.452xO4 samples.

Zn and Ti up to x ¼ 0.25 in the Li0.5ZnxTixMn0.05Fe2.452xO4. The variation of power loss is small up to frequency 1 MHz but it changes abruptly beyond this in the exciting flux density of 10 mT for all samples. Loss at low frequencies approximately below 500 kHz is due to hysteresis loss and above these frequencies the eddy current loss increases gradually with increasing frequency and becomes predominant in power loss. These materials exhibited low power losses up to 1 MHz, making them more suitable for power applications.

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FIGURE 4.23 Variation of Pcv and flux density at 50 kHz of Li0.5ZnxTixMn0.05Fe2.452xO4 samples. Where B is x ¼ 0.0, C is x ¼ 0.05, D is x ¼ 0.10, E is x ¼ 0.15, F is x ¼ 0.20, G is x ¼ 0.25, and H is x ¼ 0.30.

FIGURE 4.24 Variation of Pcv and frequency at 10 mT of Li0.5ZnxTixMn0.05Fe2.452xO4 samples. Where B is x ¼ 0.0, C is x ¼ 0.05, D is x ¼ 0.10, E is x ¼ 0.15, F is x ¼ 0.20, G is x ¼ 0.25, and H is x ¼ 0.30.

10.6 Influence of Additives on the Properties of Lithium Ferrite Magnetic properties of lithium ferrite are strongly dependent on the processing methods. Development of a high-quality, cost-effective, loss less highfrequency ferrite material for power applications is an ever-challenging aspect for investigation. Important requirements for materials of this kind

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are high-saturation magnetization and low core losses. Small amounts of additives can greatly affect the properties of ferrites. Here, it is to be mentioned that the additives do not change the lattice structure but influence the microstructure and grain boundary. Additives can be divided in to three categories (Shokrollahi and Janghorban, 2007). The first group consists of additives that seggregates to the grain boundaries and affects the grain boundary resistivity and reduces the eddy current losses (Inaba et al., 1996). Since the grain boundary phases are nonmagnetic, they reduce the permeability of ferrites. The required properties is dictated by the type and the amount of additives used in the lithium ferrite. Examples of such type of additives are CaO, SiO2, and so on. The second group consists of additives that affect microstructure like Bi2O3, V2O5, and so on (Rao et al., 2007). They are basically low melting compounds and hence results in a liquid phase sintering. The third group consists of additives like MnO2, TiO2, MoO3, Nb2O5, and so on, these are dissolved into grain and alter the magnetic properties of the parent ferrite (Topfer et al., 2005). The polycrystalline ferrites are a complex system composed of crystallites, grain boundaries and pores. Different aspects of processing, properties, effect of additives on magnetic properties and applications of these ferrites were discussed by many researchers (Gillot, 2002; Gupta et al., 2005; Kishan, 1993; Kotnala et al., 2007; Kumar et al., 1998; Sellai and Widatallah, 2004; Snelling, 1969; Sugimoto, 1999; Wolska et al., 2001). Additive materials can affect the magnetic properties, electrical properties, and microstructure of ferrites by different mechanisms (Bellad et al., 1999; Watawe et al., 2007; Qi et al., 2003; Shokrollahi and Janghorban, 2007; Verma et al., 2008). These mechanisms are (1) affecting the microstructure development by liquid-phase sintering, (2) segregation to the grain boundaries and affecting the grain boundary resistivity, and (3) dissolution into the grains and altering the magnetic properties. Some additives such as V2O5, Bi2O3, MoO3, and so on, act as grain growth accelerator by liquid phase formation. Other types of additives such as SiO2, Nb2O5, Ta2O5, CaO, and so on, can create an electrical insulating film around the grain and increase the resistivity of materials (Verma et al., 2007). Low-melting point insulating phases are formed at the grain boundaries, which increase electrical resistivity of the material. It results in a reduction of the power losses (Zaspalis et al., 2002). To improve electrical and magnetic properties of lithium ferrites, small amount of cationic substitution is widely used. The cations having valance þ2, þ3, and þ4 are soluble in lithium ferrite lattice and occupy the regular positions on the tetrahedral or octahedral sites, and change properties of the base material accordingly. Magnetic and electrical properties of ferrites depend on the control of microstructures. The grain size, grain connectivity, and porosity are the most important parameters affecting the magnetic properties of ferrite. Grain growth is closely related to the grain boundary mobility. Solute segregation has an added benefit in lowering grain boundary energy. The additives which have

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limited solubilities are not effective for grain growth. Grain growth is enhanced when dopant concentration in the grains is above solid solubility limit. On periphery of grain the main considerations exist; from the charge consideration, cations of a valence lower than the host cation are expected to form a space charge cloud around the grain boundary. Cations of a valence higher than the host cation are not expected to segregate for the same reason (Chen and Xue, 1990). According to the increased pore mobility model any tetravalent or pentavalent ions in the solid solution with spinel ferrite should increase grain boundary mobility. In case of SiO2, Ta2O5, Nb2O5 may have been reduced to other oxidation states. The boundary motion can be inhibited by second-phase particles. The drag on the boundary due to an array of insoluble particles is due to decrease in grain boundary area when a boundary intersects the particle. Therefore, to move away from the particle requires creation of new surface. Source of this drag is the displacement between the position of moving boundary and chemical potential position defined by solute distribution, assuming that there is a significant segregation of solute to or away from the boundary. Lucke and Deter proposed that a grain boundary should be able to break away from the impurity atmosphere when velocity is high enough due to a strong driving force on the grain boundary (Cahn, 1962). According to their theory, a boundary moves together with its segregated impurities (Molodov et al., 1988). If there is a strong tendency toward segregation, the boundary impurity concentration may be high, although the volume impurity concentration is small. One possible mechanism for the promotion of grain growth in lithium ferrite is the reduction of impurity and pore drag on grain boundary motion. If cations segregate to the grain boundary region and repel other segregates which are more detrimental to grain growth, the grain boundary velocity will be enhanced. Another possible grain growth promotion mechanism is the increased pore mobility due to creation of excess cation vacancies (e.g., by SiO2 addition). For a grain boundary with attached pores, the velocity increases with the pore mobility. Whereas excess vacancy formation by doping the ferrite with MO2 (SiO2) can be argued from the site and charge balance as well as the oxidationereduction equilibrium of iron. If it is postulated that titania dopant does not create excess cation vacancies, then for an addition of three Ti4þ ions, four Fe3þ ions are reduced to Fe2þ to satisfy the site and charge balance (Yan and Johnson, 1978). The dissolution of an oxide dopant with þ2 cation valence, for example, CdO, ZnO, and MnO in the lithium ferrite does not create excess cation vacancies. Furthermore, dopants with þ3 cation valence, for example, La2O3, Ta2O5, Nb2O5, Al2O3, SiO2, Mn2O3, and Fe2O3, probably generate little excess cation vacancy concentration in the ferrite lattice. In fact, simple calculation based on site balance suggests that the number of cation vacancies created by each cation in a tetravalent cation oxide is four times that created by trivalent oxide. Thus, the absence of enhanced grain growth for dopant oxides with þ2

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or þ3 cation valences is explained by the lack of a significant number of excess cation vacancies in ferrite lattice. Grain growth is rapid when a small amount of liquid wets the grain boundary area. The grain boundaries move toward their centre of curvature under the influence of surface tension forces by solution into the liquid phase from convex surface of the boundary and redeposition on the concave surface. Depending on the composition of sintering additives, the liquid phase can form an amorphous or a crystalline grain boundary phase during cooling (Hoffmann and Petzow, 1994). A liquid film between grains provides a relatively fast transport medium for host ions, the longer diffusion distance, and the solideliquid surface reaction kinetics ultimately restrains grain boundary mobility from its intrinsic value. If liquid phase is not properly discontinued, discontinuous grain growth is probable. However, if the liquid phase is properly distributed, grain growth impediments can still occur provided diffusion path between grains has been increased sufficiently to offset increased diffusion rates caused by the reactive liquid (Hendricks and Amarakoon, 1991). During the grain growth, dissolution of additive ions from flux into the ceramic is assisted by solutionereprecipitation process, which reduces the volume fraction of intergranular phases. Therefore, the flux composition, melting temperature, reactions between the flux and ferrites, and microstructural evolution during liquid-phase sintering are all very important parameters to characterize and understand any attempt to precisely control magnetic properties (Wang et al., 2000). During the different liquid-phase sintering stages, sintering rate can be increased by reduction in particle size. If large liquid content is present, complete densification can be reached by the rearrangement process and no need arises for the solutioneprecipitation phenomenon which would be expected to change grain shapes (Kingery, 1959; Kingery and Narasimhan, 1959). For small liquid contents, little densification is attained by rearrangement process, and major part of densification must take place by a solutioneprecipitation phenomena.

10.7 Influence of Nano-SiO2 on Li-Cd Ferrite The doping of SiO2 in lithium ferrite increases grain boundary resistivity by creating an insulating layer covering grain boundary significantly, it results into enhancement of dielectric value and reduction of power loss of ferrites. However, uniform distribution of such a high resistance layer is needed effectively to reduce the eddy current loss of the ferrite materials due to very small diameter of nano-SiO2 particles, their surface energy is very large accordingly. Surface atoms in nano-SiO2 particles have large number of unsaturated bonds, so nano-SiO2 particles have much higher chemical activity and are very reactive to combine with other atoms to get stabilization. An extensive study of magnetic and dielectric properties has been investigated on a series of nano silicon dioxide (10 nm) with the addition of 2, 4, 6, 8 wt% in

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Li0.35Cd0.3Fe2.35O4 prepared using solegel technique. The solegel technique is preferred over solid-state sintering because by this technique the nano-SiO2 can be dispersed uniformly throughout the material. It has been useful to obtain high-quality lithium ferrites by solegel technique. Figure 4.25 shows the microstructures of the samples. The grain size of Li0.35Cd0.3Fe2.35O4 is about 4.5 mm, which is smaller than that of the samples with nano-SiO2 except for 8 wt% of SiO2. The grain size of the samples with nano-SiO2 ¼ 2, 4 wt% are more uniform than that of the sample without SiO2 ferrite. Because the diameter of the nano-SiO2 particles is very small, their surface energy is very large accordingly. Surface atoms in nano-SiO2 particles have many unsaturated bonds, so the nano-SiO2 particles have a much greater chemical activity and are very easy to combine with other atoms to obtain stabilization. Due to this, LiCd ferrite with the addition of nano-SiO2 can promote growth of grains. On the other hand, volume of nano-SiO2 particles is greater than that of the micrometer SiO2 with equal weight, so it is easier that nano-SiO2 particles can spread into LiCd ferrites with uniform grain size. The grain growth behavior is a compromise between the driving force for grain

(a)

(b)

(c)

(d)

(e)

FIGURE 4.25 SEM micrographs of the system Li0.35Cd0.3 Fe2.35O4/nano-SiO2 (a) SiO2 ¼ 0%, (b) SiO2 ¼ 2%, (c) SiO2 ¼ 4%, (d) SiO2 ¼ 6%, (e) SiO2 ¼ 8%.

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boundary movement and the retarding force by pores (Kand et al., 1992). During the sintering process, a force is generated due to thermal energy which drives grain boundaries to grow over pores, thereby decreasing the pore volume and making material dense. When driving force of the grain boundary for each grain is homogeneous, the sintering body attains a uniform grain size distribution as in silica-added ferrite. Furthermore, strength of the driving force depends upon the diffusivity of individual grains, sintering temperature, and porosity. According to Visser et al. (1992) the nonmagnetic particles and trace amounts of impurities such as SiO2 mostly segregate at grain boundaries, forming a nonmagnetic grain boundary. Therefore, reduction in grain size of samples doped with nano-SiO2 > 2 wt% in LiCd ferrite nonuniform grain growth is observed. Porosity is also increased confirmed from SEM micrographs. This may be due to silica solubility in LiCd ferrite up to 2 wt% and for more than 2 wt% silica it begins to segregate at grain boundaries, to inhibit further grain growth and thereby increasing coercivity of the ferrite observed, as shown in Table 4.4. The values of Ms and coercivity (Hc) of Li0.35Cd0.3Fe2.35O4 are given in Table 4.4. For pristine Li0.35Cd0.3Fe2.35O4 the value of Ms is 73.7 emu/g. The value of Ms is observed to change nonmonotonically and a maximum of 2 wt% addition of nano-SiO2 is shown in Table 4.4. The variation in coercivity by the addition of SiO2 in spinel ferrite is reported by some researchers (Ding and Gong, 2001) as we observed it increases from 11.4 Oe to 16.8 Oe for SiO2 ¼ 6 wt%. The increase in magnetization Ms with nano-SiO2 up to 2 wt% may be due to the dilution of magnetization of the A-sublattice by nonmagnetic Si4þ ions in spinel-type LiCd sublattice model. After a certain limit of nano-SiO2, a sublattice is so diluted that the AeB interaction remains no longer stronger and thereby BeB sublattice interaction becomes stronger, which in turn disturbs the parallel arrangement of spin magnetic moments on the B-site and hence, spin canting occurs. Kotnala et al. (2007) reported influence of SiO2 on lithium ferrite that the excess of the amount of SiO2 starts to accumulate on grain boundaries, which may be another reason for the decrease of magnetization beyond SiO2 ¼ 2 wt% doping in Li0.35Cd0.3Fe2.35O4. With an increase in SiO2 concentration the Curie temperature of ferrite decreases drastically, it could be due to weak magnetic interaction between AeB sublattices by presence of more silica. The variation of real part of dielectric constant (ε0 ) and dielectric loss tangent (tan d) with respect to nanosilica concentration has been observed. It is found that the real part of dielectric constant (ε0 ) for Li0.35Cd0.3 Fe2.35O4 first increases and gets a maximum value about 8  103 for nano-SiO2 ¼ 2 wt% doping and moreover it starts decreasing by further increase in nano-SiO2 content. The addition of silicon dioxide increases dielectric constant of ferrite samples by enhancing material polarizibility. But in case of dielectric loss tangent (tan d) nano-SiO2-added sample attained minimum value of loss tangent in frequency range 104e106 Hz with higher resonance frequency. High

Composition

Curie
Temperature ( C)

Saturation Magnetic Moment Ms (emu/g)

Coercivity Hc (Oe)

Grain Size (mm)

tan d

SiO2 ¼ 0%

670

73.70

11.4

4.5

2.7

800

SiO2 ¼ 2%

515

79.39

12.9

9.0

0.5

7989

SiO2 ¼ 4%

440

78.06

12.0

7.2

0.4

3699

SiO2 ¼ 6%

300

40.63

16.8

5.5

0.8

2197

SiO2 ¼ 8%

225

38.56

15.8

4.3

0.9

1840

ε0

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TABLE 4.4 Properties of Nano-SiO2-Added Li0.35Cd0.3 Fe2.35O4

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356 Handbook of Magnetic Materials

dielectric constant and least dielectric losses are essential requirement of ferrite for power applications. Therefore small addition of nano-SiO2 ¼ 2 wt% in Li0.35Cd0.3 Fe2.35O4 is very useful for power application devices. This behaviour of dielectric properties may be explained qualitatively by the supposition that the mechanism of polarization process in ferrite is similar to that of conduction process. The electron-hopping model of Heikes and Johnston can explain the electric conduction mechanism Fe2þ 5Fe3þ þ e

(4.75)

In this model the electrons transfer between adjacent octahedral sites in spinel lattice has taken. One obtains local displacements of electrons in the direction of applied electric field which occurs due to displacement to determine the polarization of ferrite. It is known that the effect of polarization is reducing the electric field inside the medium. Therefore, dielectric constant of the material may decrease substantially as frequency increases. The variation of loss tangent (tan d) with frequency is explained from the following relation: tand ¼

1 2pf ε0 ε0 r

(4.76)

where f is the frequency corresponding to maximum value of tan d and r is the ac resistivity. It is found that addition of nano-SiO2 in a small amount reduced loss tangent of the Li0.35Cd0.3 Fe2.35O4 sample. Another class of additives elements used in soft ferrites is Nb2O3 and Ta2O5. The Nb2O5- and Ta2O5-doped lithium ferrite synthesized by conventional double sintering ceramic technique in which oxides or carbonates used as precursors (Yan and Johnson, 1978; Yan et al., 2007). Such attempts have shown grain growth in the microstructure of ferrites with a small enhancement in magnetization.

11. MAGNESIUM FERRITE AS HUMIDITY SENSOR The fundamental property of the ceramic humidity sensing material is due to surface sensitivity and porous microstructure. A wide variety of materials has been explored as sensing elements in humidity sensors and used for commercial devices. The choice of a suitable material is difficult, and should be based on materials that show good sensitivity over the entire range of humidity, low humidity hysteresis, and exhibit properties that are stable over time and thermal cycling, besides their inertness on exposure to the various chemicals likely to be present in the environment (Kulwicki, 1991). Conventional humidity sensing materials are slow, less sensitive, less reliable, and suffer from large hysteresis effects. The problem for ceramic oxide humidity sensors is mainly associated with periodic regeneration by heat cleaning to recover their humidity-sensitive properties. Since prolonged exposure to

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humid environments leads to the gradual formation of stable chemisorbed OH on the surface, causing a progressive drift in the resistance of the ceramic humidity sensor. The hydroxyl ions are removed by heating to temperatures higher than 400
C (Morimoto et al., 1969). Moreover, humidity sensors are usually exposed to atmospheres that contain a number of impurities, such as dust, dirt, oil, smoke, alcohol, solvents. The adhesion or adsorption of these compounds on the ceramic surface causes irreversible changes in the sensor’s response. Contaminants act in the same way as chemisorbed water, and may be removed by heating, too. Commercial sensors based on ceramic sensing elements are equipped with a heater for regeneration (Nitta, 1981). The surfacerelated phenomena of humidity sensing by ceramic oxides make these materials less resistant than polymers to surface contamination because of their porous structure (Traversa, 1995). Magnesium ferrite is a porous material possesses large specific surface area and has high electrical resistance of the order of 107 U. If the sensing material has low electrical conductivity, it is difficult to measure the impedance in low-humidity environment. On the other hand, if it has high electrical conductivity, the humidity dependence becomes relatively too small to be measured conventionally. Therefore, it is desirable that the impedance of the sensing material changes linearly from 107 to 104 U as relative humidity increases. As mentioned above, the interest of sensing materials consists in the change of their electrical properties in presence of water vapors. Depending on the materials, this change can be due to surface conduction effects. After water vapor adsorption on material surface Hþ ions hop from one water molecule to next neighboring molecule forming hydronium ion (H3Oþ) as indicated in following reactions (Chen and Lu, 2005): 2H2 O5H3 Oþ þ OH

(4.77)

H3 Oþ 5H2 O þ Hþ

(4.78)

11.1 Linear Humidity Sensing by Ceria-Added MgFe2O4 Oxygen vacancies play an important role for the performance of ceria as an oxygen storage material and as a redox catalyst. The oxygen vacancy formation in ceria results in partial reduction of the material where the two electrons, left when removing a neutral O atom, reduces Ce4þ to Ce3þ. An interesting finding by Jyoti Shah et al. (2007) for humidity sensing of magnesium ferrite has been reported. Addition of cerium oxide to pure MgFe2O4 showed an increase in sample resistance and its sensitivity to humidity at low RH. The 4 wt% cerium oxide addition shows a good linearity of log R in a wide RH range as shown in Figure 4.26. The shortest time for desorption has been observed with 6 wt% cerium oxide addition due to some uniformity in pore size distribution as described in Table 4.5.

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FIGURE 4.26 log R versus relative humidity of pure and CeO2-added MgFe2O4 samples.

11.2 Lithium-Substituted Magnesium Ferrite for Humidity Sensing A one step solid-state synthesis method for lithium substitution in magnesium ferrite has been investigated for nano-size grains synthesis extensively by Kotnala et al. (2008). Humidity sensitivity of pure magnesium ferrite was found to increase with the lithium substitution due to the large surface area, high surface charge density, and open pores formed on the bulk surface of the samples prepared. Dissolution of Liþ ions in spinel lattice facilitates quicker nucleation leading to smaller grain size distribution. Pore size distribution become smaller with lithium substitution than the pure magnesium ferrite shown in Scanning Electron Microscopic images as Figure 4.27. The peak intensity increased in FT-IR spectra with lithium concentration confirmed its diffusion in the octahedral sites shown in Figure 4.28. The highest humidity sensitivity has been recorded for x ¼ 0.2 lithium ion substitution, but the response time was longer than the pure magnesium ferrite. The change in resistance of compositions at 10%RH and 80%RH is described in Table 4.6.

11.3 Significant Increase in Humidity Sensing of MgFe2O4 by Praseodymium Doping Along with porosity, the surface charge density also acts as a critical parameter for initial water vapors dissociation. The dissociation of water vapors provides proton for the conduction; hence resistance of the sensing material decreases. For the surface charge density enhancement the addition of alkali ions greatly

Response Time (s)

Sample

Bulk Density (g/cm3)

Pore Size (mm)

Grain Size (mm)

MgFe2O4

4.4

0.15e0.16

0.4e0.5

MgFe2O4 þ 2wt%CeO2

3.3

0.3e0.8

0.6e1

MgFe2O4 þ 4wt%CeO2

3.8

2e5

MgFe2O4 þ 6wt%CeO2

3

0.15e1.5

Porosity % 2.5

Adsorption

Desorption

80

100

23

130

300

3e8

14

160

300

0.3e1

26

130

150

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TABLE 4.5 Some Useful Structural Parameters of CeO2-Added Magnesium Ferrite

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360 Handbook of Magnetic Materials

(a)

(b)

(c)

(d)

FIGURE 4.27 SEM micrographs of (a) pure MgFe2O4, (b) Mg0.8Li0.2Fe2O4, (c) Mg0.6Li0.4Fe2O4, (d) Mg0.4Li0.6Fe2O4.

FIGURE 4.28 The FTIR spectra of (a) MgFe2O4, (b) Mg0.8Li0.2Fe2O4, (c) Mg0.6Li0.4Fe2O4, and (d) Mg0.4Li0.6Fe2O4.

improved the sensitivity over the entire range of RH. The intensity of Electron Paramagnetic Resonance plot is proportional to the concentration of unpaired spins in the material. Effect of spin density on initial water vapor adsorption has been explored by Shah et al. (2011). They have reported a nominal doping of Pr in magnesium ferrite enhanced the spin density shown in Table 4.7.

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TABLE 4.6 Change in Resistance of the Samples at 10%RH and 80%RH % RH

MgFe2O4

Mg0.8Li0.2Fe2O4

Mg0.6Li0.4Fe2O4

Mg0.4Li0.6Fe2O4

10%

46.7 MU

43.2 MU

564 MU

569 MU

80%

0.378 KU

261 KU

38.4 KU

6.8 KU

Gradient jdlog R/dRHj for low 10e30%RH and high 70e90%RH of Pr-doped MgFe2O4 composition as a function of spin density and porosity % have been determined. They have analyzed that effective spin density influenced the water vapor adsorption more than porosity at lower RH as shown in Figure 4.29(a). At 70e90%RH gradient jdlog R/dRHj showed, Figure 4.29(b), abrupt increase with porosity than the spin density due to capillary condensation of the open pores at a high-humidity enhanced protonic conduction in physisorbed layers. At lower humidity unpaired spins on the sample surface play an active role for water vapors saturating the unsaturated bonds. A drift in resistance of 22%RH at 50% relative humidity and a 7%RH drift at 80% relative humidity have been reported for pure magnesium ferrite. Humidity hysteresis drastically decreased by Pr doping compared with undoped sample, as least area enclosed in hysteresis is a crucial parameter for precision measurement of humidity in sensors. Table 4.7 depicts structural and electrical properties of Pr-doped magnesium ferrite for different doping concentration.

11.4 Humidity Sensing Mechanism Exploration on Magnesium Ferrite by Heat Equation The increase in conductivity of porous materials with humidity has been explained on the basis of chemisorption and physisorption of water vapor on the material surface (Cukierman, 2006; Yamazoe and Shimizu, 1986). Chemisorption and physisorption of water vapors are associated with heat exchange during adsorption process. Heat energy involved for water vapor adsorption can be calculated by determining isosteric heat of adsorption. The magnitude of heat energy gives an understanding of adsorption process of a gas/vapor on adsorbent material. Water vapor adsorption energy has been determined either by direct calorimetry method or indirectly by fitting ClausiuseClapeyron heat equation to isothermal data (Gravelle, 1978). Conduction mechanism due to physisorption of water vapor on magnesium ferrite has been experimentally confirmed by measuring isosteric heat of adsorption by Shah and Kotnala (2012). Analysis of isosteric heat of adsorption (<0.1 eV) revealed conductivity of magnesium ferrite increased due to physisorption of water vapors when exposed to humidity. Physisorption is entirely a reversible phenomenon resulting in to least humidity hysteresis during adsorption and

Sample

Lattice Constant (A˚)

Bulk Porosity %

Grain Size Distribution

Pore Size Distribution

Sensitivity Factor Sf R10%/R90%

Spin Density  1020 per gm

MgFe2O4

8.340

8.4

75nme1 mm

15e450 nm

24

8.15

0.1 mol% Pr6O11

8.335

24

150nme1.5 mm

45e600 nm

79

11.02

0.3 mol% Pr6O11

8.335

34

150nme1.5 mm

30e300 nm

113

15.60

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TABLE 4.7 Structural and Electrical Properties of Pr-Doped Magnesium Ferrite for Different Doping Concentration

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FIGURE 4.29 (a) jdlog R/dRHj versus spin density (1020) and bulk porosity% for low 10e30% RH range at the interval of 10%RH. (b) jdlog R/dRHj versus spin density (1020) and bulk porosity% for high 70e90%RH range at the interval of 10%RH.

desorption process. Hence, no drift in conductivity values will occur with variation in relative humidity. Furthermore it explains humidity sensitivity of porous magnesium ferrite in a better way to support fast response and less recovery time observed experimentally. Predominant physisorption of water molecules on magnesium ferrite surface and protonic conduction mechanism have been reported by isosteric heat of adsorption, relative humidity hysteresis plots, and impedance spectroscopy. For describing the process of adsorption the isosteric heat of adsorption is an important parameter. The isosteric heat of sorption is a measurement of the energy or intermolecular bonding between water molecules and absorbing surfaces. It is difficult to

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measure the thermal properties of adsorption process; therefore heats of adsorption of gases are usually derived from adsorption isotherm using ClausiuseCleyperon heat Eqn (4.79). Adsorption isotherms coverage (conductance in this case) versus pressure at a constant temperature can be used to calculate heats of adsorption.

 qst 1 (79) LnðPÞ ¼  R T Magnesium ferrite compound followed the Freundlich isotherm with an exponential decrease in isotherm as shown in Figure 4.30. This model assumes the multilayer adsorption. In addition, value of heat of adsorption is low 0.14 eV at low humidity 10%RH indicating binding between adsorbateeadsorbent is physical force (<0.1 eV). Moreover, physisorption from a gas phase does not involve activation energy while chemisorption involves as binding energy. For physisorption binding energy lies in the range 0.01e0.10 eV while for chemisorption between 1 and 10 eV. There is no chemisorption phenomenon in magnesium ferrite as it requires high interaction energy (>1 eV).

11.5 Magnesium Ferrite Thin Films No one has exploited magnesium ferrite thin film for humidity sensing prior to this report despite bulk magnesium ferrite is a highly sensitive material for humidity sensing. Most of the research and development work is being pursued for humidity response of TiO2, Al2O3, ZrO2, BaTiO3, and polymers thin films (Biju and Jain, 2008; Gumano et al., 1996). Exploitation of magnesium

FIGURE 4.30 Exponential decrease in isosteric heat of adsorption of magnesium ferrite with increase in relative humidity.

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ferrite thin film for humidity sensing is highly beneficial for technological point of view. For humidity sensor, a better choice of magnesium ferrite thin film Kotnala et al. (2011) reported RF sputtered thin films. Humidity response of magnesium ferrite thin films annealed at different temperature has been explored. For humidity sensing polycrystalline and porous film has been found to be highly sensitive. Film annealed at 800
C showed a linear log R (Ohm) response toward the entire humidity range 10e90%RH. Fastest response time 4 s and recovery time 6 s was observed for 800
C annealed film. A least area in humidity hysteresis has been recorded for 800
C annealed thin film for good repeatability of its sensing characteristics as shown in Figure 4.31. Table 4.8 exhibits humidity-sensing properties of thin film.

FIGURE 4.31 temperature.

Humidity hysteresis curve for magnesium ferrite thin films annealed at different

11.6 CHR by Ceria-Added Magnesium Ferrite Thin Film by Pulsed Laser Deposition There are different thin film deposition techniques named as RF sputtering, Pulsed Laser Deposition, Metal-Organic Chemical Vapor Deposition, spin coating and dip coating, and so on. Different types of thin film deposition techniques have certain advantages and disadvantages. Among all thin film deposition techniques, PLD technique possesses versatile features in terms of good quality, uniformity, repeatability and is very attractive for stoichiometric oxide films. Contrary to deposit good quality crystalline oriented thin films, PLD is also used to deposit porous as well as columnar grown thin films (Infortuna et al., 2008; Tsoi et al., 2004). PLD-grown thin films have been also explored for change in resistance when exposed to gas and humidity

Annealing Temperature

Average Particle Diameter Distribution (AFM) (mm)

Pore Size Distribution (AFM) (mm)

RMS Roughness (nm)

Sensitivity Factor (Sf) R10%/R90%

Response/ Recovery Time (s)

400
C

0.1e0.5

0.01e0.2

51

2269

10/16




0.2e0.6

0.05e0.3

64

9090

8/15




0.5e0.9

0.07e0.9

87

20,888

4/6

600 C 800 C

366 Handbook of Magnetic Materials

TABLE 4.8 Annealing Temperature-Dependent Microstructural and Humidity-Sensing Properties of MgFe2O4 Thin Films

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FIGURE 4.32 Change in resistance (LnR) with increasing relative humidity (%RH) for pure and Ceria-added magnesium ferrite thin films.

(El Khakani et al., 2001; Kumar et al., 2006). The choice of humidity/ gas-sensing material film is equally important from its strategic applications. A colossal change in resistance has been observed in 1 wt% ceria-added magnesium ferrite thin film by exposing it in humidity present in atmosphere. A seven-order (w107) decrease in resistance has been reported by Kotnala et al. (2013) for such film. The humidoresistance [R(0%RH) R(95%RH)]/R(95%RH) measured 3  106 for 1 wt% ceria-added magnesium ferrite film. The resistance of 1 wt% Ce:MgF thin film was 1.8 TOhm at 10%RH which decreased to 754 KOhm at 95%RH exhibiting approximately a seven-order decrease in resistance. A 3  106 humidoresistance has been observed for Ce-doped MgF thin film which has been shown in Figure 4.32. It has been observed 70e80% humidoresistance contribution of the total decrease in resistance is in the range for 0e50%RH. Small drift in humidoresistance response is observed with decrease in %RH on film.

12. PERVOSKITE FERRITE AS MULTIFERROICS In intrinsic multiferroic materials there exists a single phase where at least two ferroic-order parameters show spontaneous ordering. Materials exhibiting simultaneously ferroelectric and ferromagnetic properties have proven to be rare. Although BiFeO3 is one of the extensively used orthoferrite for multiferroic application for its room temperature existence of ferroelectricity and weak ferromagnetism. However, experimentally often a low value of polarization has been obtained for BiFeO3 due to oxygen vacancies which ultimately

368 Handbook of Magnetic Materials

lead to high dielectric losses (Ederer and Spaldin, 2005). Among single-phase compound antiferromagnetic rare earth ferrite has been investigated for multiferrocity. The magnetoelectric coupling between magnetically active substituted rare earth ion and Fe3þ from first-principles calculations the contribution of rare earth orthoferrite (RFeO3) to the observed magnetization are reported. Spin-driven ferroelectricity has been explored in rare earth orthoferrites. Spin-exchange striction between Gd and Fe resulted into ferroelectricity in GdFeO3 near 2.5 K exhibited magnetoelectric coupling (Skinner, 1970). Room temperature multiferrocity in SmFeO3 is reported due to inverse D-M interaction between Fe spins (Lee et al., 2011). Surface defects in nanosized oxide materials induce ferromagnetism opening the possibility to make ferroelectric barium titanate to be ferromagnetic (Banerjee et al., 2011; Mangalam et al., 2009). However, the coexistence of ferromagnetism, ferroelectricity, and strong coupling is rarely satisfied in single-phase magnetic multiferroic compound with a great challenge in this field. It has been proposed that such a strong coupling can be realized by incorporating ferroelectric material with magnetic compounds by making composite thin films by inducing coupling through stress/strain mediation (Run et al., 1974). The stress/strain-mediated magnetoelectric effect has been observed in particulate, laminated, and nanostructure composites (Jedrecy et al., 2013; Srinivasan et al., 2002; Verma et al., 2009; Verma et al. 2008, april). Investigations of multiferrocity in bilayer ferromagnetic and ferroelectric thin films have been a great interest for research (Geprags et al., 2013; He et al., 2006; Kotnala et al., 2009; Li et al., 2009; Tian et al., 2008; Verma et al., 2009). A multilayer (ML) structure is expected to be far superior to bulk composites due to lowresistivity ferromagnetic phases reduce the overall magnetoelectric coupling and the piezoelectric layer in a multilayered structure, which can easily be poled electrically to further enhance the magnetoelectric coupling (Zheng et al., 2004). NdFeO3-PbTiO3 thin film has been investigated for magnetoelectric effect (Li et al., 2013). The voltage induced in single-phase multiferroic compounds is very low to be implemented in device application. Thus a second class of multiferroic combining two phases, ferrite and ferroelectric as composite material has been investigated to achieve practically applicable signal. There have been several studies on compositions of ferroelectric PbTiO3 and BaTiO3 with various ferromagnetic spinel ferrites. CoFe2O4 has been the most explored spinel ferrite with ferroelectric compound as nanopiller, nanostructured, and bilayer structure (Mitoseriu, 2007).

12.1 Bismuth Ferrite Bismuth ferrite is one of the most extensively investigated multiferroic magneto-electric compounds in which 6s lone pair electrons of Bi are believed to be responsible for ferroelectricity while partially filled d orbital of Fe leads to magnetic ordering. BiFeO3 has a rhombohedral structure R3c

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˚ ) at room temperature. The ferro(a ¼ b ¼ g ¼ 59.4
, a ¼ b ¼ c ¼ 5.63 A electric polarization of bismuth ferrite aligns diagonals of pervoskite unit cell ([111]pesudocubic/[001]hexagonal). The ferroelectricity in bismuth oxide is less due to leakage current (oxygen vacancies). The local short-range magnetic ordering of BiFeO3 is G-type antiferromagnetic whereas each Fe3þ spin is antiparallel to adjacent Fe3þ spins. The spins are in fact not perfectly antiparallel as there is a weak canting moment caused by the local magnetic coupling to the polarization. This canting superimposed, however, is also a long-range superstructure consisting of an incommensurate spin cycloid of the antiferromagnetically ordered sublattice. Other properties of interest are ferroelectric Curie temperature (Tc ¼ 1043 K) and Neel temperature (TN ¼ 647 K), which make them attractive for room temperature spintronic applications. Being a room temperature ferroelectric and weak ferromagnetic BiFeO3 is a unanimous choice for multiferroic application (Gautam et al., 2011). Although getting pure phase BiFeO3 sample is not an easy task. Hence to improve resistivity of BFO its solid solution with ferroelectric compound has been well studied (Singh et al., 2008a,c).

12.2 Gadolinium Ferrite Gadolinium ferrite (GdFeO3) compounds are very useful at GHz range applications, therefore to exploit multiferrocity at high frequencies is very much needed, if garnet can be converted into multiferrocity. In this direction Shah et al. have worked to get multiferrocity in GdFeO3 by Mg substitution (Shah and Kotnala, 2012). GdFeO3 crystallizes in Pbnm space group which is a distorted perovskite and exhibits weak ferromagnetic properties. However, recently it is reported that some RFeO3 systems such as EuFeO3 and GdFeO3 prepared by a low-temperature chemical route exhibit better ferromagnetic properties (Xu et al., 2008). The magnetic properties of rare earth orthoferrites are interesting because of the magnetic interactions of the two different types of magnetic ions: Fe3þ and R3þ. The competition of FeeFe, ReFe, and ReR interactions leads to a few interesting phenomena in these materials. At high temperatures the magnetic properties of RFeO3 systems depend mostly on the FeeFe interactions leading to an antiferromagnetic-type ordering with Neel temperature ranging from 620 to 740 K (Landolt-Bo¨rnstein 1994; White, 1969). As the temperature is lowered to about 100e200 K the competition of the FeeFe and ReFe interactions (Yamaguchi, 1974) leads to a so-called spin reorientation transition of the ordered Fe3þ magnetic moments. Spin reorientation is a more general phenomenon observed in many compounds containing rare earth and iron ions.

13. SPIN PUMPING INDUCED SHE Generation of spin current by ferromagnetic resonance in ferromagnetic/ paramagnetic bilayer thin film without flow of electric current across the

370 Handbook of Magnetic Materials

FIGURE 4.33 Schematic illustrations of flow of spin current Js and charge current Jc in Co/Pt bilayer thin film on Si substrate.

interface opens possibilities of low power consumed spintronic devices. Spin waves generated by resonance in conducting ferromagnetic layer experience scattering which cause less spin diffusion length. Microwave induced spinHall effect of Co/Pt bilayer thin film showed maximum dc voltage 5.78 mV at 0.1 GHz (Ahmad et al., 2013). Schematic diagram of spin pumping induced spin current injection into metallic film produces charge current as shown in Figure 4.33. Thus low magnetic loss dielectric Ytterium Iron Garnet has been extensively experimented for SHE since longer spin wave length generation in it due to weak spin damping (Kajiwara et al., 2010; Padro´nHerna´ndez et al., 2011; Weiler et al., 2013).

ACKNOWLEDGMENTS Dr. R. K. Kotnala specially thanks to Director CSIR-National Physical Laboratory, New Delhi, for all scientific support provided to enrich experience in the field. Thanks are also due to all Ph. D students/researchers associated with Dr. Kotnala. Authors are indebted to “Elsevier” for using some of the figures, data, and tables from our own papers published in Elsevier Journals.

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