Preparation, characterization and investigations of electrical and magnetic properties of some ferrites

CONTENTS

1 Introduction to ferrites
1.1 Introduction and scope of the work
1.2 Problem statement
1.3 Theory of magnetism
1.4 Ferrites
1.5 Background
1.6 Motivation and aim of the present work
1.7 Materials under consideration
1.8 Objectives and outlline of thesis

References

1 Introduction to ferrites

I take this opportunity to thank all the people who have helped me and who continue to inspire me.

In the first place, Prof. (Dr.) K. M. Jadhav, is the most influential person in my academic life, as parents gave life to my body whereas Jadhav sir gave life to my soul. You are guided me through the academic challenges and supported me in every aspect of my research and professional endeavors. You seem to have the magic power to grasp the essentials and make complicated things simple. You are also taught me to aim high, to be persevering, and above all, to embrace scientific challenges with passion and enthusiasm. I thank you for your insight, guidance and caring support, and for so much I have learned from you. I shall always look up to you for inspiration.

I am truly grateful to Prof. S. H. Behere, Prof. G. K. Bichile, Dr. D. R. Shengule who has shown an avid interest in my work and supported me at the very beginning of my academic adventure. I am also deeply indebted to Dr. S. J. Shukla for showing interest in my academic progress all through these years, your timely advice and guidance will always be appreciated.

Thanks to Hon’ Shri. Shrimantrao P. Shisode (Secretary), Shri. Ajitbhau Shisode (President) and Shri. Prabhakar More of Vivekanand Shikshan Sanstha, Dr. B. S. Salunke (Principal), Dr. (Smt.) Warudkar (Vice-principal) of Vivekanand College, Aurangabad for their kind support in my academic activities.

Bhagwan Toksha for the unwavering encouragement and generous assistance. The encouragement and enthusiasm you showed was surpassed only by your patience and willingness to extend a helping hand without restraint. You have shown me the way to be an excellent researcher. Thank you very much.

I also want to thank Dr. S. M. Patange for clarifying many questions when I first started this work. I will never forget his kindness and encouragement. Dr. Ram Kadam for introducing me with Jadhav sir and thank you for your support and believing in my capabilities. Sincere appreciation is extended to Dr. Suresh Alone, Dr. Santosh Jadhav, Dr. Asif Karim and Tids for their constant interests in my work and their invaluable friendships over the years.

I thank all the members in the Prof. Jadhav’s ferrite group and my lab buddies for showing me different aspects in different disciplines. Especially, I want to thank Atul, Mahesh, Vinod and Vishnu. The collaboration with them has been very enjoyable and fruitful. My thanks also go to the current and former members in Prof. Jadhav's group.

Many thanks are also due to Anil Gaikwad for sharing his expertise in solid-state materials. I am grateful to come across several life-long friends Vitthal, Manoj, Bharat, Santosh for sharing my joy and sadness, and offering instant help whenever needed. My college colleagues Raut sir, Aghav sir, Ahire sir, Chaudhari sir, Ganorkar madam with whom I have learned much and received a lot of help.

This work has benefited from the use of characterization facility from TIFR (Mumbai), Pune University (Pune), Shivaji University (Kolhapur), Central University (Hyderabad).

My deepest gratitude goes to Late Marutirao Jadhav and Late Sushilabai Jadhav for unflagging love and support in my early part of research; my doctoral study is simply impossible without their blessings. Although they are no longer with us, their few sentences and suggestions are forever remembered.

Finally, I would like to give my special thanks to my family for their unconditional love and for always believing in me. Without their support, I can not go through the difficulties I encountered. They have supported me in innumerable ways throughout my life and education, I owe all my accomplishments to them. I am indebted to my father, Shri. Eknathrao Shirsath, for your care and love, your trust, understanding and support are always the power for me to move on. I feel proud of my brothers, Prashant and Sandip, for your talents. You have been a role model for me and have always been my best counselors. You are also my “Field Support Engineer” on computer issues. My sister-in-law Sow Purva, I remember, most of all, your delicious dishes. I am especially grateful to Jui, who has been my 24/7 entertainment support, and above all, my source of happiness. I am lucky to have she as my niece.

I cannot ask for more from my mother, Sow Suman, as you are simply perfect. I have no suitable word that can fully describe your everlasting love to me. I remember your constant support when I encountered difficulties, for your love, patience, dedication and encouragement during all the process of my dissertation and during all over my Master’s course. The person I am today is because of you. I love you.

Thanks to all people who help me in completing my Ph. D. study I did not mention above.

Last but not least, thanks to my patience and life for this wonderful experience.

Sagar Eknathrao Shirsath

Declaration

I hereby declare that the research work submitted in the form of thesis entitled “Preparation, characterization and investigations of electrical and magnetic properties of some ferrites” has not been earlier submitted by me for the award of any other diploma or degree of this or any other university. The present research work is completely original to the best of my knowledge.

Place: Aurangabad Mr. Sagar E. Shirsath

Date: / / Research Student

illustration not visible in this excerpt

CERTIFICATE

This is to certify that the research work entitled, “Preparation, characterization and investigations of electrical and magnetic properties of some ferrites” is original and carried out by Mr. Sagar Eknathrao Shirsath under my guidance. Further, it is certified that this work has not been submitted for the award of any other degree or diploma of this university or any other university either in part or in full.

Date: / /2009 Prof. (Dr.) K. M. Jadhav

Place: Aurangabad Research Guide

1.1 Introduction and scope of the work

A continued interest in the synthesis of inorganic compounds with well- defined properties such as shape, size, polymorph modification, etc. exists in inorganic chemistry and material science. Inorganic materials produced with this mode of thinking will have advantages in areas of application where uniform size distribution and specific surface and bulk properties are key factors.

In hierarchy of materials science, ferrite material is usually believed to be fully grown in all fields of science, technology, and application. State of the art and trends in development of ferrite is truly impressive. Ferrite, the soft magnetic materials is available in numerous classes and types. Ferrite materials are recognized as more important and essential for the further development of electronics than before, and it is believed that the production of ferrites will increase by leaps and bounds as their applications become more diverse. Reviewing past of ferrite, accurately analyzing its present situation, and then thinking of future possibilities will add greatly to further development in the future. A meager but honest, rejoicing effort is thought to be necessary.

Amongst the magnetic materials, soft magnetic ferrite accounts for 22% of high-tech applications, including digital communications, EMC, RF broadband, EMI, HD displays, and auto electronics, while traditional mid- and low-end products for the rest 78%, such as TV sets, adapters of power supply, electronic ballasts, transformers for common switching power supply, and aerial rods [1]. The importance of magnetic materials in our daily life ranges from electric motors and magnetic storage devices to Brio toy trains. Research into the synthesis and characterization of magnetic materials has been conducted for more than a century. Ferrites in general are synthesis by solid- state reaction technique. The important properties of ferrites are depend on synthesis parameter and nature of dopants. There are a number of approaches to control different synthetic parameters for achieving the set targets, examples of them include

- Control of reaction conditions (temperature, concentration of reagents, pressure) during the formation of inorganic materials, [2-4]
- Usage of organic additives such as biopolymers, surfactants, polyelectrolytes, and block copolymers forming supramolecular templates to modify the crystallization process, [5-8] and
- Strategies based on the utilization of the restricted (microscale as well as nanoscale) reaction environment [9-14].

The ferrite material consists of iron oxide as their main constituent along with metal ions, are the most important magnetic materials due to their excellent twin property of electrical insulator and magnetic conductor. The focus of global magnetic materials (like ferrite) production seems to erupt very rapidly due to their numerous applications. Ferrites are the only magnetic materials available for various applications. The applications of ferrite depends on various electrical and magnetic properties. Large number of work has been carried out on ferrite to understand their basic structural, electrical and magnetic properties, which depends on various parameters. The magnetic properties are found to depend on cation distribution at A and B site. So, study of cation distribution in spinel ferrite is important to understand the magnetic behavior. IR spectral studied can provide information on cation distribution, Debye temperature and elastic properties. Wide scope is available to study these aspects of ferrite which at present to our knowledge was not probe by researchers. In relevance to the ever expanding possibilities, and potential that is available with the ferrite materials, the scope of presently undertaken work is designed carefully by selecting suitable ferrite and dopants. A sincere attempt is made to extract fruitful, exhaustive and, systematic information regarding structural, cation distribution, electrical, dielectric and magnetic aspects of the systems under investigations.

1.2 Problem statement

One of the most important tasks in the field of materials science research is the selection of proper material, choice of dopant, synthesis method and techniques used for the characterization with regard to any tailor made applications. Inappropriate or improper decisions made in selection of materials can be disastrous from both economic and safety perspectives. The selection may start with the primary suitable stage which is thought to satisfy most of the initial conditions which are going to be imposed on the final product. Once the primary target is set, one needs to select the other extreme end within the field of interest. A number of permutations and combinations can now be selected which are considered to take the material to the next advantageous stage.

Apart from the conventional approach practiced to re-evaluate the basis for the properties of materials that had long been useful, the new approaches provided much more important dividends. The ever-expanding knowledge of materials science and chemistry involved in it, made it possible not only to improve upon those properties by varying composition, structure and relevant factors in controlled amounts, but revealed the existence of completely new materials that frequently turned out to be exceedingly useful than their parent materials.

Spinel structure has tetrahedral A-sites and octahedral B-sites in AB2O4 crystal structure. Various cations can be placed in A site and B site to tune its properties. Covalent contribution in the metal-oxygen bond is also a major concern to govern the distribution of ions over available lattice sites. Therefore, the actual ionic partition may or may not be predicted on the basis of site preference of individual cations alone [15].

After the pioneering work done by Gorter [16] that comprised a detailed investigation on magnetic moments of various ferrites, different investigators on this subject have made a number of efforts by substituting different valence ions [17-18] as a mean to modify the net magnetization of the system. Earlier such studies indicated that trivalent ions like scandium, aluminium, chromium etc. have considerable influence on the magnetization of certain ferrite systems [19-21]. The improvements in these substituted ferrites have been ascribed to the site preferences of these ions [22-24].

The electrical and magnetic properties are the most important properties for ferrites that depend on the processing conditions, sintering temperature and time, chemical composition and the amount and type of the additives [25]. The resonance frequency is known to depend on the amount and type of dopant ions [26-28]. It is well known that when ferrites are sufficiently diluted with non-magnetic atoms they can show a wide spectrum of magnetic ordering from ferrimagnetism, antiferromagnetism, local canted spin (LCS) to semi-spin glass and spin glass type magnetic ordering [29-30]. The absorption bands in spinel ferrites mainly arise from lattice vibrations of oxide ions with cations, producing various frequencies of unit cell. The frequencies of the vibrations are decided by the parameters like cation oxygen bonding, lattice constants and cation mass. The infrared spectral studies of ferrite materials can be used to study the ordering phenomenon as a function of dopant concentration. Ample research scope in this direction seems to be available. The possible presence of Fe[2]+ ion and its influence on far-infrared spectra can also be studied.

Considering the existing knowledge of nature of all the three selected dopants in the present study and, the change their substitution in nickel ferrite may brought in is sensed and, we tried to connect the role of dopants of varying valence state of 2+, 3+, and 4+ of the dopants with properties of synthesized materials.

1.3 Theory of magnetism

Magnetism is a phenomenon through which materials assert an attractive or repulsive force or influence on other materials. One of the fundamental concepts in magnetism is the magnetic field. A field is generated in a volume of space when there is a change in energy of that volume. The force produced by the energy gradient can be detected by the acceleration of an electric charge moving in the field, by the force on a current-carrying conductor, or by the torque on a magnetic dipole [31]. A magnetic field is produced when there is electric charge in motion. Analogous to the electric field, the magnetic effect may be regarded as due to so-called magnetic dipoles in a permanent magnet [31, 32] , or as originating from flowing electrical currents (Oersted, 1819).

1.3.1. The Bohr theory of magnetism and spin moments

The quantum theory of matter (Niel Bohr, 1913) postulates that the electron orbit around the nucleus of the atom originates the magnetic behavior of matter (Figure 1a). The basic unit of electron magnetism is called the Bohr magneton (μB= 9.27x10-21 erg/Oe), which is the result of the orbital motion of one electron in the lowest orbit. However, the Bohr theory did not provide a complete description of the origin of magnetism. In 1925 and 1926, Goudsmit and Uhlenbeck respectively, introduced the concept of electron spin, which better explains the origin of magnetism. Spin corresponds to movement of electric charge in the electron, hence an electric current which produces a magnetic moment in the atom (Figure 1b). The net magnetic moment is the vector sum of the individual spin and orbital moments of the electrons in the outer shells [31].

illustration not visible in this excerpt

Figure 1: Classical and quantum origin of magnetism

The electron spin may adopt two modes which are commonly represented as arrows pointed up or down. In an atom, mutually opposed paired spins cancel and do not result in magnetic moment, while the unpaired spins will give rise to a net magnetic moment. Table 1 shows the number of Bohr magnetons for some ions [33].

Table 1: Bohr magneton and ionic radii in ions commonly found in magnetic materials

illustration not visible in this excerpt

1.3.2. Magnetic field and magnetic moment.

A magnetic force is exerted on moving electrically charged particles in a magnetic field [34]. This is called the Lorentz force f and relates a charge q which is moving in the magnetic field B at a velocity v by equation (1.1), as illustrated in Figure 2 [35].

illustration not visible in this excerpt

Figure 2: Lorentz force due to a movement of charge through a magnetic field

Ampère showed that a magnet could be replaced by an equivalent current which exerts forces on other currents. In this manner, the magnetic field can be manipulated easily. The measurements of Ampère were quantified by Biot and Savart by showing that the magnetic field B at a distance r from a charge in movement is

illustration not visible in this excerpt

where, μ0 is the space permeability (4π×10-[7] Henry/m). The SI unit of B is Tesla. Atomic currents (generated from orbiting electrons and spin contributions) are analogous to the electric dipole and may be considered as resulting from a small circulating current of magnitude I, and loop area dS (Figure 3).

The magnetic dipole moment m is the vector in the direction perpendicular to the loop with magnitude given by m =IdS. (1.2)

The resulting magnetic field is

illustration not visible in this excerpt

Equation (1.3) is identical to the field due to an electric dipole when one replaces μ0m by ρ/ε0.

illustration not visible in this excerpt

Figure 3: Schematic of magnetic dipole whose magnetic moment m is in the direction normal to loop

Ampère postulated that magnetic materials are composed of infinitesimal circulating current loops (Figure 4) with number density N. The magnetization vector M is defined as the magnetic dipole density:

illustration not visible in this excerpt

In SI, M has units of A/m.

As is illustrated in Figure 4, only the dipoles on either side of the edges contribute a net current through the loop.

Assuming that the dipoles along the edge do not change magnitude or direction, the total current in the z direction linked by the edges (x and x + Δx) is given by

illustration not visible in this excerpt

If Δx andΔy become small, equation (1.6) can be written as

illustration not visible in this excerpt

where Jz is the z component of the curl of the magnetization. In general, the current density or Amperian current density (generated by the motion of bound charges in a material) is given by

illustration not visible in this excerpt

Considering that magnetic fields can also be generated by these currents, Ampère’s law is written as

illustration not visible in this excerpt

where,

J f is the free current generated by the motion of free charges.

The magnetic field intensity H may be defined with respect to the magnetic flux density B by

illustration not visible in this excerpt

which we may replace in equation (1.9) to obtain

illustration not visible in this excerpt

In free space, M=0 hence B= μ0H. In SI units of H is A/m.

illustration not visible in this excerpt

Figure 4: Model for magnetic materials postulated by Ampère.

The free current density Jf generates the H field, whereas the magnetization current density Jm generates the M field. The total current (Jm +Jf ) is the source of the B field [35], multiplied by μ0 to change units.

Another concept commonly encountered is the magnetic flux Φ, which quantifies the magnetic field through a surface

illustration not visible in this excerpt

1.3.3. Magnetic behavior

Magnetic materials can be classified based on differences between their internal and external flux and the variation of the magnetization M or magnetic induction B when a magnetic field is applied (Figure 5) [34, 36]. There are two quantities that relate M and B to H: the susceptibility χ and the permeability μ:

illustration not visible in this excerpt

illustration not visible in this excerpt

In SI the permeability μ has units of Henry/m. The susceptibility is a measure of the increase in magnetic moment caused by an applied field, whereas permeability represents the relative increase in flux caused by the presence of the magnetic material [32].

Diamagnetism

Diamagnetism is an inherent result of the orbital motion of the electrons in a magnetic field. It is present when the atom has zero net magnetic moment. In this case the orbital motion generates a field opposite to the applied field (magnetization is directed oppositely to the field, as illustrated in Figure 6), described by a negative susceptibility. These materials tend to move toward regions of weaker field [32, 33].

Paramagnetism

Paramagnetic materials possess a permanent dipole moment due to incomplete cancellation of electron spin and/or orbital magnetic moments. In the absence of an applied magnetic field the dipole moments are randomly oriented, therefore the material has no net macroscopic magnetization. When a field is applied these moments tend to align by rotation towards the direction of the field and the material acquires a net magnetization (Figure 7) [34].

illustration not visible in this excerpt

Figure 5: Representation of the behavior of the flux density with respect to the magnetic field for different classes of magnetic materials.

illustration not visible in this excerpt

Figure 6: Atomic dipole configuration for a diamagnetic material

illustration not visible in this excerpt

Figure 7: Schematic of atomic dipoles for a paramagnetic material Ferromagnetism and ferrimagnetism

Ferro and ferri-magnetic materials possess a permanent magnetic moment in the absence of an external field and a very large permanent magnetization [34]. In ferromagnetic materials, this permanent magnetic moment is the result of the cooperative interaction of large numbers of atomic spins in what are called domains, regions where all spins are aligned in the same direction. In ferrimagnetic materials, on the other hand, incomplete cancellation of the magnetic dipoles in a domain results in lower permanent magnetization (Figure 8) [33].

The macroscopic magnetization of ferro- and ferri-materials is the sum of the magnetizations of the domains which make up the sample [34]. Ferrimagnets are ionic solids meaning that they are electrically insulating, whereas most ferromagnets are metals (conductors) [35].

illustration not visible in this excerpt

Figure 8: Ordering of the atomic dipoles in (a) ferromagnetic and (b) ferrimagnetic material

1.3.4. Domains

In 1907, Weiss proposed what is known as the domain theory of magnetism. This theory contends that a ferro- or ferri-magnetic material is composed of domains, each one magnetized to saturation in some direction (the magnetic moments are oriented in a fixed direction) as shown schematically in Figure 9.

illustration not visible in this excerpt

Figure 9: Illustration of domains in ferromagnetic materials

Domains typically contain from 10[12] to 10[15] atoms and are separated by domain boundaries or walls. The formation of domains allows a ferro or ferri-material to minimize its total magnetic energy. The magnetic energy is composed of several types of energy [33, 36]:

a. 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 the material.

b. Magnetocrystalline anisotropy energy: In some materials the domain magnetization tends to align in a particular crystal direction (the so-called easy axis). The material is easiest to magnetize to saturation or demagnetize from saturation if the field is applied along an easy axis. The energy difference between aligning the domain in the easy and another direction (hard direction) is called magnetocrystalline anisotropy energy. Anisotropy energy is the energy needed to rotate the moment from the easy direction to a hard direction. For materials with cubic crystalline structure (such as ferrites), the energy is expressed in terms of anisotropy constants and the direction to which the magnetization rotates.

illustration not visible in this excerpt

illustration not visible in this excerpt

where K is the anisotropy constant, θ is the angle between the easy axis and the direction of magnetization, and α ; are the direction cosines, which are the ratios of the individual components of the magnetization projected on each axis divided by the magnitude of the magnetization. A crystal is higher in anisotropy energy when the magnetization points in the hard direction rather than along the easy direction. The formation of domains permits the magnetization to point along the easy axis, resulting in a decrease in the net anisotropy energy.

c. Magnetostrictive energy: In a magnetic field, the material may change its dimensions of the order of several parts per million. This change in dimension results in what is called magnetostrictive energy, which is lowered by a reduction in the size of the domains, requiring the formation of more domains.

d. Domain wall energy: This is energy resulting from the increase or decrease in the width of the walls due to the growth/shrinkage of domains. The magnetization in a domain changes by two mechanisms: rotation of the magnetic dipoles toward the direction of the applied field and change in the domain volume (Figure 9). In the first case, a certain amount of anisotropy energy is needed to rotate the magnetization in a crystal from the easy to another axis. In the second mechanism, the volume of the domain changes, changing its contribution to the bulk magnetization, while the magnetization direction is unchanged. The change in the magnetization intensity of a domain depends on how close its direction is to the direction of the applied field. If the magnetization direction is close, the intensity in the domain increases, whereas if it is far, the intensity decreases.

illustration not visible in this excerpt

Figure 10: Change of domain magnetization by (a) domain rotation and (b) domain wall movement.

The domain volume changes due to motion of the domain wall. This movement is originated by a torque that rotates the moments of the domain in line with the field, moving the center of the wall toward the domain opposed to the field. Consequently, the volume of the domains whose direction is favorable is increased whereas the domains with unfavorable direction decrease in volume [33].

1.3.5. Magnetization curve and hysteresis loops

A great deal of information can be learned about the magnetic properties of a material by studying its hysteresis loop. A hysteresis loop shows the relationship between the induced magnetic flux density (B) and the magnetizing force (H). It is often referred to as the B-H loop. An example hysteresis loop is shown below (Fig. 12).

The magnetization curve describes the change in magnetization or magnetic flux of the material with the applied field. When a field is applied to a material with randomly oriented magnetic moments, it will be progressively magnetized due to movement of domain boundaries. Initially, when no field is applied, the magnetic dipoles are randomly oriented in domains, thus the net magnetization is zero. When a field is applied, the domains begin to rotate, increasing their size in the case of the domains with direction favorable with respect to the field, and decreasing for the domains with unfavorable direction. As the field increases, the domains continue to grow until the material becomes a single domain, which is oriented in the field direction. At this point, the material has reached saturation (Figure 11) [34].

As the magnetic field is increased or decreased continuously, the magnetization of the material increases or decreases but in a discontinuous fashion. This phenomenon is called the Barkhausen effect and is attributed to discontinuous domain boundary motion and the discontinuous rotation of the magnetization direction within a domain [31].

The typical magnetization curve can be divided into three regions:

a. Reversible region: The material can be reversibly magnetized or demagnetized. Charges in magnetization occur due to rotation of the domains with the field.

b. Irreversible region: Domain wall motion is irreversible and the slope increases greatly.

c. Saturation region: Irreversible domain rotation. It is characterized by a required large amount of energy to rotate the domains in the direction of the field.

illustration not visible in this excerpt

Figure 11: Magnetization curve with domain configurations at different stages of magnetization.

If the field is reduced from saturation, with eventual reversal of field direction, the magnetization curve does not retrace its original path, resulting in what is called a hysteresis loop. This effect is due to a decrease of the magnetization at a lower rate. The area inside the hysteresis loop is indicative of the magnetic energy losses during the magnetization process. When the field reaches zero, the material may remain magnetized (i.e., some domains are oriented in the former direction). This residual magnetization is commonly called remanence Mr. To reduce this remanent magnetization to zero, a field with opposite direction must be applied. The magnitude of field required to reduced the sample magnetization to zero is called the coercivity Hc (Figure 12).

illustration not visible in this excerpt

Figure 12: Schematic of hysteresis loop

The loop is generated by measuring the magnetic flux of a ferromagnetic material while the magnetizing force is changed. A ferromagnetic material that has never been previously magnetized or has been thoroughly demagnetized will follow the dashed line as H is increased. As the line demonstrates, the greater the amount of current applied (H+), the stronger the magnetic field in the component (B+). At point "a" almost all of the magnetic domains are aligned and an additional increase in the magnetizing force will produce very little increase in magnetic flux. The material has reached the point of magnetic saturation. When H is reduced to zero, the curve will move from point "a" to point "b." At this point, it can be seen that some magnetic flux remains in the material even though the magnetizing force is zero. This is referred to as the point of retentivity on the graph and indicates the remanence or level of residual magnetism in the material. (Some of the magnetic domains remain aligned but some have lost their alignment.) As the magnetizing force is reversed, the curve moves to point "c", where the flux has been reduced to zero. This is called the point of coercivity on the curve. (The reversed magnetizing force has flipped enough of the domains so that the net flux within the material is zero.) The force required to remove the residual magnetism from the material is called the coercive force or coercivity of the material.

As the magnetizing force is increased in the negative direction, the material will again become magnetically saturated but in the opposite direction (point "d"). Reducing H to zero brings the curve to point "e." It will have a level of residual magnetism equal to that achieved in the other direction. Increasing H back in the positive direction will return B to zero. Notice that the curve did not return to the origin of the graph because some force is required to remove the residual magnetism. The curve will take a different path from point "f" back to the saturation point where it with complete the loop.

From the hysteresis loop, a number of primary magnetic properties of a material can be determined.

- Retentivity - A measure of the residual flux density corresponding to the saturation induction of a magnetic material. In other words, it is a material's ability to retain a certain amount of residual magnetic field when the magnetizing force is removed after achieving saturation. (The value of B at point b on the hysteresis curve.)
- Residual Magnetism or Residual Flux - the magnetic flux density that remains in a material when the magnetizing force is zero. Note that residual magnetism and retentivity are the same when the material has been magnetized to the saturation point. However, the level of residual magnetism may be lower than the retentivity value when the magnetizing force did not reach the saturation level.
- Coercive Force - The amount of reverse magnetic field which must be applied to a magnetic material to make the magnetic flux return to zero. (The value of H at point c on the hysteresis curve.)
- Permeability, m - A property of a material that describes the ease with which a magnetic flux is established in the component.
- Reluctance - Is the opposition that a ferromagnetic material shows to the establishment of a magnetic field. Reluctance is analogous to the resistance in an electrical circuit.

A material can present different hysteresis loops depending on the degree of magnetization. If the maximum magnetization is less than the saturation magnetization, the loop is called a minor loop [34, 36].

1.4 Ferrites

The most important ferrimagnets are the materials known as ferrites. Ferrites are ferrimagnetic oxides and are electrically insulating. Ferrites are widely used in high-frequency applications, because an AC field does not induce undesirable eddy currents in an insulating material [34, 36]. Ferrites have two different structural symmetries which are determined by the size and charge of the metal ions that balance the charge of the oxygen ions, and their relative amounts [33].

1.4.1 Cubic ferrites

The cubic ferrite has the general formula MO · Fe2O3 where M is a divalent ion. These ferrites crystallize in the spinel structure. The spinel lattice is composed of a closepacked oxygen arrangement in which 32 oxygen ions form the unit cell (the smallest repeating unit in the crystal network). These anions are packed in a face centered cubic (FCC) arrangement leaving two kinds of spaces between anions: tetrahedrally coordinated sites (A), surrounded by four nearest oxygen atoms, and octahedrally coordinated sites (B), surrounded by six nearest neighbor oxygen atoms. These are illustrated in Figure 13. In total, there are 64 tetrahedral sites and 32 octahedral sites in the unit cell, of which only 8 tetrahedral sites and 16 octahedral sites are occupied, resulting in a structure that is electrically neutral [33, 36].

illustration not visible in this excerpt

Figure 13: Schematic of two subcells of a unit cell of the spinel structure, showing octahedral and tetrahedral sites.

The localization of ions either in the A or B sites depends fundamentally on the ion and lattice sizes. Also it has been observed to depend on the temperature and the orbital preference for specific coordination.

In general, divalent ions are larger than trivalent ions (Table 1). This is because trivalent ion nuclei produce greater electrostatic attraction, hence their electron orbits contract. The octahedral sites are larger that the tetrahedral sites, thus, the divalent ions are localized in the octahedral sites whereas trivalent ions are in the tetrahedral sites [33]. The distance and angle between the metals and oxygen atoms in the spinel structure are given in Figure 14 [33].

There are two spinel structures: normal and inverse. In the case of the normal spinel, the divalent ions are all on A sites and trivalent ions occupy B sites. A majority of these ferrites present paramagnetic behavior. In the inverse spinel, the divalent ions occupy only B sites while trivalent ions are located on both A and B sites in equal proportion. The spin moments of the trivalent ions in an inverse spinel are canceled (direction of moment on A sites is opposed to B sites) whereas the spin moments of the divalent ions are aligned, resulting in a net magnetic moment [36].

The cubic ferrite is easily magnetized and demagnetized; it has high permeability and saturation magnetization, low electrical conductivity, and the anisotropy energy is dominated by K1. If K1 is greater than zero, the easy direction is the cube edge direction (100) whereas if K1 is less than zero, the body direction is preferred (111). For most ferrites the value of K1 is negative, with the exception of cobalt ferrite [33].

Ferrites are characterized by their characteristic hysteresis loops, which originate from their large magnetocrystalline anisotropy. Additionally, they have short relaxation times, minimal mechanical strength, and low magnetostriction [36].

illustration not visible in this excerpt

Figure 14: Inter-ionic distances and angles in the spinel structure for the different types of lattice site interactions

illustration not visible in this excerpt

1.4.2 Hexagonal ferrites

Hexagonal ferrites are widely used as permanent magnets and are characterized by possessing a high coercivity [36]. Their general formula is MO ·6Fe2O3 where M can be Ba, Sr, or Pb. The hexagonal ferrite lattice is similar to the spinel structure, with the oxygen ions closely packed, but some layers include metal ions, which have practically the same ionic radii as the oxygen ions. This lattice has three different sites occupied by metals: tetrahedral, octahedral, and trigonal bi pyramid (surrounded by five oxygen ions).

1.5 Background

The compounds capable of crystallizing in the spinel system can be present in either of two structures: the normal spinel or inverse spinel. In the normal spinel such as CdFe2O4, cadmium ions are located in the tetrahedral site and are symmetrically surrounded by four O[2]− ions. In the inverse spinel examples of which are NiFe2O4, CoFe2O4, half of Fe[3]+ ions are located in the tetrahedral positions whereas the other half are in the octahedral positions. Therefore, a normal ferrite can be described as (M[2]+) [Fe2[3]+]O4 and an inverse ferrite as (Fe[3]+)[M[2]+Fe[3]+]O4 [37].

Now let us revised the background of ferrite materials at this point with due concern to their properties. Densification takes place by a sintering mechanism during a high-temperature firing procedure. Microstructure of the final product changes during firing and with sintering variations, the size and shape of pores change. Improvements in the sintering properties of the ceramic materials are one of the concerns while applying them in some technological application. Dense ceramics claim their usage in applications of magnetic or electrical devices and less dense or porous ceramics proves their usability in sensing applications [38] and reduction in density and improvement in the magnetic anisotropy makes their use as an electromagnetic wave absorber [39, 40].

Ceramics are applied in various fields that involve an intense neutron- irradiation environment, such as that encountered in thermonuclear fusion devices such as the International Thermonuclear Experimental Reactor (ITER). In machines of such kind, ceramics may be used as toroidal current break insulators, electrical insulators for magnets, windows for radiofrequency (rf) power injectors or plasma diagnostic devices, insulating coatings for suppression of magneto hydrodynamic (MHD) forces in liquid metal-cooled blankets, and solid tritium breeders [41-45].

Furthermore, ceramics can serve the purpose as first-wall protection or as structural materials where low nuclear activation and good high-temperature performance are required. The concern of prime importance during the service life of the design is adequate mechanical performance without failure. Therefore, an understanding of the changes in the mechanical properties that are due to the neutron irradiation is very important. Among many candidates ceramics with spinel structure (MgAl2O4) shows excellent characteristics, even after high fluence neutron irradiation. The spinel compounds maintain their structural integrity and show superior resistance to the formation of defect aggregates. The recombination of point defects occurs efficiently under neutron irradiation; therefore, the change in mechanical properties is not critical, up to very high neutron fluences [42].

At power electronic applications as that in automotive, lighting, electrical equipment etc., the inductive components that consists the heart of the power transformers are made of ceramic ferromagnetic materials. Usually they are designed in such a way in order to exhibit optimum magnetic performance and electromagnetic power loss minimum at moderate temperature range 80-100[0]C, which is the steady state operation temperature region for most devices.

Additions/substitutions of high valancy ions in ferrite material are often reported to be effective in controlling the losses and in improving the electrical and magnetic properties [46]. These characteristics are especially important if the investigations are to be carried out towards materials for power applications. The technological developments made in recent times demand operating frequencies for ferrites beyond 1 MHz [47].

The addition of di, tri, and tetravalent ions are known to produce desirable changes in the structural, electrical and magnetic properties of spinel ferrite systems [48-49]. Reportedly magnetic properties of ferrites can be altered by the substitution of various kinds of M[2]+ among divalent cations Mg[2]+, Cu[2]+, Mn[2]+, Ni[2]+, Co[2]+, Fe[2]+ and, Zn[2]+ etc. [50-51]. In spinel structure, the A-site and B- site spins are antialigned; the net magnetization (M) in this kind of spin arrangement can be increased by creating an imbalance between the sublattice magnetizations. This is typically done by substituting nonmagnetic cations for the ferrous ions.

Antiferromagnetic critical points are studied regularly [52], while reports on the study of ferromagnetic critical points are very rare. Study of ferromagnetic critical points in a Cerium based system would be of high value, because theories predict the magnetic, thermal and transport properties to differ between a ferromagnetic critical points and an antiferromagnetic critical point [53]. The study of these critical points are preferentially performed by applying iso-static pressure on pure compounds instead of alloying, because the intrinsic disorder of an alloy induces additional effects which are not well understood. However, in pure compounds ferromagnetic state is now suspected to end with a first-order transition disappearing at a classical critical point at finite temperature. On the contrary, disorder is suspected to lead to a quantum critical point where TC goes continuously down to absolute zero temperature making cerium based systems more interesting for the study of ferromagnetic critical points than pure compounds.

It is a fact of matter that adding a small amount of cerium to the gray iron before casting produces a distinctly different microstructure and set of mechanical properties. Graphite forms sphere like particles instead of flakes better known as nodules. The resulting alloy is called nodular or ductile iron. Castings are stronger and much more ductile than gray iron. In fact, ductile iron has mechanical characteristics approaching those of steel. Ferritic ductile iron has very high tensile strength and low ductilities. Typical applications for such kind of material include valves, pump bodies, crankshafts, gears, and other automotive and machine components [54].

High dielectric constant and least dielectric loss are essential requirement of ferrite for power applications. Reportedly, Cerium substituted lithium ferrites attain minimum value of loss tangent in higher resonance frequency range. Higher concentration of cerium which has large ionic radius may lead to secondary phases therefore low concentration of cerium in ferrite would be very useful for power application devices [52].

1.6 Motivation and aim of the present work

Experimentalists select spinel ferrites preferentially out of tremendous possibilities that materials science provides, study these materials mostly and develop new ideas for their use as ferrimagnetic materials [55, 56], catalysts and pigments [57, 58], sensing materials [58-61], in high density memory devices and so on. Soft magnets residing in space group Fd-3m, with low coercivities, high permeability and high resistivities are rendered themselves for industrial applications in satellite communication, transformers, audio-video in digital recording, and as ferrite core. High resistivity and low eddy current losses are the prime requirements for high frequency applications. Materials that would be used in radio frequency circuits, high quality filters, rod antennas, transformer cores, and, read/write heads for high-speed digital tape and operating devices needs to satisfy these requirements [62].

To yield an optimized material for particular applications one needs to consider the influence of a substitution which will modify the properties like saturation magnetization for microwave applications and to modify the hysteresis loop related properties for memory core applications.

The magnetic permeability is a necessary property for the existence of a magnetic component beside this, another important parameter for the operation of ferrite magnetic components, particularly in high power transformer applications, is the magnitude of the electromagnetic power losses. These power losses are the expressions of the amount of electromagnetic energy not being transformed inductively into useful energy but dissipated inside the material in the form of heat. The total power losses are the sum of the power losses due to different and often simultaneously taking place loss mechanisms e.g. hysteresis losses, eddy current losses, resonance losses etc. [63, 64].

Some electrochemical and structural data reported in literature on iron oxides are regarded as the consequence of an insertion of lithium into, and iron extrusion from, the cubic close-packed lattice. The products of a complete discharge were identified as Li2O and α-Fe [65].

The potential use of binary transition metal oxides (MxOy with M = Fe, Cu, Co, and Ni) as anode materials for lithium ion batteries recently reported [66]. A mechanism of the lithium reaction that differs from either the conventional lithium insertion/extraction in graphite or the formation of lithium-tin intermetallic is proposed recently. Assuming that the only condition for the feasibility of this redox reaction is exoergicity, other transition metal compounds such as nickel and iron oxides are possible electrode candidates. In fact, these oxides have been also researched to evaluate the electrochemical performance in lithium cells [67]. In addition, other compounds including chalcogenides [68, 69], halides [70], phosphides [71], oxysalts [72] are demonstrated to undergo conversion reactions. However, some drawbacks as the Li2S solubility or low electronic conductivity of fluorides hinder an electrochemical behaviour as performing as that of the oxides. A different research topic is the evaluation of mixed transition metal oxides. The reversibility of conversion reactions in compounds such as NiCo2O4 [73, 74] and NiFe2O4 [75] has been evidenced.

Magnetic semiconductors synonyms for polycrystalline soft ferrites which cannot be replaced by any other magnetic materials considering their extraordinary properties like stability, relatively inexpensiveness, easy manufacturing procedures The crystal structure of these materials controls their physical properties. Magnetic dilution due to substitution of diamagnetic atoms gives rise to interesting magnetic features in compounds with spinel structure. These properties mainly depend upon chemical composition, method of preparation, stoechiometry, sintering time and temperature, sintering atmosphere, porosity etc. [76].

Technologies of perpendicular magnetization for ferrite loaded cavities are developed and used preferably. Ferrite loaded cavity is usually used in proton synchrotron with a magnetic biasing field which is in parallel direction with the RF magnetic field. The resonant frequency of the cavity is tuned by varying the biasing field that is nothing but the permeability of the ferrite. It is an established fact that if the direction of the biasing field is changed to perpendicular with the RF magnetic field, the RF losses of the ferrite will be greatly reduced [77]. It is because if the material is magnetized to saturation beyond the gyromagnetic resonance field, there is no longer any possibility of resonance occur.

Yttrium Garnet ferrite are available with very low saturation magnetization fields, so it is widely used for cavities with perpendicular biasing [78]. Yttrium Garnet ferrite is generally used for these cases with higher frequency range of mid MHz. The cost of Garnet systems asks us to look for some other options which may be cost effective and will serve the purpose and research work in this direction is of immediate interest.

Some new materials of magnetic alloys are developed and used for RF cavity instead of ferrite because of their special advantages [79], ferrite systems with low saturation biasing field are prime candidates. These facts finger points towards the systems involving Nickel ferrite to be suitable under the condition of perpendicular magnetization. What the characteristics of these materials under perpendicular magnetization are of great interest. An attempt to measure characteristics of such materials needs to be carried out. Nickel ferrite, NiFe2O4, is known to be residing in inverse spinel in which the tetrahedral sites (A) are occupied by Fe[3]+ ions and the octahedral sites (B) by Fe[3]+ and Ni[2]+ ions [80], is largely used in electric and electronic devices as magnetic material, and also applied to catalysis and gas sensor due to its semiconductive property [81]. The Ni ion has an orbital magnetic moment and is a relaxing ion; so nickel ferrite is rarely used in devices with very low insertion losses, but rather used in those devices which require withstanding a certain peak power [82].

1.7 Materials under consideration

The magnetic properties of ferrite systems can be modified by substituting diamagnetic cations on either sublattice to allow the material be tailored for specific applications. Al[3]+, for instance, is known to have a strong octahedral B- site preference and therefore works very well for magnetization reduction [83]. The known magnetic moment for Zn[2]+ ions is 0μB [84]. Diamagnetic Zn[2]+ ion substitution in ferrite is known to affect several properties of the material [85]. It predominantly has the tetrahedral site attraction and influence of zinc substitution on the magnetic properties has been the subject of many investigations [86-89]. Non magnetic Zn substitution in ferrite matrix will give rise to unusual magnetic properties. Canting angle famously known as the Yafet-Kittel angle will appear to explain this behaviour of Zn substituted ferrite materials. Such angle occurs when B-B interaction is comparable with the A-B interaction. The addition of zinc promotes densification and grain growth processes and thus has a beneficial effect on the preparation procedures and on tailoring properties such as the coercive field and the microwave resonance linewidth. Further, the addition of zinc does not produce adverse effect on the dielectric properties at microwave frequencies [90].

Zinc ferrite and zinc doped ferrites, as well as the solid solutions with spinel type structure which have accommodated two and three valence metals have been widely used as gas desulfurization absorbents, anticorrosive electrode materials in alumina electrolysis, oxidation catalysts, anticorrosive pigments, or magnetic materials in the electronic industry [91]. The major contribution to the magnetic losses in ferrites is due to hysteresis losses, which in turn is based on damping phenomena associated with irreversible wall displacement and spin rotations. In high-frequency range, the hysteresis loss becomes less important because the wall displacement is mainly damped and the hysteresis loss will be due to spin rotation [92].

There are studies present which infer the fact that indium ions have remarkably enhances initial permeability. The tan d values are found to be small even at higher frequencies for indium substituted ferrite samples, which is one of the criteria for the materials to be used in microwave devices and for deflection yoke [93, 94]. Defect distribution plays a dominant role in tuning the properties of ferrites. From available literature it can be believed that indium prefers tetrahedral site in its smaller dopants levels and for higher values of dopant variable ‘x’ indium starts entering in octahedral site [29, 30]. Increase in indium concentration will give rise interesting magnetic ordering.

[...]