Magnetic Properties
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Magnetic Properties


We have talked about so far these many non-mechanical
properties of the materials, let us just try to kind of list them, we have talked about
optical properties, we have talked about thermal property, we have talked about electrical
property, which is in 2 phases we have talked about the conductive materials and the resistive
materials. Now one more we would like to add on that the final one that is the magnetic
property that is what we will be discussing today that is the magnetic property of the
materials. So you add that with your list of knowledge
on the mechanical property, I can say now at the end of the course at the very fag end
of the course, now you have more or less a very good kit of material properties with
you to go ahead design of product development. So in this lecture, we are going to give a
small introduction to the magnetism and basic terminologies, types of magnetism, influence
of temperature on magnetism, magnetic domains and hysteresis and magnetic anisotropy. As
that magnet is always a very-very mysterious material. People say that even Cleopatra used
to take a bath in magnetic beads thinking that it has some kind of correlationship with
the longevity of a human being. It all happened because of that Mystic Force
that you cannot see of course, but the force is there which is working on you, so it is
considered to be a very Mystic Force. So magnetic field is a force which is generated due to
energy change in a volume of space and this is produced by an electrical change in motion
for example, if there is a current flowing in a conductor or orbital movement and spin
of electrons. So if there is a current loop, you will see that there are the magnetic fields,
which are happening here so in any current loop.
And if you consider a permanent magnet like a bar magnet for example, you would see that
the magnetic field is generating from North and getting over at South that how the magnetic
lines of forces the magnetic loops are working on the system. So basically you can have the
magnetic field due to the intrinsic property of a material or you can have it by external
electric field in the system. Now, similar to our electric dipoles, there
are magnetic dipoles. In this case it is not a positive or negative charge, but it is this
north and the south poles, so magnetic dipoles are found to exist in magnetic materials which
are very much analogous to electric dipoles. And this magnetic dipole you can almost think
like a miniature magnet which is composed of north and south poles instead of positive
and negative charges. Within a magnetic field, the force of field exerts a torque that tends
to reorient these dipoles with the field. So it is already for example this is a magnetic
dipole and then I am applying a magnetic field here B, so this field will actually apply
a force here F, which will force it to align itself towards the direction of the magnetic
field. Now it is very similar to the electric field based movement of the system. So magnetic
dipole moment is the measure of the ability of a dipole to rotate itself and come into
alignment with the magnetic field. Much the easily readily it can do, the more magnetic
is of course the material. And we generally denote this magnetic moment by an arrow like
this. Now, what are the origins of such magnetic
moments? Well, there are 2 sources; one is the orbital motion of electrons around the
nucleus because they are like very-very small current loop each electron orbiting around
the nucleus of an atomic nucleus of a system. So each electron during their motion must
generate a magnetic moment along its axis of rotation, magnetic moment gets generated.
Then there is this spin of electrons, this also produces a magnetic moment along the
spinning axis of the electron, so it is like each individual electron now which is spinning
and that is creating a magnetic moment. So there are 2 motions that are there right,
maybe you can think of it very much analogous to the motion of earth around the sun that
you have motion of earth around its own axis, which is like the spinning motion and you
have also the orbital motion, so the orbital motion generates one of the magnetic moment
and the spinning motion generates another magnetic moment, both of these are bound to
happen because why, because the electrons carry the electric field, so the change of
electric field that is going to generate the magnetic field. So magnetism in a material
arises due to alignment of magnetic moments that is in a microscopic scale, we will talk
about it. Now, every material has atoms, so it has orbital
and spinning electrons then are all materials magnet? The answer is no. So even at microscopic
scale it does not happen, so why it does not happen? Two reasons, one reason it is called the Pauli
exclusion rule, which says that 2 electrons with same energy level if it has, then it
must have opposite spins. So thus, their magnetic moments are going to cancel each other, so
even though there are if there are 2 electrons, they cannot get the same spin, they will be
in the opposite spin as a result, magnetic moment due to spinning is going to cancel.
Then as far as the orbital moment is concerned, that also cancel out each other and there
is no net magnetic moment if there is no unpaired electron.
So the clue is that if you have unpaired electrons, only then this result will get manifested
in the microscopic scale otherwise, they are going to cancel each other. Some elements
such as transition elements lanthanides and actinides, they have a net magnetic moment
and some of the energy levels have an unpaired electron that is why they show this kind of
a magnetic moment. Now there are some basic terminologies with
respect to this magnetism, first thing in the magnetic field strength H, this is the
externally applied magnetic field and it is generally described in terms of 3 parameters,
number 1 is N that is total number of turns and the length that is L on which you are
giving the turns, suppose this is a solenoid then the length of the solenoid L, so this
is the L and the current I, so if I increase the current in the coil I get more magnetic
field. If I increase the length, then the magnetic
field intensity comes down, if I increase the number of turns, if I make it denser then
I get actually more magnetic field out of the same length, so the number of turns plays
also an important role. Now, next to H, H is fine H equals N I over L that now and which
has a unit of ampere per meter. Next to that is the magnetic flux density B, this represents
the magnitude of the internal field strength within a substance that is subjected to an
H field. So H is the field strength, but the density of that field which gets all around
that density is actually measured with respect to B which has unit of Tesla or Weber per
square meter or volt second per meter square. The simple relationship here is B=Mu H,
for vacuum of course it is Mu 0 H, so where Mu is now the permeability of the medium through
which the H field passes that means if the medium is more permeable, then with the same
magnetic field strength you are going to get higher magnetic flux density, so permeability
Mu is a very important factor for us. Next the permeability of course is measured
here in terms of the relative permeability Mu r, Mu over Mu 0. And higher the value of
the permeability of the medium, then Mu r is higher which is fine with us. The other
point is that, just like polarization there is something called magnetization M which
presents in a material. So with respect to external will relationship was b=Mu 0 H,
but what if the material is like I already told lanthanides, etc., so there is a magnetisation
that is there. So we have to extend it to Mu 0 plus H Mu
0 M, where M is once again it can be expressed as a function of the field strength H with
the help of something called Kappa m, where Kappa m is the magnetic susceptibility and
this is Mu r minus 1. So essentially the property once again remains the same that is the relative
permeability because Kappa also depends on the same, so this is how the magnetic field
and the magnetic flux density are related to each other. Now let us talk about the manifestation
of this magnetism on different materials. There are 3 types of magnetism that you will
generally see, one is called Diamagnetism, another is called Paramagnetism, another is
called Ferromagnetism course, there are some of the other variations but these are the
basics 3 that you will see in a material. What is the Diamagnetism? This is actually the weakest form of magnetism
which arises only when external field is applied. This arises due to the change in the orbital
motion of electrons on applications of magnetic field the orbital motion is going to get change.
There are no magnetic dipoles in the absence of a magnetic field and when a magnetic field
is applied the dipole moments are aligned opposite to field direction. Like initially
there is no dipole moment and the moment you apply the magnetic field, you are going to
see that the dipole moments are coming; they are trying to balance opposite to the direction
of the magnetic field, so this is the diamagnetic material.
The magnetic susceptibility of course in this case is Mu r minus 1 which is negative and
B in a diamagnetic material is actually less than that of vacuum and are repelled by the
applied magnetic field. The examples of diamagnetic materials are like Al2O3, copper, Gold, silicon,
Zinc, etc. One of the good uses of diamagnetic material is in terms of shielding from the
electromagnetic interaction, so we try to use this type of material so that if you imagine
that you have a series of such diamagnetic materials there as a protective coat.
And you have a very sensitive electronic circuitry in that are there here, so some ICs are there.
Then if you apply a magnetic field, this immediately generates the opposite direction of this magnetic
dipoles, which will nullify this effect and as a result this IC will be saved from the
effect of the magnetic field intensity, so that is how the diamagnetic materials are
very-very useful as a protective coating against electromagnetic interference, we call it EMI
interference. Now paramagnetic materials, in this the cancellation
of magnetic moments this actually already has some unpaired electrons means it has some
internal magnetic moments, but in general they will not manifest why, because they are
random so they are going to cancel each other. When a magnetic field is applied for paramagnetic
material, they are going to align themselves towards the direction, so they are the traitors,
they are going to align themselves towards the direction and hence they are slightly
more magnetic than the diamagnetic materials. Examples are aluminium, chromium, molybdenum,
titanium, zirconium, etc. So that is the paramagnetic materials, no little go to another group.
But before we go to the Ferromagnetic, this is like a chart which gives us the susceptibility
of diamagnetic materials because there we are measuring it in terms of the susceptibility,
not the permeability. So it is like the if you consider aluminium
oxide on the diamagnetic, one of the highest in terms of susceptibility of course even
higher is the gold, mercury for example, then silver for example, then there are other materials
like sodium chloride, zinc, etc. In terms of the paramagnetic materials, the one which
will top the list is the sodium as you can see, some metals are also paramagnetic like
let us say aluminium, chromium, then there are some compounds like chromium chloride,
magnesium sulphate, molybdenum, titanium, zirconium, et cetera.
So these materials are non-magnetic because they exhibit magnetization only in the presence
of an external field. And if I increase this external field H, then the magnetic flux density
increases, for the time magnetic material it is still much lower than the vacuum and
for the paramagnetic material, it increases slightly with the help of the magnetic field
H, so that is the diamagnetic and the paramagnetic material. Let us now come to the next group
that is the ferromagnetic material. Certain materials possess permanent magnetic
moments in the absence of an external magnetic field, this is known as ferromagnetism. It
is related with ferrous because iron is one of such components. Permanent magnetic moments
arise due to uncancelled electron spins by virtue of their electron structure. The coupling
interaction of electron spins of adjacent atoms cause alignment of moments with one
another. So not only they have the magnetic moments, but even with H=0, they are approximately
aligned against each other that is the beauty of such material.
The origin of this coupling is attributed to the electron structure, this is the maximum
will talk about it in this particular series. So iron for example you see the structure,
it has incompletely d orbits and hence it has unpaired electron spins, so this is one
such material which shows ferromagnetic effect. Now, there is something which is also known
as Anti-ferromagnetism. If the coupling of electron spins results
in antiparallel alignment, then spins will cancel each other and you will not get a net
magnetic moment which will arise. So even though there are magnetic moments, they are
aligned but it can happen that they are opposite in directions, so then it will become anti-ferromagnetic
system. One of the interesting examples is manganese oxide, which shows no net magnetic
moment because of the anti-ferromagnetic system that it has. Then another interesting version is called
Ferrimagnetism and this happens in ionic solids which has particularly a kind of common formula
of MFe2O4, where M is any metal. This shows permanent magnetism, but it is termed as ferrimagnetism
due to partial cancellation of spin moments. For example in Fe3O4, the iron ions can exist
in both 2 plus and 3 plus states as Fe 2 plus O2 minus and Fe3 plus O2 minus in 1 is to
2 ratio. The antiparallel coupling between irons half in A sides and half in B moments,
these moments will cancel each other. Fe 2 plus moment on the other hand, are aligned
in same direction and result in a net magnetic moment, so you can see it here that from the
lattice structure Fe 3 plus for example, they also in the lattice structure will be showing
similar to Fe 2 plus, the octahedral lattice side. But in the tetrahedral lattice side,
you will see that they have this opposing magnetic moment, whereas they do not have
and as a result, they have a complete cancellation for Fe 3 plus net magnetic moment, but for
Fe 2 plus you are going to see some magnetic moment in the system.
So this Fe 2 plus moments are aligned in the same direction and they result in a net magnetic
moment, so hence wherever you have this Fe 2 plus with the octahedral lattice side, this
is going to show the magnetic moment whereas, the Fe 3 plus octahedral and Fe 3 plus tetrahedral
are going to cancel each other, so this is a typical of a Ferrimagnetic material, where
you have a partial cancellation of spin the moments, not a complete cancellation of the
spin moment. Now let us summarize the whole thing. So Diamagnetism, sign is negative for susceptibility,
magnitude is small and constant. Paramagnetism, positive susceptibility, small, constant.
Ferromagnetism, positive, large, function of H. Antiferromagnetism, positive but small
constant, and ferrimagnetism positive, large, function of H. Extremely small magnetic flux
density B is generated in materials that experience only diamagnetic and paramagnetic behavior,
that is why they are considered to be non-magnetic. So for a ferromagnetism material, how does
it behave? How does the magnetic field changes with respect to the magnetic field strength
H? So this is a typical H versus B curve as you
can see it here that it is initially the B is increasing at a very fast rate and then
there is a saturation that is happening. So, essentially you have for example in a unit
volume you have all these dipoles, so initially all these dipoles will very fast try to align
themselves as a result the magnetic flux density increases sharply, after some point of time
what we will see is that all of them are nearly aligned as a result to the field so that means
nothing more is happening in terms of the flux density, so there is a saturation that
will happen to this kind of a system. So how this property does changes with respect
to temperature because many times temperature becomes a factor in our applications? Now,
we know that atomic vibrations increases with increase in temperature and this leads to
misalignment of magnetic moments as they are free to rotate. Above a certain temperature,
all the moments are misaligned that means they become random in nature and hence the
magnetism is lost, this temperature is known as the Curie temperature. Beyond that, it
will be so much misaligned that the magnetism is lost.
So below the curie temperature you are getting the alignment, about the Curie temperature
you are getting this random distribution. And if you want to plot temperature versus
saturation magnetization, you will see that it sharply drops beyond a particular temperature.
This temperature of course varies from material to material for example, for iron it is 768
degree centigrade, cobalt 1120, one thing you can notice that it is close to its melting
point, nickel 335, Fe3O4 about 585 degrees centigrade, so that is the temperature influence
on the magnetic behavior. Now, below Curie temperature we have already
seen the existence of the domains mean there are regions where the magnetic dipoles are
all parallel. Then there is another region where then again they are parallel inside
that set. So ferromagnetic materials exhibit such small volume regions in which magnetic
moments are actually aligned in the same direction, these regions are called domains. The different
domains are separated by the domain boundaries. The direction of magnetization changes across
the boundaries. The magnitude of magnetization in the material
is then the vector sum of magnetization of all these domains. So once you integrate it
across the domain, you are going to get the net magnitude of magnetization in the material.
Then the other part is the magnetization saturation. So, when a magnetic field is applied to a
ferromagnetic material, these domains tend to align in the direction of the field by
domain boundary movement and hence the flux density or magnetization increases. This is
just what I wanted to show you earlier that suppose this is your initial permeability
and then suddenly there is growth of domains that means all these domains that you have
seen in a volume suppose, you have some such domains. The domains are not stationary nature,
so each domain size are going to increase with respect to the magnetic field, so it
may become more chunk and bigger and bigger. So this is the growth of domain and as a result
the magnetization also is increasing. But beyond a certain point, the entire all the
domains favorably oriented to field direction grow at the expense of the unfavorably oriented
ones that is this point. And then ones domains are aligned to the field direction at high
field strength and the material reaches the saturation magnetization Ms, then this whole
activity becomes once again very much saturated so there is no net change in magnetization
anymore with respect to the change of the magnetic field, so that is how we get that
famous S curve in it. There is one interesting thing, if you change
the direction of magnetization then what happens. So if the field is reduced from saturation
by magnetic reversal, there is a hysteresis that will develop. As the field is reverse,
the favorably oriented domains tend to align to the new direction. When H reaches zero,
some of the domains still remain aligned in the previous direction, this gives you a magnitude
of Remanence this gives you a residual magnetization called Remanence. The reverse field strength
at which the magnetization becomes zero is called the Coercivity.
Coercivity is the inverse field strength for the magnetization becomes 0. There are 2 important
things in magnetic hysteresis, one is called as I told you the Remanence that means when
you are reversing the magnetic field, we will still find that some domains have not really
aligned themselves or it is still keeping this alignment that is what the Remanence
Br is. And then when you are having already a negative magnetic field, you will still
find that suddenly it will become 0, so that is the coercivity when the magnetization will
become 0. The other thing is that this is the initial
route and then you are reversing the magnetic field, so up to this you are increasing and
then you are reversing it and as we are reversing it, we are going down like this. And when
you are again reversing the magnetic field, it is coming in a different line meaning thereby
you will have an area inside, which is the hysteresis of the magnetic hysteresis.
So there is some amount of energy which will be basically loose, you are losing that that
is what is signified by this hysteresis and that happens in every magnetization-demagnetization
cycle. Where does the energy go? Well, it goes for heat energy for example, acoustic
energy, et cetera that is the magnetic hysteresis in the system. There are 2 different types
of magnets that we categorize in terms of this hysteresis; one is called soft magnet
which has a narrow hysteresis curve and another is a hard magnet. So the comparison is that indeed soft has
a narrow hysteresis curve, it has high initial permeability and low coercivity that is easy
movement of domain wall. And in terms of hard magnet, it has low initial permeability, high
hysteresis energy losses, but high coercivity also, look at it, it has a high coercivity.
Soft magnets are easy to magnetize and demagnetize, but hard magnets are difficult to demagnetize.
Soft magnets like iron, iron silicon, iron nickel, they are useful when rapid magnetization
and demagnetization is required in a transformer core for example. Hard magnets on the other
hand, they are used in all permanent magnets in applications such as power drills, motors,
speakers, etc, but they have high hysteresis field.
The energy product which is in terms of kilo joule per meter cube that is the area of the
largest B-H rectangle that can be constructed within the second quadrant of the hysteresis
curve. This is the second quadrant of the hysteresis curve, so this is one of the measures
that is the largest B-H rectangle that you can fit here that is a measure like this one
that is the measure of the hysteresis. This represents energy required to demagnetize
a permanent magnet, based on that you can, so larger the B-H max harder is the material
in terms of its magnetic characteristics. So we have talked about the magnetic field
permeability, now we have a new one that is the B-H max, which is important in terms of
categorization of soft and hard magnets. Next is magnetic anisotropy, the dependence
of the magnetic behavior on crystallographic orientation is termed as the Magnetic Anisotropy
because as that not all the directions it is easy for the magnetization, so the crystallographic
direction in which the magnetization is easiest that means, magnetic saturation is achieved
at the lowest external field these are called the easy axis. For example, for iron it is
1 0 0, we already told you that how for the axis setting we have already talked about
it, so for iron it is 1 0 0, for nickel it is 1 1 1.
That means for iron it is anyone of these principle axis, whereas for nickel these are
the diagonal axis 1 1 1 which is what so if you try to put it for nickel, then it is the
diagonal from one end to the other that is the axis in which if you apply H, that is
the easy axis for it whereas, for iron it is any one of these axis 1 0 0, which are
the axis in which you can actually do it. So this anisotropy exists and you have to
know for each material, which is the easy direction because you can then very easily
get it magnetized accordingly. So this is where we are going to close all
our lectures related to the material properties. Now, finally I want to give you some of the
demonstrations at my laboratory this is the smart material structures and systems laboratory
at the mechanical department of IIT Kanpur, where you will see some of these instruments
and materials in function and that is how we will close our lecture, thank you. Keywords- Magnetism, influence of temperature
on magnetism, magnetic domains, hysteresis and magnetic anisotropy

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