1. MAGNETIC
MATERIALS

2. 1) Magnetic Induction or Magnetic Flux density (B): The magnetic induction or magnetic flux density is the number of lines of magnetic force passing through unit area perpendicularly. Where Φ is the magnetic flux and A is the area of cross section. Units: Weber/m2 or Tesla.
2) Magnetic Field Intensity or Intensity of Magnetic Field (H): Magnetic Field Intensity at any point in the magnetic field is the force experienced by an unit north pole placed at that point. Units: A/m.

3. 3) Magnetic Permeability (µ): It describes the nature of the material i.e. it is a material property. It is the ease with which the material allows magnetic lines of force to pass through it or the degree to which magnetic field can penetrate a given medium. Mathematically it is equal to the ratio of magnetic induction B inside a material to the applied magnetic field intensity H. Units: H/m.

4. 4) Magnetization: Process of converting a non magnetic material into magnetic sample. 5) Intensity of Magnetization (M): It is a material property. It is defined as magnetic moment per unit volume in a material. Units: A/m.

8. Magnetic Properties N = total number of turns magnetic field H
• Created by current through a coil:
magnetic field H
current I
N = total number of turns
L = length of the coil
• Relation for the applied magnetic field, H:
applied magnetic field
units = (ampere-turns/m)
current

9. Response to a Magnetic Field
• Magnetic induction results in the material
current I
B = Magnetic Induction (tesla)
inside the material

11. ORIGIN OF MAGNETISM IN MATERIALS
A moving electric charge, macroscopically or “microscopically” is responsible for Magnetism
Nuclear spin
Very Weak effect
Unpaired electrons required for net Magnetic Moment
Origin of Magnetism
Spin of electrons
Orbital motion of electrons
Weak effect.
Magnetic Moment resultant from the spin of a single unpaired electron → Bohr Magneton = x 1024 A/m2

12. Origin of magnetic dipoles
The spin of the electron produces a magnetic field with a direction dependent on the quantum number ml.

13. Origin of magnetic dipoles
The spin of the electron produces a magnetic field with a direction dependent on the quantum number ms.

14. Electrons orbiting around the nucleus create a magnetic field around the atom.

15. Classification of magnetic Materials
Permanent Dipoles No
Yes
Para, Ferro, Anti ferro,
Ferri magnetic materials
Dia magnetic materials
Alignment of dipoles
Random
Uniform
Ferro, Anti ferro, Ferri
Para
Same
Direction of dipoles
Opposite
Ferro
Anti ferro, Ferri
Magnitudes of dipoles
Different
Same
Ferri
Anti ferro

16. Diamagnetic Materials

17. Properties It is a weak form of magnetism
Diamagnetism is because of orbital magnetic moment.
No permanent dipoles are present so net magnetic moment is zero.
Persists only when external field is applied.
The number of orientations of electronic orbits is such that the vector sum of the magnetic moments is zero.
Dipoles are induced by change in orbital motion of electrons due to applied magnetic field.

18. Diamagnetic materials
No Applied
Magnetic Field (H = 0)
Applied
Magnetic Field (H)
none
opposing

20. External field will cause a rotation action on the individual electronic orbits.
The external magnetic field produces induced magnetic moment which is due to orbital magnetic moment.
Induced magnetic moment is always in opposite direction of the applied magnetic field.
So magnetic induction in the specimen decreases.
Magnetic susceptibility is small and negative.
Repels magnetic lines of force.

21. Diamagnetic susceptibility is independent of temperature and applied magnetic field strength.
Susceptibility is of the order of
Relative permeability is less than one.
It is present in all materials, but since it is so weak it can be observed only when other types of magnetism are totally absent.
Examples: Bi, Zn, gold, H2O, alkali earth elements (Be, Mg, Ca, Sr), superconducting elements in superconducting state.

22. paramagnetic Materials

23. Properties Possess permanent dipoles.
If the orbital's are not completely filled or spins not balanced, an overall small magnetic moment may exist.
i.e. paramagnetism is because of orbital and spin magnetic moments of the electron.
In the absence of external magnetic field
all dipoles are randomly oriented
so net magnetic moment is zero.
Spin alignment is random.
The magnetic dipoles do not interact

24. Paramagnetic Materials
No Applied
Magnetic Field (H = 0)
Applied
Magnetic Field (H)
random
aligned

25. In presence of magnetic field the
material gets feebly magnetized i.e. the material allows few magnetic lines of force to pass through it.
Relative permeability µr >1 (barely, ≈ to 1.01).
The orientation of magnetic dipoles depends on temperature and applied field.
Susceptibility is independent of applied mag. field & depends on temperature
C is Curie constant

27. With increase in temperature susceptibility decreases.
Susceptibility is small and positive.
These materials are used in lasers.
Paramagnetic property of oxygen is used in NMR technique for medical diagnose.
The susceptibility range from 10-5 to 10-2.
Examples: alkali metals (Li, Na, K, Rb), transition metals, Al, Pt, Mn, Cr etc.

30. Ferromagnetic Materials

31. Properties
Permanent dipoles are present so possess net magnetic moment
Origin for magnetism in Ferro mag. Materials are due to Spin magnetic moment.
Material shows magnetic properties even in the absence of external magnetic field.
Possess spontaneous magnetization.
Spontaneous magnetization is because of interaction between dipoles called EXCHANGE COUPLING.

32. aligned
No Applied
Magnetic Field (H = 0)
Applied
Magnetic Field (H)

33. Magnetic susceptibility is as high as 106.
So H << M. thus Bs = µoMs
Magnetic induction
B (tesla)
Strength of applied magnetic field (H)
(ampere-turns/m)
Ferromagnetic

34. When placed in external mag
When placed in external mag. field it strongly attracts magnetic lines of force.
All spins are aligned parallel & in same direction.
Susceptibility is large and positive, it is given by Curie Weiss Law
C is Curie constant & θ is Curie temperature.
When temp is greater than curie temp then the material gets converted in to paramagnetic.
They possess the property of HYSTERESIS.
Material gets divided into small regions called domains.
Examples: Fe, Co, Ni.

35. Ferro magnetic Materials
Even when H = 0, the dipoles tend to strongly align over small patches.
When H is applied, the domains align to produce a large net magnetization.

36. Thermal energy can randomize the spin
Tcurie
Ferromagnetic
Paramagnetic
Heat
Tc for different materials: Fe=1043 K, Ni=631 K,
Co=1400 K, Gd= 298 K

37. Curie Temperature
The temperature above (Tc) which ferromagnetic material become paramagnetic.
Below the Curie temperature, the ferromagnetic is ordered and above it, disordered.
The saturation magnetization goes to zero at the Curie temperature.

38. Antiferro magnetic Material

39. Properties The spin alignment is in antiparallel manner.
So net magnetic moment is zero.
Susceptibility depends on temperature.
Susceptibility is small and positive.
Initially susceptibility increases with increase in temperature and beyond Neel temperature the susceptibility decreases with temperature.
At Neel temperature susceptibility is maximum.
Examples: FeO, MnO, Cr2O3 and salts of transition elements.

42. Ferrimagnetic Materials

43. Ferrimagnetic Materials
Classification of Ferrimagnetic Materials
Ferrimagnetic Materials
Cubic Ferrites
MFe2O4
Hexagonal Ferrites
AB12O19
Garnets
M3Fe5O12

44. Properties Special type of ferro and antiferromagnetic material.
Generally oxides in nature.
Ionic in nature
Ceramic in nature so high resistivity (insulators)
The spin alignment is antiparallel but different magnitude.
So they possess net magnetic moment.
Also called ferrites.
General form MFe2O4 where M is a divalent metal ion.
Susceptibility is very large and positive.
Examples: ferrous ferrite, nickle ferrite

45. Ion
Spin Orientation
Net Spin S
Magnetic Moment
E.C
Mn2+
3d5
5/2
5µB
Fe2+
3d6 2
4µB
Co2+
3d7
3/2
3µB
Ni2+
3d8 1
2µB
Cu2+
3d9
1/2
1µB

46. Net magnetic moment atom crystal Na 3s1 1 B 4 B 2.2 B Fe 3d64s2
Unpaired electrons give rise to ferromagnetism in alkali metals
Net magnetic moment
atom
crystal
Na 3s1
1 B
4 B
2.2 B
Fe 3d64s2
3 B
Co 3d74s2
1.7 B
Ni 3d84s2
2 B
0.6 B

47. Ferrimagnetism All Fe2+ have a spin magnetic moment.
Half of Fe3+ have a spin moment in one direction, the other half in the other (decreasing the overall moment to just that contributed by the Fe2+ ions).
Simpler picture showing a net magnetic moment.

48. Ferrimagnetism-Structure

50. Domain Theory of Ferromagnetic Materials

52. What happens when magnetic field is applied to the ferromagnetic crystal?

53. Ferromagnetism Materials that retain a magnetization in zero field
Quantum mechanical exchange interactions favour parallel alignment of moments
Examples: iron, cobalt

54. According to Becker, there are two independent processes which take place and lead to magnetization when magnetic field is applied.
Domain wall moment or Domain growth:
Domain rotation:

55. Domain wall moment or Domain wall growth
Volume of favorably oriented domains will increase.
Occurs at low magnetic field.
It is a reversible process.
Rotation of Domains
Rotation of less favorably oriented domains takes place.
Occurs at large magnetic field.
It is a irreversible process.

56. Domain Structure and the Hysteresis Loop
Domain growth:
Each domain is magnetized in a different direction
2. Applying a field changes domain structure. Domains with magnetization in direction of field grow.
3. Other domains shrink
Domain rotation:
Finally by applying very strong fields can saturate magnetization by creating single domain

57. Domain Structure and the Hysteresis Loop
Bloch walls - The boundaries between magnetic domains.
The entire change in spin direction between domains does not occur in one sudden jump across a single atomic plane rather takes place in a gradual way extending over many atomic planes.
Bloch Wall
The magnetic moments in adjoining atoms change direction continuously across the boundary between domains.

58. Magnetic domains
Applying very strong fields can saturate magnetization by creating single domain

59. Hysteresis Curve
Means lagging or retarding of an effect behind the cause of the effect.
Here effect is B & cause of the effect is H.
Also called B H curve.
Hysteresis in magnetic materials means lagging of magnetic induction (B) or magnetization (M) behind the magnetizing field (H).

61. Domain Structure and the Hysteresis Loop
ferromagnetic or ferrimagnetic material initially unmagnetized
H = 0
Applied Magnetic Field (H)
Magnetic
induction (B) B
sat H
• As the applied field (H) increases...
---the magnetic moment aligns with H.
• “Domains” with
aligned magnetic
moment grow at
expense of poorly
aligned ones!

62. Domain Structure and the Hysteresis Loop
When a magnetic field is first applied to a magnetic material, magnetization initially increases slowly, then more rapidly as the domains begin to grow.
Later, magnetization slows, as domains must eventually rotate to reach saturation.
Notice the permeability values depend upon the magnitude of H.

63. Hysteresis Loop
Hysteresis loop - The loop traced out by magnetization in a ferromagnetic or ferrimagnetic material as the magnetic field is cycled. OR
Removing the field does not necessarily return domain structure to original state. Hence results in magnetic hysteresis. B
2. apply H, cause
alignment
3. remove H, alignment stays!
=> permanent magnet! 4
Negative H needed to demagnitize!
. Coercivity, HC
Applied Magnetic
Field (H)
1. initial (unmagnetized state)

64. Ferromagnetism: Magnetic hysteresis
Mrs Hc Ms
Ms – Saturation magnetization
Mrs – Saturation remanent magnetization
Hc – Coercive force (the field needed to bring the magnetization back to zero)

65. remanent magnetization = M0
coercivity = Hc

66. Hysteresis Loop
Magnetization by domain rotation
Domain growth irreversible boundary displacements.
Means lagging or retarding of an effect behind the cause of the effect.
Here effect is B & cause of the effect is H.
Also called B H curve.
Hysteresis in magnetic materials means lagging of magnetic induction (B) or magnetization (M) behind the magnetizing field (H).
Domain growth reversible boundary displacements.

67. Hysteresis, Remanence, & Coercivity of Ferromagnetic Materials

68. “hard” ferromagnetic material has a large M0 and large Hc.
“soft” ferromagnetic material has both a small M0 and Hc.

71. Hard versus Soft Magnets
Characteristics of soft magnetic materials:
High initial permeability.
Low coercivity.
Reaches to saturation magnetization with a relatively low applied magnetic field.
It can be easily magnetized and demagnetized.
Low Hysteresis loss.
Applications involve, generators, motors, dynamos, Cores of transformers and switching circuits.

72. Importance of Soft Magnetic Materials:
Saturation magnetization can be changed by altering composition of the materials.
Ex:- substitution of Ni2+ in place of Fe2+ changes saturation magnetization of ferrous-Ferrite.
Susceptibility and coercivity which also influence the shape of the Hysteresis curve are sensitive to the structural variables rather than composition.
Low value of coercivity corresponds to the easy movement of domain walls as magnetic field changes magnitude and/ or direction.

73. Hard versus Soft Magnets
Hard Magnets:
Characteristics of Hard magnetic materials:
Low initial permeability.
High coercivity and High remanence.
High saturation flux density.
Reaches to saturation magnetization with a high applied magnetic field.
It can not be easily magnetized and demagnetized.
High Hysteresis loss.
Used as permanent magnets.

74. Importance of Hard magnetic material:
Two important characteristics related to applications of these materials are (i) Coercivity and (ii) energy product expressed as (BH)max with units in kJ/m3.
This corresponds to the area of largest B-H rectangle that can be constructed within the second quadrant of the Hysteresis curve.
Larger the value of energy product harder is the material in terms of its magnetic characteristics.
Schematic magnetization curve that displays hysteresis. Within the second quadrant are drawn two B–H energy product rectangles; the area of that rectangle labeled (BH)max is the largest possible, which is greater than the area defined by Bd–Hd

75. Who to get larger area of (BH)max i.e., who to produce Hard magnets?
Energy product represents the amount of energy required to demagnetize a permanent magnet.
Hysteresis behaviour depends upon the movement of domain walls.
The movement of domain walls depends on the final microstructure.
Ex: the size, shape and orientation of crystal domains and impurities.
Microstructure will depend upon how the material is processed.
In a hard magnetic material, impurities are purposely introduced, to make it hard. Due to these impurities domain walls cannot move easily.
Finally the coercivity can increase and susceptibility can be decrease.
So large external field is required to demagnetization i.e., difficult to move the domain walls.

76. Hard Magnetic Material
Soft Magnetic Material
Have large hysteresis loss.
Have low hysteresis loss.
Domain wall moment is difficult
Domain wall moment is relatively easier.
Coercivity & Retentivity are large.
Coercivity & Retentivity are small.
Cannot be easily magnetized & demagnetized
Can be easily magnetized & demagnetized.
Magneto static energy is large.
Magneto static energy is small.
Have small values of permeability and susceptibility
Have large values of susceptibility and permeability.
Used to make permanent magnets.
Used to make electromagnets.
Iron-nickel-aluminum alloys, copper-nickle-iron alloys, copper–nickel– cobalt alloys
Iron- silicon alloys, ferrous- nickel alloys, ferrites, garnets.

77. Problems
Calculate (a) the saturation magnetization and (b) the saturation flux density for nickel, which has a density of 8.90 g/cm3 atomic weight is g/mol and Avogadro’s number is 6.023x1023 atoms/mol.
A coil of wire 0.25 m long and having 400 turns carries a current of 15 A. (a) What is the magnitude of the magnetic field strength H? (b) Compute the flux density B if the coil is in a vacuum. (c) Compute the flux density inside a bar of chromium that is positioned within the coil. The susceptibility for chromium is 3.13x10-4 (d) Compute the magnitude of the magnetization M.
Demonstrate that the relative permeability and the magnetic susceptibility are related to each other.
The magnetic flux density within a bar of some material is tesla at an H field of 5x105 A/m. Compute the following for this material: (a) the magnetic permeability, and (b) the magnetic susceptibility. (c) What type(s) of magnetism would you suggest is(are) being displayed by this material? Why?

78. The magnetization within a bar of some metal alloy is 1
The magnetization within a bar of some metal alloy is 1.2x106 A/m at an H field of 200 A/m. Compute the following:(a) the magnetic susceptibility, (b) the permeability, and (c) the magnetic flux density within this material. (d) What type(s) of magnetism would you suggest as being displayed by this material? Why?
Compute (a) the saturation magnetization and (b) the saturation flux density for iron, which has a net magnetic moment per atom of 2.2 Bohr magnetons and a density of 7.87 g/cm3.
A coil of wire 0.5 m long and having 20 turns carries a current of 1.0 A. (a) Compute the flux density if the coil is within a vacuum. (b) A bar of an iron–silicon alloy, the B-H behavior for which is shown in below Figure, is positioned within the coil. What is the flux density within this bar? (c) Suppose that a bar of molybdenum is now situated within the coil. The susceptibility of Mo is 1.19x10-4. What current must be used to produce the same B field in the Mo as was produced in the iron–silicon alloy (part b) using 1.0 A?

80. An iron bar magnet having a coercivity of 7000 A/m is to be demagnetized. If the bar is inserted within a cylindrical wire coil 0.25 m long and having 150 turns, what electric current is required to generate the necessary magnetic field?
A bar of an iron–silicon alloy having the B–H behavior shown in above Figure is inserted within a coil of wire 0.40 m long and having 50 turns, through which passes a current of 0.1 A.(a) What is the B field within this bar? (b) At this magnetic field, (i) What is the permeability? (ii) What is the relative permeability? (iii) What is the susceptibility? (iv) What is the magnetization?
Below figure shows the B-versus-H curve for a nickel–iron alloy. (a) What is the saturation flux density? (b) What is the saturation magnetization? (c) What is the remanence? (d) What is the coercivity? (e) On the basis of data in Tables 20.5 and 20.6, would you classify this material as a soft or hard magnetic material? Why?