1. UNIT-TWO-MATERIAL SCIENCE MAGNETIC,DIELECTRIC & ENGG. MATERIALS
I-SEM SRMUH
PH0102 LECTURE-1
PREM CHAND

2. CONTENTS Magnetism: BASIC DEFINITIONS of magnetism Magnetic Materials
Garnets
Spinel & Inverse Spinel Structures
Ferrites
ENGINEERING MATERIALS
PH0102 SRMUH U-2-L1-I-SEM P-2

3. Introduction Magnetic materials
Magnetic materials are the materials, which get magnetized in a magnetic field. Some of these materials have the ability to create a self magnetic field in the presence of an external magnetic field or even in the absence of the external magnetic field.
Types of magnetic materials
diamagnetic,
paramagnetic,
ferromagnetic,
antiferromagnetic
and ferrimagnetic materials.

4. It is expressed in terms of Nuclear Magneton
MAGNETISM OF AN ATOM
1. Orbital magnetic moment of the electrons
This corresponds to permanent orbital magnetic dipole moments. µl = - eL/2me :where, e= electronic charge, me is the mass of electron, L is the angular momentum of the electron
According to Bohr L = n h/2π. Hence µl = -n eh/4πme = -n µB
µB = eh/4πme is called Bohr Magneton and n is the orbital quantum number. The –ve sign indicates that the magnetic moment is directed opposite to the angular momentum vector.
2. Electron spin angular momentum ( S= (1/2) h/2π)
This corresponds to electron spin magnetic moments (µB .).
3. Nuclear spin angular momentum
This corresponds to nuclear magnetic moments.
It is expressed in terms of Nuclear Magneton
µN = eh/4πmp Here mp is the mass of proton
To Do: calculate the values of Bohr and Nuclear magnetons. Compare their magnitudes.

5. Basic Definitions
Magnetic dipole : Two equal and opposite magnetic poles separated by a small distance ‘d’ constitute a magnetic dipole .

6. Magnetic dipole moment
When an electric current of ‘I’ amperes flows through a circular loop of 1 turn having an area of cross section ‘A’ m2, then it is said to have a magnetic moment µm : µm = IxA [A-m2]
The Direction of magnetic moment vector is determined by Right Hand Screw Rule : Rotate the screw in the direction of current , the translation of the screw tip is the direction of the magnetic moment vector. µm
A=area of loop (metre square) I
To Do: (a)In an atom an electron is revolving around the nucleus at an speed of 6.5x 10**15 revolutions per second. The radius of the orbit is 0.54 A. Calculate the magnetic moment of the electron. [ 10** means 10 raised to power & A is Angstrom ]
(b) Calculate the magnetic moment of a circular coil cntaining 100 turns and a diameter equal to 10 cm.

7. Few Definitions
1. MAGNETIC FLUX φ : TOTAL NUMBER OF LINES OF FORCE PASSING
PERPENDICULAR TO A GIVEN AREA IS CALLED FLUX. UNIT IS WEBER
2. MAGNETIC INDUCTION OR FLUX DENSITY B : It is equal to magnetic flux per unit area i.e. φ /A. Its unit is weber/metre square or Tesla . Also 1T = Gauss.
3. MAGNETIC FIELD STRENGTH OR MAGNETIC FIELD INTENSITY H: It is equal to the flux per unit area in free space and is expressed in units of ampere turns per metre.
4. MAGNETIZATION OR INTENSIT Y OF MAGNETIZATION ‘M’: It is the magnetic
moment per unit volume. It is expressed in ampere/metre.
5. MAGNETIC SUSCEPTIBLITY χ : χ = M/H ( NO UNITS )
6. MAGNETIC PERMEABILITY µ : µ = B/H &
RELATIVE PERMEABILITY µr : / µ0 , Here µ0 is the permeability of free space.
7. B = [H+M] & µ = µ0 [1+ χ ] µ0

8. Classification of Magnetic Materials
Materials not having any permanent atomic magnetic moment :
diamagnetic materials [are magnetic by induced effects purely]
Repels magnetic flux.
Those having permanent magnetic moment:
para-, ferro-, antiferro- and ferri-magnetic materials. [ Show magnetism due to ordering of atomic magnets ]
B-Ordered by H ,M ll to H
A-random order with net M=0
Removal of H causes back situation A
This is the case of disordered magnetism
This is the property of para-magnetic materials

9. ORDERED MAGNETISM
a -ATOMIC MAGNETS ARE ALIGNED IN PARALLEL
This is called Ferro-magnetic Order [FM Order]
b- anti-parallel order of equal magnetic moments.
This is referred to Anti –Ferro-Magnetic Order
[AFM ORDER ]. Net M=0.
c- AFM ORDER OF UNEQUAL MAGNETIC MOMENTS.
NET MAGNETIC MOMENT EXISTS. SUCH MATERIALS
ARE CALLED FERRI-MAGNETIC MATERIALS OR FERRITES

11. Ferromagnetism

14. Origin of Ferromagnetism
Hund’s rule
Fe: [Ar]3d64s2

15. Structure of Ferrites
The general chemical formula of a ferrites is: 8[M(II) O Fe(III)2 O3] Where M(II) = Divalent metal Such as Mg, Zn, Fe, Cu ,Co etc.
Ferrites crystallize in the form of a cubic closed packed structure of oxygen. Each corner of a ferrite unit cell consists of a ferrite molecule [M(II) O Fe(III)2 O3]
The simplest ferrite has been Magnetite [Load stone, FeOFe2 O3 ]
The crystal structure is called Spinel Structure Since it resembles to mineral ‘Spinel’
MgOAl2O3 or AOB2O3
There are 8 formula units [AOB2O3 ] i.e per unit cell. Hence there are 8 A-sites(Tetrahedral Sites, i.e. coordinated to four oxygen atoms) and 16 B-sites (Octahedral sites, i.e. coordinated to six oxygen atoms)
The structure with A-sites occupied by Divalent atoms and B-sites with Trivalent atoms is referred to the regular spinel structure.
8[M(II) O Fe(III)2 O3]
Tetrahedral coordination
oxygen
Octahedral
coordination

16. Regular spinel structure
In this type, each divalent metal ion occupies tetrahedral (A) sites and each trivalent metal ion occupies octahedral (B) sites. Totally in an unit cell, there will be 8 tetrahedral ( A) sites and 16 octahedral (B) sites.
Hence, the sites A and B combined to form a regular spinel ferrite structure is shown in Fig.
The schematic representation of zinc ferrite molecule is shown in Fig.

17. Ferrimagnets and Antiferromagnetism
Ions in most ferrimagnets and antiferromagnets are positioned on two sublattices, such that the spins on each sublattice tend to be aligned with each other, but spins on different sublattices tend be to oriented in opposite directions.
Unit cell and magnetic structure of the ferrimagnetic intermetallic compound GdCo5. The magnetic moments of Gd (blue) are directed antiparallel to the moments of Co (green).

18. Ferrimagnets and Antiferromagnetism
Crystal Structure of Magnetite
Magnetite, Fe3O4 crystallizes in the spinel structure. Large oxygen ions are close packed in a cubic arrangement and the smaller iron ions fill in the gaps.
The lattice sites come in two flavors:
A-Site tetrahedral site: Fe ion is surrounded by 4 oxygen ions
B-Site octahedral site: Fe ion is surrounded by 6 oxygen ions
The tetrahedral and octahedral sites form the two magnetic sublattices, A and B, respectively. The spins on the A sublattice are antiparallel to those on the B sublattice. The two crystal sites are very different and result in complex forms of exchange interactions of the iron ions between and within the two types of sites.

19. Hysteresis
When a ferromagnetic material is magnetized in one direction, it will not relax back to zero magnetization when the imposed magnetizing field is removed. It must be driven back to zero by a field in the opposite direction. If an alternating magnetic field is applied to the material, its magnetization will trace out a loop called a hysteresis loop. The lack of retraceability of the magnetization curve is the property called hysteresis and it is related to the magnetic domains in the material. Once the magnetic domains are reoriented, it takes some energy to turn them back again. This property of ferrromagnetic materials is useful as a magnetic "memory". Some compositions of ferromagnetic materials will retain an imposed magnetization indefinitely and are useful as "permanent magnets". The magnetic memory aspects of iron and chromium oxides make them useful in audio tape recording and for the magnetic storage of data on computer disks.

20. HYSTERESIS Hysteresis
When a ferromagnetic material is magnetized in one direction, it will not relax back to zero magnetization when the imposed magnetizing field is removed. It must be driven back to zero by a field in the opposite direction. If an alternating magnetic field is applied to the material, its magnetization will trace out a loop called a hysteresis loop. The lack of retrace ability of the magnetization curve is the property called hysteresis and it is related to the existence of magnetic domains in the material. Once the magnetic domains are reoriented, it takes some energy to turn them back again. This property of ferromagnetic materials is useful as a magnetic "memory". Some compositions of ferromagnetic materials will retain an imposed magnetization indefinitely and are useful as "permanent magnets". The magnetic memory aspects of iron and chromium oxides make them useful in audio tape recording and for the magnetic storage of data on computer disks.

21. 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.

22. 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  or field- 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,  µ = B/H  - A property of a material that describes the ease with which a magnetic flux is established in the material.
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.

23. INVERSE SPINEL STRUCTURE [Mg2TiO4] :
In this type half of the 16 B-sites ( i.e. 8sites) are occupied by divalent metal ions and the remaining half of the B sites ( i.e. 8 sites) and all the A sites are occupied by the trivalent metal ions, as shown in Fig. below for Magnetite [ ferrous ferrite]:
Inverse Regular
Inverse Spinel Structure of spins in Magnetite [ ferrous ferrite]

24. The anti parallel alignment of a ferrous ferrite molecule in inverse spinel structure is explained by the calculation of its magnetic moment. In a ferrous ferrite molecule, there are one ferrous ion and 2 ferric ions.
When the Fe atom is ionized to form the Fe2+ ions, there are 4 unpaired 3d electrons left after the loss of two 4s electrons.
When the Fe atom is ionized to form the Fe3+ ions, there are 5 unpaired 3d electrons left after the loss of two 4s electrons and one 3d electron. It is shown in the following electronic configuration
Table d electronic configuration of Fe2+ and Fe3+
Ion
No. of electrons
3d electronic configuration
Ionic magnetic moment
Fe 2+
24 3d 6
4µB
Fe 3+
233d 5
5µB

25. Since each unpaired 3d electron has a magnetic moment of one B , the Fe 2+ ion has a moment of 4 B , and Fe3+ ion has a moment of 5 B as discussed in Table-1 earlier.
If parallel alignments i.e FM order of ferrous and ferric ions are considered, the total dipole moment per formula unit FeOFe2 O3  4 B + (25) B 14 B .
This value doesn’t agree with the experimental value.
Now consider anti-parallel alignment i.e. AFM order of ferrous and ferric ions in inverse spinel structure.
If one ferrous ion and one ferric ion are in one direction and another ferric ion is in opposite direction then the dipole moment is, 51) + 4  (51) B  4 B .
This calculated value is in good agreement with the experimental value and hence this confirms the anti parallel alignment of dipoles in ferrous ferrites.

26. Ferrites are manufactured by powder metallurgical process by mixing, compacting and then sintering at high temperatures followed by age hardening in magnetic fields.
Properties of Ferrites:
Mechanically, they have pure iron character.
They have low tensile strength and are brittle and soft.
They are bad conductors with high resistivity of 1 k- m.
They are soft magnetic materials and bad conductor of electricity. so they have low eddy current losses and hysteresis losses.
Due to high resistivity and low losses ferrites are used as cores for radio frequency transformers

27. USES OF FERRITES:
Ferrites are used in digital computers and data processing circuits. Ferrites are used to produce low frequency ultra sonic waves by magnetostriction principle.
Ferrites are widely used in non-reciprocal microwave devices. Examples for non-reciprocal microwave devices are Gyrator, Isolator and Circulator.
Ferrites are also used in power limiting devices.
Ferrites can also be used in the design of ferromagnetic amplifiers of microwave signals.
Ferrite core can be used as a bit-able element.
The rectangular shape ferrite cores can be used as a magnetic shift register.
Hard ferrites are used to make permanent magnets.
The permanent magnets (hard ferrites) are used in instruments like galvanometers, ammeter, voltmeter, flux meters, speedometers, wattmeter, compasses and recorders.

28. Garnets Garnets general formula is X3Y2(SiO4)3.
Garnets are a group of minerals that have been used since the Bronze Age as gemstones and abrasives. Garnets are found in many colors including red, orange, yellow, green, blue, purple, brown, black, pink or colorless. Garnets crystallize in the isometric[Cubic] system. Garnets do not show cleavage, so when they fracture under stress, sharp irregular pieces are formed.
Garnets general formula is X3Y2(SiO4)3.
X site is usually occupied by divalent cations such as: (Ca2+, Mg2+, Fe2+, Mn2+ etc.) and Y site by trivalent cations such as: (Al3+, Fe3+, Cr3+, Mn3+, V3+) in an octahedral /tetrahedral framework with [SiO4]4− providing the tetrahedra.
Three important garnets are: YAG [Y3Al2(AlO4 ) 3] , YIG[ Y3Fe2(FeO4 ) 3] &
GGG [Gd3Ga2(GaO4 ) 3]
Nd- YAG Neodymium ( Nd3+ ) doped yttrium aluminum garnet is used to make Nd- YAG Laser . A Nd YAG laser is used in medical, industry and research applications.
YIG  yttrium iron garnet is used in microwave components . It is a ferromagnetic material having a Curie temperature of 550 K.
GGG Is used to make magnetic bubble memory. In computers.
Mixed with very high pressure water, hard garnet particles are used to cut steel and other strong materials by water jets.
Garnet sand is also used for water filtration media.

29. Magnetic bubbles [MB] :
Definition
It is a tiny movable magnetized cylindrical volume in a thin magnetic material . Magnetic bubbles can be used to represent a bit of information (as in a computer) . These are used in computer memory.
A thin wafer of Ferromagnetic Garnet reveals its magnetic domain alignment as light and dark serpentine patterns when viewed between crossed polarizer.
These domains can be flipped by an external magnetic field, changing the pattern structure
The preferred or "easy" axis of orientation is perpendicular to (in or out of) the crystal surface. With no external magnetic field, the domains in the crystal orient up or down in roughly equal amounts.
Polarized light passing through the crystal will have its plane of polarization rotated by due to interaction with the magnetic field of the domains (an effect called Faraday rotation).
For the 'up' domains, the light will be crossed with respect to the exiting Polaroid therefore appearing dark, and for 'down' domains uncrossed (or vice versa) so appearing bright.
The domains appear as serpentine patterns [Fig.] of alternating bright and dark. Application of an external magnetic field (provided by a built-in electromagnet) flips the domains to one preferred orientation.
As the field is increased, the serpentine patterns gradually disappear and isolated magnetic bubble may be available.

30. BEAUTIFUL X-TALS OF GARNET
BRIGHT GREEN GARNET

31. Serpentine patterns of magnetic bubbles MBs
Isolated MB
Bubble domain
Serpentine patterns of magnetic bubbles MBs
Fig. Formation of Magnetic bubbles
Working
The magnetic bubble apparatus consists of a thin (8-12μm) single crystal film of Ferromagnetic Garnet (FMG) such as YIG or GGG sandwiched between a pair of crossed Polaroids.
The FMG crystals are magnetically anisotropic, that is, they have a strong tendency to orient themselves in fixed directions [called the easy direction] under the influence of an external magnetic field.

32. Magnetoresistance effect
Magnetoresistance is the property of a material to change the value of its electrical resistance when an external magnetic field is applied to it. This effect was later called ordinary magnetoresistance (OMR).
Magnetoresistance effect
The magnetoreisitance effect occurs in metals only at very high magnetic fields and low temperatures. For example, in pure copper at 4 K a field of 10 T produces a factor of 10 change in the resistance . Because of the large fields and low temperatures, magnetoresistance in metals originally had few potential application possibilities.
Giant magnetoresistance (GMR)
It is a quantum mechanical effect, a type of magnetoresistance effect, observed in thin film structures composed of alternating ferromagnetic and nonmagnetic metal layers.
The effect manifests itself as a significant decrease in electrical resistance in the presence of a magnetic field..
In the absence of an applied magnetic field, the direction of magnetization of adjacent ferromagnetic layers is antiparallel due to a weak anti-ferromagnetic coupling between layers, and it decreases to a lower level of resistance when the magnetization of the adjacent layers align due to an applied external field.
The spins of the electrons of the nonmagnetic metal align parallel or antiparallel with an applied magnetic field in equal numbers, and therefore suffer less magnetic scattering when the magnetizations of the ferromagnetic layers are parallel.

33. Schematic representation of layered structure for GMR
A schematic representation of the layered structure and the alternating orientation of the magnetization in the ferromagnetic layers are shown here .
The effect was first observed in films made of alternating layers of iron and chromium, but since then other layered materials composed of alternating layers of cobalt and copper have also been made.
These cobalt and copper layers display much higher magnetoresistive effects.
The magnitude of the change in the resistance depends on the thickness of the iron layer and it reaches a maximum at a thickness of about 7 nm.

34. Colossal magnetoresistance (CMR)
It is a property of some materials, mostly manganese-based perovskite oxides, that enables them to dramatically change their electrical resistance in the presence of a magnetic field.
The magnetoresistance of conventional materials enables changes in resistance of up to 5%, but materials featuring CMR may demonstrate resistance changes by orders of magnitude.
Colossal Magnetoresistance has been predominantly discovered in manganese-based perovskite oxides.
This arises because of strong mutual coupling of spin, charge and lattice degrees of freedom.
Hence not only high temperature superconductivity, but also new magnetoelectronic properties are increasingly discovered in materials with perovskite structures.
The perovskite like material ‘LaMnO3‘ has manganese in the Mn3+ valence state. If the La3+ is partially replaced with ions having a valence of 2+, such as Ca, Ba, Sr, Pd or Cd, some Mn3+ ions transform to Mn4+ to preserve the elcetrical neutrality.
The result is a mixed valence system. These has been shown to exhibit very large magnetoresistive effects.

36. Applications of CMR and GMR materials
The understanding and application of CMR offers tremendous opportunities for the development of new technologies such as read/write heads for high-capacity magnetic storage, sensing elements in magnetometers and spintronics.
The largest technological application of GMR is in the data storage industry.
On-chip GMR sensors are available commercially from Non-Volatile Electronics.
Other applications are as diverse as solid-state compasses, automotive sensors, non-volatile magnetic memory and the detection of landmines.
Read sensors that employ the GMR effect are available for detecting the fields from tiny regions of magnetization. .
It is expected that the GMR effect will allow disk drive manufacturers to continue increasing density at least until disk capacity reaches 10 Gb per square inch.