1) Permanent magnetic dipoles in matter originate from unpaired electrons in atoms. The magnetic moment of electrons is expressed in Bohr magnetons. 2) In solids, overlapping atomic orbitals can reduce magnetic moments. For example, Fe has a moment of 4 Bohr magnetons individually but 2.2 in crystal form due to orbital overlap. 3) Materials exhibit paramagnetism, diamagnetism, ferromagnetism or ferrimagnetism depending on their electron configuration. Ferromagnetic materials have spontaneous magnetization above their Curie temperature due to positive exchange energy between atomic spins.

1. BMS COLLEGE OF ENGINEERING
Subject: Electricals and Electronics Engineering Materials
Subject Code: 19EE7CE2EM
ORIGIN OF PERMANENT MAGNETIC DIPOLES IN MATTER
By:
Akarsh K
Gagan Gowda G N
Rakshith J
Sanjeev C Achar

2. Few basic definitions
● Magnetic flux density (B) is defined as the number of magnetic flux lines passing through a unit area, that is,
B= 𝛟/A.
● The intensity of magnetic field or magnetic field strength is denoted by H.
● B and H are related as: B=μ0H, where μ0 is the permeability of free space. If the setup is not placed in
vacuum, then μ0 is replaced by μ, the permeability of that medium.
● When susceptibility (The degree of magnetization in response to an applied magnetic field
), 𝝌 is taken into account, we get: B=μ 0(1+ 𝝌 )H.

3. The Bohr magneton
 Any moving, charge-carrying particle produces its own magnetic field. So does an electron, spinning
about its own axis.
 The magnetic moment of an electron is expressed in Bohr magnetons. 1 Bohr magneton=9.273 x 10-24
Am2.
 The net magnetic moment of paired electrons is always zero, based on Pauli’s principle as one electron
would have a spin of +1/2 and the other of -1/2.
 Partially filled degenerate orbitals tend to have higher magnetic moment.

4. The scenario in solids
 In solids, there is an overlap of orbitals as the atoms are packed very closely.
 For example, in case of the d-block elements, there is a partial overlap of 4s and 3d orbitals.
 Due to this, the 4s electrons spend some time in 3d band. There is thus, a reduction in net
magnetic moment caused due to overlapping of orbitals.
 For example, Fe in elemental state has a magnetic moment of 4 units and a magnetic
moment of 2.2 units in crystal state.
 Magnetization, is defined as the sum of magnetic moments per unit volume.

5.  Paramagnetism is the phenomena by which paramagnetic materials (materials having unpaired electron(s))
are slightly attracted by magnetic fields.
 In the absence of magnetic field, these materials have permanent magnetic moments due to unpaired
electron(s). For example, Aluminium.
 Diamagnetism is exhibited in those elements which have completely paired electrons. Such electrons are
called as diamagnetic electrons and their net spin is zero.
 These materials are repelled by an electromagnetic field as it creates induced magnetic field in the ooposite
direction. For example, Magnesium.
Paramagnetism and diamagnetism
Fig.1. A diamagnetic material slightly
repelling the magnetic field lines
Fig.2. A paramagnetic material
slightly attracting magnetic
field lines

6. Ferromagnetism and related phenomena
 In solids, the outer electronic orbitals of neighboring atoms overlap and produce energy bands.
 For example, in first transition metals, the 3d orbitals are large enough to overlap with the 3d orbitals of
adjacent atoms. The 3d bands would then contain all paired electrons and hence net magnetic moment will
be zero. This is known as antiferromagnetic coupling.
 Along the period, the atomic radius decreases and hence the degree of overlap decreases. Exceptions are
Fe, Ni and Co.
 However, this lowering is offset by an increase in Fermi level and that in kinetic energy of electrons.
 The net gain in energy, is a function of ratio of atomic diameter to the diameter of 3d orbital. It is found that
when this ration is between 1.5 and 2, then the exchange of energy is positive and the spins are favoured.
Among the common metals, only Fe, Ni and Co show such spontaneous magnetization.
 Curie temperature is that temperature at which ferromagnetic materials behave as paramagnetic materials.

7. Ferrimagnetism
 Ferrimagnetism can be defined as a kind of magnetism where magnetic moments have opposing moments
similar to that of antiferromagnetism; however, the antiparallel moments do not cancel each other out, and a
spontaneous magnetization occurs in absence of H.
 Examples are Co+2, Ba+2 and ferrites of these.
Fig.3a. Electron spin in
ferromagnetic materials
Fig.3b. Electron spin in
antiferromagnetic
materials
Fig.3c. Electron spin in
ferrimagnetic materials

8. The domain structure
 Iron has a high Curie temperature and all the spins are aligned. Yet, at room temperature, a piece of iron is
not magnetic. This discrepancy was explained by Weiss, by giving the idea of magnetic domains.
 He stated that, an iron piece consists of several domains. Each domain has spins that are all parallel.
However, the adjacent domains have anti-parallel spins, and hence they cancel out each other, thereby
giving net magnetic moment as zero.
 Weiss also stated that magnetization of a crystal is alignment of various domains which are already
ferromagnetic
 The magnetostatic energy of a ferromagnetic solid can be reduced if a number of domains are arranged such
that no poles exist at the surface and no lines of force go out of the material

9. The domain structure
Fig.4. With one domain, the
magnetic lines of force go out
of the material.
Fig.4. The magnetic lines do
not go out if a number of
domains are present.

10. Pros
The Hysteresis loop

11. Applications
In the design of
PMMC, EMMC, and MI.
2.
Superconductors
(perfectly
diamagnetic) are used
in MRI systems.
4.
Magnetic levitation of
bullet trains.
3.
Iron losses in transformers
1.

12. References
1. Raghavan, V. (2015). Materials science and engineering: A first course. PHI Learning Private Limited.
2. Explain the origin of diamagnetism and paramagnetism: Socratic. Socratic.org. (2017, August 29). Retrieved
January 4, 2023, from https://socratic.org/questions/explain-the-origin-of-diamagnetism-and-paramagnetism
3. Ferrimagnetism. Ferrimagnetism - an overview | ScienceDirect Topics. (n.d.). Retrieved January 4, 2023, from
https://www.sciencedirect.com/topics/materials-science/ferrimagnetism#:~:text=2.5%20Ferrimagnetism-
,Ferrimagnetism%20can%20be%20defined%20as%20a%20kind%20of%20magnetism%20where,N%C3%A9
el%20temperature%20(TN)
4. Pravallika, P. (2021, March 30). Bohr magneton - definitation, derivation & explanation. ProtonsTalk.
Retrieved January 4, 2023, from https://protonstalk.com/moving-charges-and-magnetism/bohr-magneton/

13. Thank you