III–5 Magnetic Properties of
Materials
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Main Topics
•
•
•
•
•
Introduction to Magnetic Properties
Magnetism on the Microscopic Scale.
Diamagnetism.
Paramagnetism.
Ferromagnetism.
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Introduction Into Magnetic
Properties I
• Magnetic properties of materials are
generally more complicated than the electric
ones even on the macroscopic scale. We had
conductors in which the electric field was
zero and dielectrics (either polar or nonpolar), in which the field was always
weakened. Other behaviour is rare. More
subtle differences can be revealed only by
studying thermal or frequency properties.
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Introduction Into Magnetic
Properties II
• If a material is exposed to an external
magnetic field is gets magnetized
and an

internal magnetic field Bm appears in. It can
be described as the density of magnetic

dipole moments:

m
Bm 
V
• The volume V is small on macroscopic but
large on the atomic scale.
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Introduction Into Magnetic
Properties III
• The total field in the magnetized material can be

then written as a superposition of the original field B0

and internal field Bm :
 

B  B0  Bm
• Here, we can shall deal only with linear behavior:


Bm   m B0
• The parameter m is the magnetic susceptibility
which can now be greater or less than zero.
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Introduction Into Magnetic
Properties IV
• We can combine these equations:



B  (1   m ) B0  r B0
and define the relative permeability Km ,
usually also written as r.
• The absolute permeability is defined as:
 = 0 r = 0 Km
• The internal field of a long solenoid with a
core can then be written as: B = nI.
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Introduction Into Magnetic
Properties V
• Three common types of magnetic behavior
exist. The external field in materials can be
• weakened (m< 0 or Km < 1) this is called
diamagnetism
• slightly intensified, (m> 0 or Km >1) this is
called paramagnetism
• considerably intensified, (m>> 0 or Km >> 1)
this is called ferromagnetism.
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Introduction Into Magnetic
Properties VI
• If a material can be ferromagnetic is is a
dominant behavior which masks other
behavior (diamagnetism) that is also always
present but is much weaker.
• But the dominant behavior may disappear
with high temperature. Ferromagnetism
changes to paramagnetisms above Courie’s
temperature.
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Magnetism on Microscopic Scale
I
• Magnetic behavior of materials is an open
field of research. But the main types of
behavior can be illustrated by means of
relatively simple models. All must start
from the microscopic picture.
• We know that if we cut a piece of any size
and shape from a permanent magnet, we get
again a permanent magnet with both poles.
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Magnetism on Microscopic Scale
II
• If we continue to cut a permanent magnet we
would once get to the atomic scale. The question
is: which elementary particles are responsible for
magnetic behavior?
• We shall show that elementary magnetic dipole
moment is proportional to the specific charge so
electrons are responsible for the dominant
magnetic properties.
• Experiments exist, however, which are sensitive to
nucleus magnetic moment (NMR, Neutron Diff.).
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Magnetism on Microscopic Scale
III
• Electrons can generate magnetism in three
ways:
• As moving charges as current.
• Due to their spin.
• Due to their orbital rotation around a core.
• The later two mechanisms add together and
the way it is done is responsible for
magnetic behavior in particular material.
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Magnetism on Microscopic Scale
IV
• Electrons can be viewed as a tiny spinning
negative charged particles. The quantum
theory predicts spin angular momentum s:
s = h/4 = 5.27 10-35 Js
• Here h = 6.63 10-34 Js is the Planck constant
• Since electron is charged it also has a
magnetic dipole moment due to the spin:
1 ms = eh/4me = 9.27 10-24 J/T
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Magnetism on Microscopic Scale
V
• ms = mb is called Bohr magneton and it is
the smallest magnetic dipole moment which
can exist in Nature. So it serves as a
microscopic unit for dipole moments.
• We see that magnetic dipole is quantised.
• Spin is a quantum effect not a simple
classical rotation. Electron would irradiate
energy and slow down and fall on the core.
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Magnetism on Microscopic Scale
VI
• When electrons are bound in atoms they
also have orbital angular momentum. It also
is a quantum effect.
• It is illustrative to look at a classical
planetary model of electron, even if it is not
realistic, to see where the dependence on
the specific charge comes from.
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Magnetism on Microscopic Scale
VII
• Even in a very small but macroscopic piece of
material there is enormous number of electrons,
each having some spin and some angular
momentum. The total internal magnetic field is a
superposition of all electron dipole moments.
• The magnetic behavior generally depends on
whether all the magnetic moments are
compensated or if some residual magnetic moment
remains.
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Diamagnetism I
• Materials, in which all magnetic moments
are exactly compensated are diamagnetic.
Their internal induced magnetic field
weakens the external magnetic field.
• We can explain this behavior on (nonrealistic but sometimes useful) planetary
model of one electron orbiting around an
atom.
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Diamagnetism II
• Due to an external magnetic field a radial
force acts on the electron. It points toward
or out of the center depending on the
direction of the field. The force can’t
change the radius but if it points toward the
center it speeds the electron and if out it
slows it. This leads to a change in the
magnetic moment which is always opposite
to the field. So the field is weakened.
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Paramagnetism I
• Every electron is primarily diamagnetic but
if atoms have internal rest magnetic dipole
moment diamagnetism is masked by much
stronger effects. If the spin and orbital
moments in matter are not fully
compensated, the atoms as a whole have
magnetic moments and they behave like
magnetic dipoles. They tend to line up with
the external field and thereby reinforce it.
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Paramagnetism II
• The measure of organizing of dipoles due to
the external field depends on its strength
and it is disturbed by temperature
movement.
• For fields and temperatures of reasonable
values Curie’s law is valid:
Bm = CB/T
where C is a material parameter.
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Ferromagnetism I
• If we think of magnetism, we usually have
in mind the strongest effect ferromagnetism.
• In some materials (Fe, Ni, Co, Ga and many
special alloys) a quantum effect, called
exchanged coupling leads to rigid parallel
organizing of atomic magnetic moments in
spite of the randomizing tendency of
thermal motions.
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Ferromagnetism II
• Atomic magnetic moments are rigidly
organized in domains which are
microscopic but at the same time large on
the atomic scale.
• Their typical volumes are 10-12 – 10-8 m3 ,
yet they still contain 1017 – 1021 atoms.
• If the matter is not magnetized the moments
of domains are random and compensated.
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Ferromagnetism III
• In external magnetic field the domains
whose moments were originally in the
direction of the field grow and the magnetic
moment of some other can collectively
switch its direction to that of the field.
• This leads to macroscopic magnetization.
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Ferromagnetism IV
• Ferromagnetic magnetization:
•
•
•
•
•
Is a strong effect r  1000!
Depends on the external field.
Ends in saturation.
Has hysteresis and thereby it can be permanent.
Disappears if T > TC, Curie’s temperature.
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Ferromagnetism V
• The internal magnetization is saturated at
some point. That means it can’t be further
increased by increasing of the external field.
• The alignment at saturation can be of the
order of 75%.
• The Curie’s temperature for Fe is 1043 K.
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Ferromagnetism VI
• The hysteresis is due the fact that domains
can’t return at low temperatures and in
reasonable times to their original random
configuration. Due to this, so called
memory effect, some permanent
magnetization remains.
• This effect is widely used e.g. to store
information on floppy and hard-drives.
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Homework
• Homework from yesterday is due
tomorrow!
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Things to read
• This Lecture Covers
Chapter 28 – 7, 8, 9, 10
• Advance Reading
Chapter 29 – 1, 2, 3, 5
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Planetary model of a charge I
Let’s have a charge q with speed v on orbit of
the radius r and calculate its magnetic dipole
moment m0 = IA.
The area is simply A = r2.
To get the current we first have to find the
period of rotation: T = 2r/v.
Then if we realize that every T one charge of
q passes, the current is: I = q/T = qv/2r.
Planetary model of a charge II
Now the magnetic moment m0 = IA =rqv/2.
On the other hand the angular momentum is:
b = mvr.
If we put this together, we finally get:
m0 = b q/2m.
This can be generalized into a vector form:

q
m0  b
2m
If the charge is an electron q = -e so the
vectors of the magnetic moment and orbital
momentum have opposite directions.
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