CLASS NOTE

1. A material is said to be magnetic material if it can alter the magnetic flux density
when placed in an external magnetic field, H.
Magnetic Flux in
vacuum
Magnetic Flux in presence of a Magnetic Material
Magnetic Properties of Compounds
Dr. Saroj L. Samal
Department of Chemistry

2. Origin of Magnetism
The magnetic moment is the measure of
the strength of the magnet and is the
ability to be affected by an external
magnetic field H.
Macroscopic Origin
Magnetic Moment Vector (m). |m| = IA,
Units: [Am2] or [Joule/Tesla].
Magnetic field strength/Magnetizing force (H). (Measure of the strength
of the externally applied field). Units: [A/m]
Dr. Saroj L. Samal
Department of Chemistry
If a loop of area A is carrying a current I, the
intrinsic intensity of the magnetic field is given
by the magnetic moment vector (m) directed
from the north pole to the south pole.
Magnetic moment vector (m) is the product of the current flowing and the area.

3. Magnetic Moment
Magnetization: M = Magnetic Moment per unit Volume
I = current
R Q
m = I(pR2) n

= L
Q
2m
M =
Si mi
V
(A/m)
3
Dr. Saroj L. Samal
Department of Chemistry
L is the angular momentum
m mass of the particle
Q is the charge of the particle
Magnetic moment

4. Atomic Origin of Magnetic Moment
i) Nuclear spin (which is slow and small contribution to the overall magnetic effect)
ii) Spin of electrons
iii) Orbital motion of electrons around the nucleus
Origin of Magnetism
Dr. Saroj L. Samal
Department of Chemistry
Microscopic Origin of Magnetism

5. The magnitude of the orbital magnetic momentum of an electron with orbital-angular
momentum quantum l is
m = eℏ/2me[l(l+1)]1/2 = μB[l(l+1)]1/2
The magnetic moment due to spin is equal to the magnetic moment due to orbital motion in
the first Bohr orbit and is approximately expressed in terms of the Bohr magneton (B):
Origin of Magnetism
Dr. Saroj L. Samal
Department of Chemistry
Bohr Magneton
As the orbital angular momentum is quantized and is given by nħ
m = g L
Q
2m
Electron: Orbital Angular Momentum (l; g = 1)
Quantum Mechanics:
m = gμB[l(l+1)]1/2
m = g S
Q
2m
Spin Angular Momentum (s = ½; g  2)

6. Magnetic Effect
Magnetic effects are determined by measuring the response to an external magnetic
field H, which sets up a magnetic induction B within the macroscopic body.
B = H + 4pM Gaussian (cgs) units
Vacuum (M = 0) Paramagnetic
Substance
Diamagnetic
Substance
INDUCTION
(Flux Density)
FIELD
(Field Intensity)
MAGNETIZATION
6
Dr. Saroj L. Samal
Department of Chemistry

7. Magnetization (M) = magnetic moment (m) per unit volume (V).
Magnetic induction/Magnetic flux density (B) = Magnetic flux per unit area
Units: [Tesla = Weber/m2]
B is the magnetic flux density inside the material
M measures the materials response to the applied field H
Or M is the magnetization induced by the applied external magnetic field H.
M = m/V
Magnetic Effect
Dr. Saroj L. Samal
Department of Chemistry
Units: [A/m]

8. cv (Volume Susceptibility): how sensitive the
material towards the external magnetic field
B = H and M = cvH
B = H + 4pM (In CGS system)
𝐵
𝐻
= 1 + 4𝜋
𝑀
𝐻
μ = 1 + 4pχv
Gaussian Units MKS Units
B = H + 4pM B = 0(H + M)
H = H + 4pcvH H = 0(H + cvH)
 = 1 + 4pcv  = 0(1 + cv)
cv = ( - 1)/4p cv = (/0) - 1
Magnetic Induction vs. Magnetic Field
c  M/H (the symbol cv is also used to emphasize that the
quantity is per unit volume)
Dr. Saroj L. Samal
Department of Chemistry
 (Permeability): Measure of concentration of lines of
force per unit area compare to that in the vacuum
Units: [dimensionless]
μ =
𝐵
𝐻
χv =
𝑀
𝐻
and

9. Magnetic Susceptibility
Gram Susceptibility: cg = cv / Density
Molar Susceptibility: cM = cg  FW (FW = formula weight)
= cv  FW / Density
9
μ = 1 + 4pχv μ =
𝐵
𝐻
Dr. Saroj L. Samal
Department of Chemistry
Vacuum (M = 0) Paramagnetic
Substance
Diamagnetic
Substance
Diamagnetism:  < 1;
Paramagnetism:  > 1;
Ferromagnetism:  >> 1;
Superconductors:  = 0;
since in a superconductor the field B is zero – the field is
completely screened from the interior of the material

10. Diamagnetism Ideal Paramagnetism
Ferromagnetism
Antiferromagnetism
Types of Magnetic Order
10
Ferromagnetic

11. Ferrimagnetism
Type of Magnetism ( strength/magnitude)
Weak Strong
Diamagnetic &
Paramagnetic
Materials
Ferromagnetic,
Antiferromagnetic &
Ferrimagnetic
Materials
Ferrimagnetic
Types of Magnetic Order
Dr. Saroj L. Samal
Department of Chemistry

12. Magnetic moment of an atom or ion in free space is given by = gJ B J
B = 9.2740  10-24 J/T (Bohr magneton)
(J = │L + S│ for orbitals more than half filled )
= │L −S│ for orbitals less than half filled
gJ = 1 + J (J + 1) + S (S + 1) - L (L + 1)
2J (J + 1)
Paramagnetism
gJ is Landé g-factor
Saturation magnetic moment: Maximum value of the moment by aligning all
dipoles with a field (high field strength, low temperature).
Or, sat = gJ Jz B
“Spin-Only”: sat = 2 S B
Magnetic Field H || z = gJ B Jz
Dr. Saroj L. Samal
Department of Chemistry

13. Paramagnetism
Effective magnetic moment: eff = |mpara| = gJ [J (J + 1)]1/2 B
“Spin-Only”: eff = 2 [S (S + 1)]1/2 B
(When Orbital Angular Momentum is quenched…)
sat < eff.
Dr. Saroj L. Samal
Department of Chemistry
gJ = 1 +
J (J + 1) + S (S + 1) - L (L + 1)
2J (J + 1)
dn Examples 2S+1LJ L S J
d1 Sc, Ti3 2D3/2 2 1/2 3/2
d2 Ti, V3+ 3F2 3 1 2
d3 V, Cr3+ 4F3/2 3 3/2 3/2
d4 Mn3+, Ru4+ 5D0 2 2 0
d5 Mn, Fe3+ 6S5/2 0 5/2 5/2
d6 Fe, Co3+ 5D4 2 2 4
d7 Co, Co2+ 4F9/2 3 3/2 9/2
d8 Ni, Ni2+ 3F4 3 1 4
d9 Cu2+ 2D5/2 2 1/2 5/2
   
2 1 2
eff B B
S S n n
  
   
n = # of unpaired electrons

14. Electrons in the d Subshell
0 1 2 3 4 5 6 7 8 9 10
Magnetic
Moment
0
1
2
3
4
5
6
7
J Calculated
S Calculated
eff Experimental
Spin-Only Moment is a good approximation
for transition metals
Orbital angular momentum often quenched
gJ = 1 +
J (J + 1) + S (S + 1) - L (L + 1)
2J (J + 1)
14
Transition Metals (d n)
Dr. Saroj L. Samal
Department of Chemistry
Paramagnetic Atoms and Ions
dn Examples J = gJ [J(J+1)]1/2 S = 2[S(S+1)]1/2 eff (exp)
d1 Sc, Ti3 1.549 1.732 1.7-1.8
d2 Ti, V3+ 1.633 2.828 2.6-2.8
d3 V, Cr3+ 0.775 3.873 3.8
d4 Mn3+, Ru4+ 0.000 4.899 4.9
d5 Mn, Fe3+ 5.916 5.916 5.9
d6 Fe, Co3+ 6.708 4.899 5.1-5.5
d7 Co, Co2+ 6.633 3.873 4.1-5.2
d8 Ni, Ni2+ 5.590 2.828 2.8-4.0
d9 Cu2+ 3.550 1.732 1.7-2.2
(Units of B)
“SPIN-ONLY”
   
2 1 2
eff B B
S S n n
  
   
n = # of unpaired electrons

15. Paramagnetic Atoms
Electrons in the f Subshell
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Magnetic
Moment
0
2
4
6
8
10
J Calculated
S Calculated
eff Experimental
Must include spin-orbit coupling
Largest deviations for f 5 and f 6
15
Lanthanide Metals (f n)
Dr. Saroj L. Samal
Department of Chemistry

16. Temperature Dependence of Magnetization
 
eff 1
J B
g J J
 
 
16
𝑀 =
𝑁𝐴𝜇2
𝑒𝑓𝑓
3𝑘𝑇
𝐻
𝜒𝑀 =
𝑀
𝐻
=
𝑁𝐴𝜇2
𝑒𝑓𝑓
3𝑘𝑇
Dr. Saroj L. Samal
Department of Chemistry
High temperature / Low field:
Low temperature / High field:
M = NA gJ J B = Msat
sat J B
g J
 


17. Temperature Dependence of Magnetization
17
Curie’s Law:
M
C
T
c 
Where 𝐶 =
𝑁𝐴
𝜇2
𝑒𝑓𝑓
3𝑘
= 𝐶𝑢𝑟𝑖𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Susceptibility is inversely proportional to temperature
Or, C = 0.1252
eff
2
M
0.125 eff
T

c 
2
M 0.125 eff
T
c 

2
M
1 8
eff
T
c 
 
  
 
 
Dr. Saroj L. Samal
Department of Chemistry
𝜒𝑀 =
𝑀
𝐻
=
𝑁𝐴𝜇2
𝑒𝑓𝑓
3𝑘𝑇
B = 9.2740  10-24 J/T
k = 1.38 × 10−23 joule per kelvin
NA = 6.023 x 1023 mol-1

18. Temperature Dependence of Magnetization
T (K)
0 50 100 150 200 250 300
0.0
0.1
0.2
0.3
0.4
0.5
T (K)
0 50 100 150 200 250 300
T (K)
0 50 100 150 200 250 300
T
0.0
0.5
1.0
1.5
2.0
2
M
0.125 eff
T

c 
2
M
1 8
eff
T
c 
 
  
 
 
2
M 0.125 eff
T
c 

“Example”: Cr3+ (d 3)
S = 3.873 B (g = 2.00)
18
M
M
8
2.828
eff T
T
 c
c


Dr. Saroj L. Samal
Department of Chemistry

19. Slope = 8/μ2
eff = 1/C
μeff = 8𝐶
T (K)
0 50 100 150 200 250 300
2
M
1 8
eff
T
c 
 
  
 
 
As C = 0.1252
eff
dn Examples J = gJ [J(J+1)]1/2 S = 2[S(S+1)]1/2 eff (exp)
d1 Sc, Ti3 1.549 1.732 1.7-1.8
d2 Ti, V3+ 1.633 2.828 2.6-2.8
d3 V, Cr3+ 0.775 3.873 3.8
d4 Mn3+, Ru4+ 0.000 4.899 4.9
d5 Mn, Fe3+ 5.916 5.916 5.9
d6 Fe, Co3+ 6.708 4.899 5.1-5.5
d7 Co, Co2+ 6.633 3.873 4.1-5.2
d8 Ni, Ni2+ 5.590 2.828 2.8-4.0
d9 Cu2+ 3.550 1.732 1.7-2.2
Temperature Dependence of Magnetization
Dr. Saroj L. Samal
Department of Chemistry

20. Non-Ideal Paramagnets: Deviations from the Curie Law
M
C
T
c


-
Curie-Weiss Law:
Curie Constant
Weiss Constant
1
M
1
T
C C

c-    
 -
   
   
 = 0  > 0
 < 0 TN
T
TC
Antiferromagnetic Ferromagnetic
2
eff
0.125
C 

AFM and FM effects are
Interatomic.
20
Curie
(Paramagnetic)
Dr. Saroj L. Samal
Department of Chemistry

21. Effective magnetic moment: eff = |mpara| = gJ [J (J + 1)]1/2 B
   
2 1 2
eff B B
S S n n
  
   
Spin only magnetic moment
Curie’s Law: M
C
T
c  (C =Curie Constant = 0.1252
eff
2
M
1 8
eff
T
c 
 
  
 
 
μeff = 8𝐶
T (K)
0 50 100 150 200 250 300
2
M
1 8
eff
T
c 
 
  
 
 
(1/C)
IMPORTANT EQUATIONS
Saturated magnetic moment: sat = gJ Jz B
Dr. Saroj L. Samal
Department of Chemistry