Magnetic Susceptibility of magnetic materials

1. Kingdom of Saudi Arabia
Al-Imam Mohammad Ibn Saud Islamic
University
College of Sciences
Department of Physics
Title : Magnetic Susceptibility of magnetic materials
Prepared by: Samia Abdullah A_lotaibi
Supervisor: Dr. Mohamed Alamen
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2. Introduction
This final project will be dived in two parts :
1) first part: we will study each type of magnetic materials by
giving the definition, magnetic susceptibility, the properties and
some examples. Four type of magnetic materials are reviewed:
diamagnetic, paramagnetic, ferromagnetic and anti-
ferromagnetic.
2) second part: we will determine experimentally the type of some
magnetic materials based on the magnetic susceptibility by using
vibrator sample magnetometer (VSM) located at physics
department –Al imam University.
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3. * First part *
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4. Magnetic Susceptibility
Magnetic Susceptibility : is the ratio of the intensity of magnetism induced (M) in
a substance to the magnetizing force or intensity of field (B) .
Magnetic susceptibility reflects a material's degree of sensitivity to magnetic fields .
, (CGS)
* magnetic field intensity have two expression which are equally (B = H).
* units of χ is dimensionless.
Where :
χ : is the magnetic susceptibility of material .
M : is the Magnetization of material or the total magnetic moment per unit
volume .
B : is the magnetic field intensity (applied magnetic field).
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5. Types of magnetic materials :
1) Diamagnetic
2) paramagnetic
3) ferromagnetic
4) anti-ferromagnetic
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6. Diamagnetic Materials
Diamagnetic substances are composed of atoms which have no net
magnetic moments.
A negative magnetization is produced when the material is exposed
to external magnetic field, thus the susceptibility is negative .
Figure 1. Relationship between temperature and magnetic
susceptibility for diamagnetic materials
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7. In diamagnetic materials, the magnetic susceptibility can be
accurately predicted by Langevin's classical theory of
electromagnetism as follows :
Where :
: frequently a susceptibility is defined referred to unit mass or to a mole of the substance ,
which means The molar susceptibility .
: the magnetic permeability of a vacuum in H.
Z : the atomic number of the atom .
n : the atomic density in
e : the elementary charge in C .
: the root mean square of the square of the atomic radius in .
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8. Properties of diamagnetic materials :
• Diamagnetic materials exhibit small and negative magnetic susceptibility
in the range .
• Relative magnetic permeability of diamagnetic materials is always less than unity
that is μr < 1 .
• Magnetic susceptibility of diamagnetic materials does not change with temperature
Examples of diamagnetic materials are :
• Gases such as hydrogen, nitrogen, chlorine, and bromine and noble gases such as He,
Ne, Ar, Kr, Xe .
• The chemical elements from group IIA(2): Be; group IIIA(13): B, Ga, In, Tl; group
IVA(14): C, Si, Ge, Pb; group VA(15): P, As, Sb, Bi, group VIA(16) S, Se, Te; group
IA(11): Cu, Ag and Au; group IIA(12): Zn, Cd, Hg .
• Crystalline solid materials such as (MgO) and diamond .
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9. Paramagnetic Materials
In the paramagnetic materials, the magnetic moments do not interact with each
other and they are randomly arranged in the absence of a magnetic field .
Figure 3: Spin orientation in paramagnetic materials before and
after applying magnetic field
When a field is applied, the atomic magnetic moments are aligned in the
direction of the field and that will induce a net positive magnetization and
positive susceptibility.9 21/12/14399

10. The efficiency of the field in aligning the moments is opposed by
the randomizing effects of temperature.
This results in a temperature dependent susceptibility, known as
the Curie Law.
Figure 4: Relationship between temperature and
magnetic susceptibility for paramagnetic materials.
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11. The temperature dependence of the magnetic susceptibility of paramagnetic
materials is given by the Curie Law :
Curie Law
where:
: it is the magnetic permeability of a vacuum in .
n : it is the atomic density in
m : it is the microscopic dipolar magnetic moment of an atom in A.
k : it is the Boltzmann constant in J.
T : it is the absolute thermodynamic temperature in K
: the paramagnetic Curie temperature in K at which the susceptibility reaches its
maximum value.
C : it is the the paramagnetic Curie constant in
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12. Properties of paramagnetic materials :
1) The magnetic lines of forces due to the applied field are attracted towards the
paramagnetic material.
2) When placed in a non-uniform magnetic field, the paramagnetic materials move
from weaker parts of the field to the stronger parts.
3) Permeability of paramagnetic material is greater than 1.
4) Magnetic susceptibility of paramagnetic material is
positive
5) Susceptibility of paramagnetic materials varies inversely with the temperature
(Curie law).
6) Arises from permanent dipole moments on the atoms.
Examples of paramagnetic materials :
Gases for example: oxygen , and all the chemical elements dealing with diamagnets
for example :Li , Na , Mn , and all the platinum-group metals: Ru, Os, Pt.
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13. Ferromagnetic Materials
Ferromagnetic materials have magnetic dipolar moments aligned parallel
to each other even without an external applied magnetic field.
Figure 5 : Spin orientation in ferromagnetic materials
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14. Curie temperature
The Curie temperature is the temperature above it the ferromagnetic
materials become paramagnetic .
Figure 6 : Relationship between magnetic susceptibility
and temperatures for ferromagnetic materials
Materials Co Fe Ni Gd Fe2O3 MnAs
Curie temperature(K) 1388 1043 627 292 948 318
* Examples of Curie temperature for some materials:
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15. Properties of ferromagnetic materials :
1) A ferromagnetic materials has a spontaneous magnetic moment- a magnetic moment
even in zero applied magnetic field (at H = 0) below .
2) All ferromagnetic materials become paramagnetic above a temperature called Curie
temperature Tc .
3) Permeability is greater than 1 .
4) Magnetic susceptibility is large and positive .
5) Magnetic susceptibility decreases with the rise in temperature according to Curie law.
6) The source of ferromagnetism is the spin of the electrons.
Examples of ferromagnetic materials :
Nickel , cobalt, iron .
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16. Anti-ferromagnetic materials
In the antiferromagnetic materials, the alignment of the spin moments of
neighboring atoms or ions in exactly opposite directions
Figure 7: Spin orientation of anti-ferromagnetic materials
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17. Neel temperature
The Neel temperature is the temperature above it the anti-ferromagnetic
materials become paramagnetic .
Figure 8: Relationship between susceptibility and
temperatures for antiferromagnetic materials
Examples of Neel temperature for some materials:
Materials Cr NiO FeO MnO CoO MnS
Neel temperature(K) 308 525 198 116 291 160
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18. Properties of antiferromagnetic materials :
1) The antiferromagnetism will not produce any magnetisation because of the two
opposing spin components .
2) When we applied external field , the net magnetization will be different of zero due
to that the maximum spin are in the same direction .
3) Antiferromagnetism is a special case of ferrimagnetism .
4) Neel temperature is the critical temperature for the antiferromagnetic
materials .
Examples of antiferromagnetic materials : MnO , FeO, MnF2 .
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19. * Second part *
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20. Experimental results
In this part, we studied the magnetic properties of three materials by using
vibrator sample magnetometer (VSM) equipment
located at physics department. An external magnetic field is applied on the
powders materials and the magnetization values are registered. Based on the
definition of magnetic susceptibility in the first part of this report, we will
determine the type of each materials by calculating the value for each
materials.
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21. ZnO powder
Fig.9 shows the magnetization of ZnO powders . If we compare this figure
to Figure 1 in the first part of this report, we can conclude that the
behavior is similar to diamagnetic materials.
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
-6000 -4000 -2000 0 2000 4000 6000
Moment(emu)
Magnetic Field (G)
Graph of ZnO material
Figure 9. : Magnetization of ZnO powder
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22. We can confirm this conclusion by calculating also the magnetic susceptibility
for this materials . The magnetic susceptibility is :
If we take : (x , y) = (m ,B) , where : m = Magnetic Field (G) , B =Moment (emu)
magnetic susceptibility for two points :
So we conclude from the calculation of the magnetic susceptibility of the Zno
materials which are negative that ZnO is diamagnetic materials .
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23. ZnO:Mn powder
We showed in Fig.9 that ZnO is diamagnetic materials. If we doped it with ferromagnetic
materials, we are expecting that this magnetic behavior changes. Fig.10 shows the
magnetization of ZnO doped with 5% of Mn. It can be seen that ZnO change behavior
comparing to Fig.9. If we compare Fig.10 to Fig.4 of the first part, we can conclude that
(ZnO:Mn) is a paramagnetic material.
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
-60000 -40000 -20000 0 20000 40000 60000
Moment(emu)
Magnetic Field (Oe)
Graph of ZnO:Mn material
Figure 10. : Magnetization of ZnO doped Mn powder
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24. From the data table the magnetic susceptibility :
If we take : (x , y) = (m ,B) , where : m = Magnetic Field (G) , B =Moment (emu)
magnetic susceptibility for two points :
We conclude from the figure and from the positive value of the magnetic
susceptibility that ZnO:Mn powder is paramagnetic material .
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25. Ni powder
Fig.11 shows the magnetization of Ni powders. It is clear that the
behavior is different from the previous materials (ZnO and ZnO:Mn) .
-5
-4
-3
-2
-1
0
1
2
3
4
5
-15000 -10000 -5000 0 5000 10000 15000
Moment(emu)
Magnetic Field (G)
Graph of Ni metal
Figure 11. : Magnetization of Ni
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26. From the data table the magnetic susceptibility :
If we take : (x , y) = (m ,B) , where : m = Magnetic Field (G) , B =Moment (emu)
magnetic susceptibility for two points :
So we conclude from the calculation the magnetic susceptibility of the Ni
powder which is a positive and high that Ni materials is ferromagnetic
materials.
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