This document discusses the magnetic properties of materials. Some key points: 1. Magnetic properties are studied using parameters like magnetic dipoles, magnetization, magnetic susceptibility, and permeability. Materials respond differently to external magnetic fields based on these properties. 2. The magnetic moment of a material arises from the orbital and spin motions of electrons and the nuclear spin. Only partially filled electron shells contribute to the net magnetic moment. 3. Materials are classified as diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, or ferrimagnetic based on their magnetic ordering and response to external fields. Ferromagnetic materials exhibit spontaneous magnetization from internal fields arising via exchange interactions between domains. 4. H

1. Magnetic Property
The response of the materials to external magnetic field degree of
response varies, which is measured in terms of their magnetization
(strong or weak)

2. The parameters used to study the magnetic behaviors of
the materials are as follows:
1.Magnetic dipoles & magnetic moment:
Magnetic dipoles are analogous to electric dipoles ;
consists of a north pole and a south pole of strength
‘m’ each separated by a small distance ‘2l’
Magnetic moment = m x 2l
A circular current loop is equivalent to a magnetic
dipole, magnetic moment
μM = I x A ( amp. m2)
Where ‘I’ is the current in the loop
and ‘A’ is the area of the loop
Torque on the dipole τ = μM X B
N S
2l
μM
I
Right hand
Screw rule

3. 2. Magnetisation = dipole moment / volume
M = μ / V ( amp. / met.)
3.Magnetic susceptibility = magnetization / mag. field strength
χ = M / H (no unit)
4.Magnetic permeability = magnetic induction / mag. field strength
μ = B / H (Wb / amp. met. = H/met)
μ =μ0 μr
5.Relative permeability μr = μ / μ0,
μ0 = absolute permeability = 4πX 10 -7 H/m
6.Relation between H, B & M is
B = μ0 (M+H) = μ0 (χH + H) = μ0 (1 + χ) H
7. Relative permeability & Susceptibility
B = μ H = μ0 μr H so μr =(1 + χ)

4. Origin of magnetic moment
• The three sources of magnetic moment in an atom of any material are
[1] Orbital motion of the electron
[2] Spin motion of the electron
[3] Nuclear spin
• If the vector sum of all the contribution is zero then net magnetization
is zero :- material is nonmagnetic.
1. Orbital motion of the electron
• Motion of the electron (charged particle)around the nucleus in a
circular orbit (orbital motion) is equivalent to a circular current and
behaves as a magnetic dipole.
• Associated magnetic moment is
μM = Ix A ( amp. m2)
• if ‘T’ is the time period for one rotation
& ‘v’ is the velocity of the electron
in the orbit , then T = 2 π r / v
v
r+
Orbital magnetic
moment
Electron
motion
Current

5. • Current I = - q/T
• magnetic moment μM = (- q v / 2 π r ) (A) = - ( q v / 2 π r ) (π r2 )
• qvr/2 = - q/ 2m ( mvr)
• = - (q/ 2m ) L
• Orbital magnetic moment
 Quantum no. associated with ‘L’ is √* l(l+1) ħ+ ,
‘l’ is the orbital quantum no.
• l=0---s shell, l=1---p shell,
• l=2-----d shell, l=3------f shell
2. Spin motion of the electron
Similarly, the spin motion of the electron around their own axis give
rise to spin magnetic moment
where γ is called spin gyromagnetic ratio. (γ=2)
μorb = - (q/ 2m ) L
μspin = -γ (q/ 2m ) S
μorb = -√l(l+1) (qћ / 2m )

6.  Quantum no. associated with ‘S’ is ± ħ/2
3. Nuclear magnetic moment
Due to the spin of nucleus ( protons & neutrons) , a magnetic moment is
associated which is very small as compared to the electronic
contribution as heavy mass is involved (10-3 times) is masked by
electronic mag. mom.
 Total magnetic moment is due to electron motion inside the atom
μM = - g (q/ 2m ) (L+S) = - g (q/ 2m ) J,
‘J’ is the total angular momentum varying from |L+S| to |L- S|
 If magnetic field is applied along z-direction , the component of the
total magnetic moment in that direction is,
μM = - g (qħ/2m) mj
 Where ‘mj ‘is the magnetic quantum no. varying from (J to -J)
 g is called Lande’s g-factor,
 for spin moment g=2

7. • g =
• Calculation rules
 1.If electrons are in the s-orbit, orbital magnetic moment is zero
(l=0)
 2. For completely filled shell, orbital magnetic moment is zero (l=0)
As ml = l to –l (s shell=0, p shell, l=1, d shell, l=2 and f shell, l=3..)
 3.If all electrons are paired, spin magnetic momentum is zero
 4. Only partially filled p, d and f shells contribute to orbital
magnetic moment
)1(2
)1()1()1(
1



JJ
LLSSJJ

8. Bohr magnetron
• If there is a single electron it will have spin magnetic moment
only
• μs = -2 (q ħ / 2m) ±1/2 , as g=2 and mj= ±1/2
• ‘μB‘ = = 9.27x 10-24 Am2
• This is the fundamental magnetic moment, called Bohr
magnetron ‘μB‘—it is the magnetic moment of an isolated
single electron or the magnetic moment of Hydrogen atom
• Usually magnetic moments of materials are expressed in terms
of ‘μB‘
• Spin magnetic moment can be expressed as μ = g μBS
• Hydrogen atom:- One electron in s shell. So l = 0 and s= +1/2 or
-1/2 implies that orbital magnetic mom. is zero and spin mag.
Mom. is same as the Bohr magnetron
2. Helium atom ?...calculate
m
q
2


9. • Hund’s rule:
• 1. spins of electrons remain parallel to each other to the max.
Extent
• 2. max . Value of L is consistent with the spin S
• 3. if shell is less than half filled J= |L- S| ,
if more than half filled J= |L+ S| &
if exactly half filled then L=0 and J=S

10. Classification of magnetic materials
• Diamagnetic material:- Have even no. of electrons, so no permanent
moment. When placed in external magnetic field get slightly
magnetised, in a direction opposite to the applied magnetic field.
• Paramagnetic materials:- Have net moment in the absence of ext.
magnetic field(partially filled p,d,f orbitals and unpaired electrons).
When placed in external magnetic field are magnetised in the
direction of the external magnetic field applied.
• Ferromagnetic materials:- Exhibit spontaneous magnetisation due to
an internal field arising due to mutual interaction between the
domains. When placed in ext. magnetic field acquire very large and
permanent magnetisation in the direction of the field.
 Antiferromagnetic materials:-Individual magnetic dipoles have
magnetic moment, but due to antiparallel arrangement net
magnetisation become zero.
 Ferrimagnetic materials:-Individual magnetic moments are
antiparallel, but having different magnitude do not cancel out
completely.

11. Diamagnetism Paramagnetism Ferromagnetism
1.Normally referred as non-
magnetic as the response is
very weak
2.In ext. magnetic field
magnetic moment induced
in a direction opposite to
applied field– repelled by
the field
H=0, M=0 H=H→
M= - M←
3. Permeability μ<1
4. susceptibility χ <0
5. Susceptibility does not
depend on temperature
5. Ex; Cu, Ag, Hg, Au, Zn, SC
1.Normally referred as non-
magnetic as the response is
weak
2. Posses permanent magnetic
moments, which are randomly
oriented in the absence of ext.
magnetic field., so net
magnetization is zero. When a
field is applied dipoles get
aligned in the field direction,
giving positive magnetization
3. Permeability μ>1
H=0, M=0 H=H→ M= M
4. susceptibility χ is positive,
small and temp. dependant
χ = C/ T →Curie law
5.Ex; Al, Cr, Na, Ti, Zr
1.Referred as magnetic as
response is strong( due to
exchange coupling)
2. Posses permanent dipoles
3.Show spontaneous
magnetization—even in the
absence of ext. field,
magnetization shown is high,
when field is applied, M
increases
4.Permeability μ>1
5.susceptibility χ is positive,
large and temp. dependant
χ = C/ T-θ →Curie – Weiss
law
6. ferromagnetic domain
show
spontaneous
magnetisation
7. Show hysteresis
Classification of magnetic materials

12. Ferromagnetic theory ( Weiss Theory)
• Weiss predicted that, in ferromagnetic materials Spontaneous
magnetization is observed, which is due to a strong internal field
arising from an exchange interaction between the magnetic
moments in the neighborhood domains
• exchange interaction
between two atoms ‘I’ and ‘j’
• = U= -2 J SiSj
‘J’ is called the exchange integral
• H int = λM , where ‘λ’ is called Weiss constant
• H tot= H appl + Hint
• H tot= H appl + λM

13. • Ferromagnetic domains( 1-100 μm) :-
Domains in a favorable direction grow in size at the expense of
other domains till saturation is reached; there is only one
domain. Energy involved in the orientation is obtained from
the hysteresis curve.
B
Domain wall ≈ 10-2 μm

14. Ferromagnetic hysteresis
Ms(0)
T
Tc
Ms= saturation magnetisation
Mr = remanent magnetisation
is the measure of the strength
of the ferromagnetic material
as a permanent magnet (is the
magnetisation in the absence
of the external field).
Hc= coercive field
Temp. dependence of Ms
Ms

15. Easy direction:- is the crystallographic direction, along which when magnetic field
is applied, a ferromagnetic single crystal is easily magnetised.(for fairly low field).
SOFT & HARD FERROMAGNETIC HYSTERESIS LOOPS

16. Soft and Hard Magnetic materials
Soft ferromagnetic Hard ferromagnetic
1. Can be easily magnetized or
demagnetized
2. Thin and long hysteresis loop
3. High permeability and low coercive
field
4. Large susceptibility & low
remanent mag.
5. As area of the loop is small,
magnetic energy loss per volume is
less during magnetisation and
demagnetisation
6. Application: electromagnet, in
motors, generators, dynamos and
switching circuits
7. Ex: Fe-Si alloy , Fe-Co-Mn alloy and
Fe-Ni alloy
1. Can not be magnetised or
demagnetised easily
2. Wide hysteresis loop
3. Low permeability and high
coercive field
4. small susceptibility & high
remanent mag.
5. Large area of the loop indicates,
magnetic energy loss per volume is
high during magnetisation and
demagnetisation
6. For permanent magnet in speakers,
clocks
7. Rare earth alloys with Mn, Fe, Co,
Ni

17. Antiferromagnetism:
• when exchange interaction between adjacent or neighboring
domains give rise to ordered antiparallel spin arrangement,
below a temp. called Neel temp. ex.- MnO,MnS,FeCl2, Co O. Net
moment or magnetisation is Zero
χ= C / (T +TN )
TTN
χ

18. Ferrimagnetic & Antiferromagnetic materials
• Ferrimagnetic material are special class of ferromagnetic material
called ‘ ferrites’ with high permeability, saturation
magnetisation and they show hysteresis (square loop)
• They are different from the ferromagnetic materials only in the
way the spin magnetic moments are arranged in them.
• Formula: Me2+O Fe2
3+O3 :- Me is a divalent atom
(Fe, Mn, Zn,Cd,Cu,Ni,Co,Mg )
 Crystal structure: Inverse spinel
 cubic cell has ‘8’ molecules.
 In the unit cell, 32 O-2 ions ,
16 Fe3+ ions ,
8 Me2+ ions.

19. Ferrites :- Me2+O Fe3+
2O3
Me=
Fe, Mn, Co, Ni, Cu, Mg, Zn, Cd
8 Me2+ ions and 8- Fe 3+, are
surrounded by 6 oxygen ions :-
Octahedral
8 Fe 3+ ions are surrounded by 4
oxygen ions :- Tetrahedral

20. • Octahedral site :- 8 Me2+ ions and 8- Fe 3+, are surrounded by
6 oxygen ions and have parallel spins.
• Tetrahedral site :- 8 Fe 3+ ions are surrounded by 4 oxygen ions
and spins antiparallel.
So net magnetic moment of Fe 3+ ions cancel ( 8 up spin and 8 down spin)
Only, 8 Me2+ ions contribute to magnetic moment.
Fe3+
Me2+
S= 5/2
S = 8 x [μm of
one Me 2+]
octahedral
Fe3+
S= 5/2
tetrahedral
Spinmomentsinferrites

21. Magnetisation of a ferrite
• Spin magnetic moment of one Me2+ atom μM = g μBs
• There are 8 Me2+ atoms in a unit cell ,
total moment in unit cell = 8 x μM
• Magnetisation
M = total moment per volume
• So, M = ( 8 x μM ) / a3
where ‘a’ is lattice parameter

22. Mn2+= 3d5
So,μ = g μBS
= 2 x 5/2 x μB = 5μB
Fe2+ = 3d6 μ = 4 μB
Co2+= 3d7 μ = 3 μB
Ni 2+= 3d8 μ = 2μB
Cu2+= 3d9 μ = 1μB
H
M
+Ms
-Ms
Hysteresis curve of ferrites
Find the spin magnetic moment of Ni3+

23. • Applications: resistivity of ferrites are very high so suitably
applied for high frequency application (eddy current energy
loss less) and in special magnetic devices.
• Ferrites have square hysteresis loop. So used for digital
storage device ( two values of magnetisation +Ms & - Ms; so
1 or 0 )
• Soft ferrites are used for high freq. Transformer core,
computer memory, hard disc, floppy disk audio video
cassette, recorder head
• Hard ferrites are used for permanent magnets in generator,
motor, loud speaker, telephone
• Non-volatile memory called magnetic bubbles(magnetic
domains in thin films)
• Mixed ferrites are produced by combining two different
divalent ions in suitable ratios, to obtain a specific
magnetisation desired.

24. Magnetic Anisotropy and Magnetostriction