Transcript Magnetism

1
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Microstructure-Properties: I
Lecture 4A: Mathematical
Descriptions of Properties;
Magnetic Microstructure
27-301
Fall, 2002
Prof. A. D. Rollett
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Bibliography
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Objective
Linear
Props.
Magnetism
Ferromagnets
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Domains
Wall
motion
Glossary
Magnetism
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De Graef, M., lecture notes for 27-201.
Nye, J. F. (1957). Physical Properties of Crystals. Oxford, Clarendon Press.
Chen, C.-W. (1977). Magnetism and metallurgy of soft magnetic materials. New
York, Dover.
Chikazumi, S. (1996). Physics of Ferromagnetism. Oxford, Oxford University
Press.
Attwood, S. S. (1956). Electric and Magnetic Fields. New York, Dover.
Newey, C. and G. Weaver (1991). Materials Principles and Practice. Oxford,
England, Butterworth-Heinemann.
T. Courtney, Mechanical Behavior of Materials, McGraw-Hill, 0-07-013265-8,
620.11292 C86M.
Kocks, U. F., C. Tomé, et al., Eds. (1998). Texture and Anisotropy, Cambridge
University Press, Cambridge, UK.
Reid, C. N. (1973). Deformation Geometry for Materials Scientists. Oxford, UK,
Pergamon.
Braithwaite, N. and G. Weaver (1991). Electronic Materials. The Open
University, England, Butterworth-Heinemann.
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Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Objective of Lecture 4A
• The objective of this lecture is to relate magnetic
properties to microstructure as an important example
of a non-linear, anisotropic property. This example is
illustrated by reference to ferromagnetic materials. In
these materials the domain structure provides an
additional degree of microstructural complexity that
affects properties such as permeability.
• The presence of defects (microstructure) in the
material has a profound on the magnetic properties of
a material. For example, the presence of second
phase particles makes a material magnetically hard,
just as it makes it mechanically hard.
4
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
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motion
Glossary
Magnetism
Mathematical Descriptions
• Mathematical descriptions of properties are available.
• Mathematics, or a type of mathematics provides a
quantitative framework. It is always necessary,
however, to make a correspondence between
mathematical variables and physical quantities.
• In group theory one might say that there is a set of
mathematical operations & parameters, and a set of
physical quantities and processes: if the mathematics
is a good description, then the two sets are
isomorphous.
5
Math of Microstructure-Property Relationships
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
• In order to describe properties, we must first
relate a response to a stimulus with a
property.
• A stimulus is something that one does to a
material, e.g. apply a load.
• A response is something that is the result of
applying a stimulus, e.g. if you apply a load
(stress), the material will change shape
(strain).
• The material property is the connection
between the stimulus and the response.
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Stimulus  PropertyResponse
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
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motion
Glossary
Magnetism
• Mathematical framework for this approach?
• The Property is equivalent to a function, P,
and the {stimulus, F, response, R} are
variables. The stimulus is also called a field
because in many cases, the stimulus is
actually an applied electrical or magnetic
field.
• The response is a function of the field:
R = R(F)

R = P(F)
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Scalar, Linear Properties
Modulus
Objective
Linear
Props.
Magnetism
Ferromagnets
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motion
Glossary
Magnetism
Temperature
• In many instances, both
stimulus and response are
scalar quantities, meaning that
you only need one number to
prescribe them, so the property
is also scalar.
• To further simplify, some
properties are linear, which
means that the response is
linearly proportional to the
stimulus: R = P  F. However,
the property is generally
dependent on other variables.
• Example: elastic stiffness in
tension/compression as a
function of temperature:
R = P(T)  F.
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Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Scalar, non-linear properties
• Unfortunately not all properties are linear!
• What do we do? In many cases, it useful to expand
about a known point (Taylor series).
F P
F2  2 P
R  PF   P0 


2
1! F F 0 2! F F 0
Fn  n P
n
n! F F 0
• The response function (property) is expanded about
the zero field value, assuming that it is a smooth
function and therefore differentiable according to the
rules of calculus.
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Scalar, non-linear properties, contd.
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
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motion
Glossary
Magnetism
• In the previous expression,
the state of the material at
zero field is defined by R0
which is sometimes zero
(e.g. elastic strain in the
absence of applied stress)
and sometimes non-zero
(e.g. in ferromagnetic
materials in the absence of
an external magnetic field).
• Example: magnetization of
iron-3%Si alloy, used for
transformers [Chen].
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Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
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motion
Glossary
Magnetism
Example: magnetization
• Magnetization, or B-H curve, in a ferromagnetic
material measures the extent to which the atomic
scale magnetic moments (atomic magnets, if you
like) are aligned.
• The stimulus is the applied magnetic field, H,
measured in Oersteds (Oe). The response is the
Induction, B, measured in kilo-Gauss (kG).
• As shown in the plot, the magnetization is a nonlinear function of the applied field. Even more
interesting is the hysteresis that occurs when you
reverse the stimulus. For alternating directions of
field, this means that energy is dissipated in the
material during each cycle.
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Example: magnetization: linearization
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
• An important feature of this example is the possibility
of linearization.
• How? Take a portion of the property curve and fit a
straight line to it. Around H=0, this is the magnetic
permeability.
F P
F2  2 P
Fn  n P
R  PF   P0 
1! F F 0

2! F
B
Slope  µ  permeability
Wall
motion
Glossary
Magnetism
H

2
F 0
n! F n
F 0
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Example: magnetization: µstructure
Objective
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Props.
Magnetism
Ferromagnets
Domains
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motion
Glossary
Magnetism
• How does magnetization depend on microstructure?
• In a soft magnetic material, of which Fe-3Si is an
example, all the atomic moments are aligned with
one another, i.e. the material is fully magnetized.
However, there are domains within which all the
atomic moments point the same way. The
magnetization within each domain, however, points in
a different direction.
• Generally speaking, domains are smaller than grains.
• Anisotropy means that the magnetization within each
domain points along a <100> direction.
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Magnetism: basics
•
•
Objective •
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
An elementary understanding of magnetism at the atomic level is
assumed.
The basic magnetic properties of a material are often described by a
“B-H curve.”
Non-magnetic materials either slightly reject magnetic fields
(diamagnetism) or reinforce them (paramagnetism). A limited set of
materials (Fe,Co,Ni,Gd and some transition metal oxides) exhibit
ferromagnetism, i.e. spontaneous alignment of atomic spins.
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Notation
BS
Br
Objective
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Props.
Magnetism
Ferromagnets
Domains
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motion
Glossary
Magnetism
Hc
µ
c
µ0
µr
Ms
Wh
BHmax
Saturation flux density/ induction
Remanence; flux density remaining after applied
field is removed
Coercivity; field required to bring the net flux
density to zero.
Permeability; = B/H
Susceptibility; = M/H
Permeability of free space; 4π.10-7 henry per
meter
Relative permeability, = B/µ0H
Saturation magnetization; BS=µ0 Ms
Energy lost per cycle; often the most important
parameter for a soft magnetic material.
Energy product; often the most important
parameter for a hard magnetic material.
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Objective
Linear
Props.
Magnetism
Magnetic Domains
• A useful exercise is to see how domain walls arise
from the anisotropy of magnetism in a ferromagnetic
material such as Fe.
• The interaction between atomic magnets in Fe is
such that the local magnetization at any point is
parallel to one of the six <100> directions.
[001]
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
[010]
_
[100]
_
[010]
[100]
_
[001]
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Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Magnetocrystalline Anisotropy
• The fact that different
directions magnetize
more easily than others
in ferromagnetic
materials is known as
magnetocrystalline
anisotropy. This can
be measured by
applying fields along
different directions, e.g.
here along 100, 110
and 111 [Chen].
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Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
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motion
Glossary
Magnetism
Domains
• The local magnetization can point in directions other
than a <100> direction, but only if a strong enough
external field is applied that can rotate it away from
its preferred direction.
• Domains are regions in which the local atomic
moments all point in the same <100> direction.
• At the point (plane, actually) where the local
magnetization switches from one <100> direction to
another, there is a domain wall.
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Magnetization: domains
<100>
Objective
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Props.
Magnetism
Ferromagnets
Domains
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motion
Glossary
Magnetism
DOMAINS in Fe (Chikazumi);
domain walls appear as light and
dark lines.
GRAINS (Smith);
Domains within grains
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Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Magnetic Anisotropy
• Why does the magnetization always point along a
<100> direction (in Fe)? An over-simple answer is
that this is a consequence of the interaction between
the atomic moments and that different materials
prefer to magnetize along different crystal directions.
• An important consequence of this anisotropy is that
the local direction of magnetization has to change
direction at a grain boundary but this raises the
energy of the system. As a result, the domain
structure is more complex near the boundary. The
next few slides review this effect.
20
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Domain Walls
• Since domains of like-oriented moments are volumes
like grains, there are (planar) interfaces between
domains called domain walls.
• Bloch first pointed out that the minimum energy
configuration means that the magnetization changes
gradually across the wall, 3.10b, not abruptly, 3.10a.
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90° Domain Walls
• Here is an example of a 90° domain wall.
Objective
Linear
Props.
[010]
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
[100]
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Objective
Linear
Props.
180° Domain Wall
• By contrast, here is a 180° domain wall with
the local magnetic moments pointing in
opposite directions.
[010]
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
[100]
23
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Domain Walls, contd.
• In a cubic material with 6 different <100> directions, it
is possible to have both 180° walls, and 90° walls.
• Domain walls have the lowest energy when they
coincide with low index planes (one can say that
there is an inclination dependence of the domain wall
energy).
• Example: in iron, the lowest energy domain walls lie
on {001}, {110} and {111}. This explains the way in
which the domain walls are straight lines along a
small number of directions in the figure.
• Just as for grain boundaries, the free energy of a
domain wall is always positive.
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Grain Boundary Domain Structure
Objective
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Props.
Magnetism
Ferromagnets
Domains
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motion
Glossary
Magnetism
• Note how the domain structure, visible as
stripes of alternating gray contrast, changes
in the vicinity of a grain boundary [Chen].
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Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Demagnetizing Effect (Field)
• In a single crystal (no grain boundaries), why does a
ferromagnetic material not magnetize in a single
direction, with no domains? At the surface of the
mono-domain body, there would be free magnetic
poles because of the change in magnetization (as for
a permanent magnet). A large magnetic field would
exist outside the body with which a large amount of
(magnetostatic) energy would be associated. By
rearranging the internal directions into domains, there
is a large reduction in total energy by (near)
elimination of the magnetostatic energy.
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Objective
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Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Hard versus Soft Magnets
• We can now understand qualitatively at least,
the difference between hard and soft
magnets.
• In soft magnets, e.g. Fe-3Si, the body has no
external field but the domains can be easily
brought into alignment with an externally
applied field.
• In hard magnets, e.g. Alnico, the body does
have an external field because the domains
have been prevented from changing their
alignment.
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Hard versus Soft Magnets, contd.
Objective
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Props.
Magnetism
Ferromagnets
Domains
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motion
Glossary
Magnetism
• The reasons for some materials being soft
and some being hard lie in the microstructure,
which we will examine further. In simple
terms, soft magnets are single phase and
coarse grained: hard magnets are multiphase
and fine grained.
• There is an important parallel between
magnetic and mechanical hardness. The
same microstructural features that promote
magnetic hardness also promote mechanical
hardness.
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Soft magnetic materials
Iron
Fe
1043
2.2
4
2.105
0.1
30
Mild steel
Fe-C
1000
2.1
143
2.105
0.10
500
Transformer
steel
Fe-3Si
1030
2.0
12
4.104
0.5
30
Ferromagnets
Permalloy
Fe79Ni
800
1.1
4
1.105
0.2
Domains
Supermalloy
Fe79Ni5Mo
0.80
0.16
1.106
0.6
570
0.25
0.8
1.5.103
106
13
630
1.6
> 105
103
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Linear
Props.
Magnetism
Wall
motion
Glossary
Magnetism
Ferroxcube
Amorphous
iron
FeBSi
Bs (T)
µr
Resistivity
(µWm)
WH (J.m3.cycle-1)
Composition
Objective
Tc (K)
Hc (A.m-1)
Material
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Hard magnetic materials
Material
Composition
Objective
Alnico IV H
1160
0.6
63
13
Linear
Props.
12Al26Ni8Co2C
u
Alnico V
8Al13.5Ni24Co3
Cu
1160
1.35
64
44
Barium ferrite
BaO(Fe2O3)6
720
0.4
264
28
Samarium colbalt
SmCo5
1000
0.85
600
140
Neodymium iron
boron
Nd2Fe14B
620
1.1
890
216
g iron oxide
Fe2O3
0.21
25
Magnetite
FeOFe2O3
0.27
25
Magnetism
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Glossary
Magnetism
Tc (K)
850
Remanence
BT (T)
Coercivity
Hc (A.m-1)
BH max
(kJ.m-3)
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Objective
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Glossary
Magnetism
Changing Domain Structures
• There are two ways in which domain
structures can change.
• A: the domain wall between two domains
moves such that the volume of one domain
increases and the other decreases. This
applies at small fields.
• B: the magnetization within a grain rotates (to
become aligned with an external field). This
only applies at large external fields.
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Objective
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Props.
Magnetism
Ferromagnets
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motion
Glossary
Magnetism
Magnetization Curve
• [Chen] The figure below illustrates the difference
between the early part of the curve for which domain
wall movement is dominant and the later portion
where domain rotation dominates. The external field
is applied along a non-easy axis (not <100>).
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Domain Wall Motion
• The process of magnetization can be
illustrated with a single crystal example (Fe).
Objective
Linear
Props.
Zero field
Medium field
Magnetism
Ferromagnets
Low field
High field
Domains
Wall
motion
Glossary
Magnetism
Domain
wall
motion
Domain
rotation
Applied field direction
33
Irreversible Domain Wall Motion
• The graph on a previous slide mentioned the “Barkhausen
effect” which is observed as a series of jumps in the
magnetization curve as the field is increased.
Objective • These jumps in magnetization are irreversible - if you take the
field off, the domain wall(s) does not make the reverse motion
Linear
Props.
and decrease the net magnetization.
Magne• Why the irreversibility?! There are obstacles to domain wall
tism
motion that require a certain minimum driving force to force the
wall past them. The same barrier exists if you try to force the
Ferrowall back in the opposite direction.
magnets
Domains • The barrier is precisely the same as barriers to dislocation
motion and in fact, are also precipitates, solute atoms, for
Wall
example.
motion
Glossary • This is the basic explanation for magnetic hardness being the
same as mechanical hardness.
Magnetism
34
Objective
Linear
Props.
180° Domain Wall
• Moving the domain wall involves “flipping”
some of the local magnetic moments to the
opposite direction.
[010]
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
[100]
35
Obstacles to domain wall motion
Objective
Linear
Props.
• Anything that interacts with a domain wall
will make moving it more difficult. For
example, a second phase particle will
require some extra driving force in order to
pull the domain wall past it.
Magnetism
Domain wall motion
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
particle
36
Objective
Linear
Props.
Domain Wall obstacles
• A more detailed look at what is going on near
particles reveals that magnetostatic energy plays a
role in forcing a special domain structure to exist next
to a [non-magnetic] particle.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Domain wall motion
Magnetism
[Electronic Materials]
37
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Particle Pinning of Interfaces
• A domain wall is an example of a (planar) interface.
• The reason that particles (or voids) exert a pinning
effect on domain wall motion (or any other kind of
planar defect) is that some of the interfacial area is
removed from the system when the interface
intersects the particle. This lowers the free energy of
the system. In order for the interface to move away
from the particle, energy must be put back into the
system in order to re-create interfacial area.
• Later on (302) we will estimate the energy of domain
walls and thus the magnitude of the pinning effect.
38
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
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motion
Glossary
Magnetism
Why Domain Walls?
• Why should domain walls exist? Answer: because
the atomic magnets only like to point in certain
directions (as discussed previously).
• Can we estimate how much energy it takes to pull a
domain away from its preferred direction? Answer:
yes, easily. How? Integrate the area under the curve
for an easy direction and compare that to the curve
for a hard direction.
• The area that we need is given by HdM ≈ µ0H2/2.
• Think of the difference in areas between the 100 and
111 directions as the difference in energy required to
move the crystals of different orientations into the
field.
39
Objective
Linear
Props.
Magnetism
Area under the curve
• The area that we need is given by HdM ≈ µ0H2/2.
• The energy difference = area(111)-area(100) ≈
area(111).
100
area
111
area
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
[Chen]
40
Objective
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Props.
Magnetism
Ferromagnets
Domains
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motion
Glossary
Magnetism
Energy anisotropy estimate: Fe
• Area(111) ~
4π x 18.105 A.m-1
x 3.104 A.m-1 / 2
= 3.4.104 J.m-3
• Compare with the
accepted
value of the anisotropy
coefficient for iron, which
is K1 = 4.8 104 J.m-3.
• The estimated anisotropy
is very close to the
measured value!
111
area
41
How big are domains?
• It is reasonable to ask how big domains have to be. One
approach to compare the total energy difference for a particle
against the available thermal energy.
Objective • Total energy for a particle, comparing magnetization in the easy
direction (100 in Fe) against the hard direction (111 in Fe) is just
Linear
Props.
the particle volume multiplied by the anisotropy energy (density):
E = VK1 = 4πr3/3 K1.
Magnetism
• The thermal energy is Ethermal = kT which at room temperature
gives Ethermal = 4.10-21J.
Ferromagnets • Thus the radius at which the energies are similar, for Fe, is:
Domains
Wall
motion
Glossary
Magnetism
rcritical = 3√{3kT/4πK1} ~ 1.3 nm
42
Superparamagnetism?
• This limiting size, below which we expect a single particle to not
have domains because thermal energy can move the
magnetization direction around “randomly” is very important
technologically.
Objective
• Small enough particles (relative to the magnetic anisotropy) are
Linear
called superparamagnetic because they behave like a
Props.
paramagnetic material even though the bulk form is
Magneferromagnetic.
tism
• For magnetic recording, you cannot expect the recording (in the
sense of regions of magnetization that remain fixed until the
Ferronext time you read them) to be stable if thermal energy can
magnets
change it.
Domains
• Thus a physical limit exists to the bit density on disks or tapes.
Wall
• To be safe, the particles need to be much bigger than our
motion
estimate - say, 10 times larger.
Glossary
Magnetism
43
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Magnetocrystalline Anisotropy
• The fact that different
directions magnetize
more easily than others
in ferromagnetic
materials is known as
magnetocrystalline
anisotropy. This can
be measured by
applying fields along
different directions, e.g.
here along 100, 110
and 111 [Chen].
44
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Labs
• Later in the course we will do a lab exercise on
imaging domain structures in a sample of Fe-3Si,
which is the standard material for manufacturing
transformers. We will use cross-polars and rely on
the Kerr effect which is where the presence of a
magnetic field at the surface of a material rotates the
plane of polarization of light. Different directions of
magnetization in different domains rotate the
polarization differently. This is how the example
image of domain structure was obtained.
45
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Application of soft magnetic
materials: transformers
• A major application of soft magnetic materials is in
transformers that step alternating current electrical
power up or down in voltage (and therefore current).
• The requirement is that a sufficient field is contained
within the transformer core, and that it switches each
AC cycle with minimal losses (from the hysteresis of
the magnetization curve)
46
Objective
Linear
Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Transformer materials, contd.
• Other important issues constrain the selection of
transformer materials.
• Saturation magnetization is a function of atomic
species and iron has the highest value for low cost
materials.
• Silicon is added to iron to raise the resistivity in order
to minimize losses. The 3% level represents the
maximum that still permits conventional
thermomechanical processing (TMP).
• Specialized TMP is used to develop near-singlecrystal texture, called the Goss texture, {110}<001>.
47
Objective
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Props.
Magnetism
Ferromagnets
Domains
Wall
motion
Glossary
Magnetism
Supplemental Slides
• The following slides contain some useful
definitions of terms in magnetism and
magnetic materials.
48
Appendix: Glossary of Magnetism
•
•
•
•
Objective
Linear
Props.
Magnetism
•
•
•
•
•
•
•
•
Ferromagnets
•
•
•
•
Domains
•
Wall
motion
Glossary
Magnetism
•
•
•
•
•
Ageing: Change in magnetic properties with time, especially in the apparent remanence of a permanent magnet; can be reduced or anticipated
by artificial ageing (magnetic, thermal, mechanical).
Air Gap: Space between the poles of a magnet in which there exists a useable magnetic field.
AMR-effect: Non isotropic magneto resistive effect, (see also XMR-effect).
Alnico: Magnet alloys composed of Aluminium, Nickel, Cobalt, Iron and other additives - produced by casting or sintering - can only be
processed by grinding.
Alnico P: DIN 17410 designation for plastic bonded Alnico materials.
A/m: amperes per meter : unit of magnetic field strength; 1 A/m= 0,01 A/cm (= 0,01256 Oersted).
Anisotropy: Directional dependence of a physical quantity ; in the case of permanent magnets this relates to remanence, coercivity etc.
Axial magnetization: Magnetization along the symmetric achsis of a bar magnet or along one edge of a block magnet.
B = Induction or flux density: Unit: 1 Tesla = 1 Vs/m2 = 10-4 Vs/cm2 = 104 Gauß.
B (H) Curve: A curve representing the relationship between induction B and field strength H (see also hysteresis loop).
(B • H): Product of the respective induction B and field strength H within a magnet (see also energy density). Unit: 1 J/m3 = 10-3 kJ/m3 =
125,6 Gauß • Oersted = 125,6 • 10-6 MGOe
(B • H)max - Value: Maximum product resulting from B and H on the demagnetization curve, i.e. the largest rectangle which can be drawn
within the B (H) curve in the second quadrant of the hysteresis curve; this usually corresponds to the optimal working point.
cgs-units: Physical units which are based on the three fundamental units cm, gram and second (see also SI-units).
CMR-effect: Colossal magneto resistive effect (see also XMR-effect).
Coercive Field Strength Hc, Coercivity: Strength of the demagnetizing field where B = 0 ( HcB ) or J = 0 ( HcJ ).
Columnar crystalline materials: Especially AlNiCo alloys where an orientation of the crystals is formed by a controlled solidification of the
melting charge. The material AlNiCo 700 shows a very distinct anisotropy.in contrast to those types where an anisotropy is produced only by
applying a magnetic field during heat treatment.
Curie Temperature: The temperature above which the remanence of polarization in a ferro-magnetic material becomes Jr = 0. At all
temperatures above the Curie temperature all ferromagnetic materials are paramagnetic.
Demagnetization: Reduction of induction to B = 0; this is obtained practically by the application of an alternating field of decreasing amplitude.
Demagnetization Curve: The second quadrant of the hysteresis loop which is of great importance for permanent magnets.
Demagnetization Factor N: Shape dependent factor which determines the angle between working line and B-axis. N is the tangent of this angle.
Diamagnetism: Magnetic property of materials whose permeability m is smaller than 1, e.g. bismuth.
Dimensional Relationship: Relationship L/D = length / diameter of a bar magnet. For each magnet material the optimal working point
corresponds to a fixed L/D value.
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Dipole field: first approximation of the field of a magnet at a large distance. The dipole field is defined only by orientation and amount of the
magnetic moment and decreases according to 1/r3 with increasing distance r.
Dipole moment: see moment (magnetic)
Eddy current: A current induced in a conductor by a changing magnetic field. It is exploited for example in electricity meters for retarding without
any contact. On the other hand it causes losses and undesirable heating in motors, transformers etc.
Effective Flux: Part of the magnetic flux which passes through the air gap.
Energy Density: 1/2 B • H = half of the product resulting from the magnetic induction B and the field strength H (half of the rectangle within the
demagnetization curve with its corner at the working point)
Ferromagnetism: Magnetic property of materials with a permeability m >>1, e.g. iron, nickel, cobalt and many of their alloys and compounds.
Field: space having physical properties (see also magnetic field).
Field Constant, Magnetic: m0 = B/H in the vacuum, with m0 = 1,256-10-6 T m / A = 1,256- 10-6 \/s / Am.
Field Line: Means of evident representation of fields. In force fields (e.g. magnetic fields) the tangents to the field lines represent the direction
of the effective forces; the density of field lines is a measure of the strength of effective forces.
Field Strength (magnetic) H : a quantitative representation of the strength and the direction (vector) of a magnetic field. Unit 1 A/m = 0,01
A/cm = 0,01256 Oersted.
Flux Density B: No. of field lines per unit of surface. Unit: 1 Tesla = 1 Vs/m2 = 10-4 Vs/cm2 = 104 Gauss.
Flux, magnetic: When a magnetic field is represented by field lines, the total number of lines through a given surface is known as the magnetic
flux: measured as an electrical impulse in a coil surrounding this surface on appearance or disappearance of this flux. Unit : 1 Weber (Wb) =
1 Vs = 108 Maxwell.
Fluxmeter: Electronic integrator for measuring a magnetic flux or induction.
Force Line: Visible representation of a force field, especially a magnetic field.
Gauß: Old unit of magnetic induction, 1 Gauß = 10-4 Tesla = 10-8 Vs/cm.
Gaußmeter: Instrument for measuring magnetic induction B. Instruments for measuring magnetic field strength H (Oerstedmeters) are often
referred to as Gaußmeters.
Gilbert: Old unit of magnetic tension; 1 Gilbert = 1 Oe cm = 0,796 A.
GMR-effect: Gigantic magneto resistive effect (see also XMR-effect).
H = magnetic field strength, Unit : 1 A/m = 0,01 A/cm = 0,01256 Oe.
Halbach-system: An arrangement of magnets named after the American physicist K. Halbach which produces precise and very homogeneous
multipole fields( for example a dipole field) .
Hall probe: Semiconductor probe for measuring magnetic fields (e.g. in an air gap of a magnet system). Hall-probes always are used connected
to a gaußmeter.
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Hard Ferrite: Term used in DIN 17410 for Oxide magnet materials.
Hard Ferrite P: Term used in DIN 17410 for plastic bonded oxide magnet materials.
Helmholtz-coil: A double coil to produce extremely homogeneous fields. The distance between the two coils is equivalent to their radius. The
coil is used for measuring magnetic moments.
Hybrid-material: Plastic bonded material containing several kinds of magnetic powders to adjust certain magnetic properties by using for
example Neofer and oxide-powders to reach a predicted price.
Hysteresis - loop: Representation of induction B resp. Polarization J in relation to the magnetizing field strength H.
Induction: 1.The ability of the magnetic field to surround itself with an electric field whilst it is changing. 2.The term induction is also used to
mean flux density B.
Induction Constant: See field constant, magnetic.
Isotropy: Equality of physical properties in all directions.
J = magnetic polarization: Density of aligned magnetic moments in a magnetized material Unit 1 T = 1 VS / m2 = 10-4 VS / m2.
Magnetic: Commonly used to denote all materials with noticeably high permeability (especially iron, nickel, cobalt and their alloys); all other
materials (gold, brass, copper, wood, stone, etc.) are considered to be non-magnetic.
Magnetic Circuit: Total of parts and gaps through which a magnetic flux passes; in the case of a permanent magnet this consists of the magnet
itself, the pole shoes, the air gap and the stray field.
Magnetic Field: Space in which mechanical forces have an effect on magnetic charges or where induction occurs.
Magnetic Field Strength H: See field strength (magnetic).
Magnetic flux: See Flux, magnetic.
Magnetization: 1) The noun arising from "magnetizing” 2) Polarization divided by the magnetic field constant M = J / m0, B = m0 (H+M) =
m0 H + J.
Magnetizing: Process of aligning the molecular magnets by an external magnetic field.
Magnetism: Sum of magnetic phenomena as a part of the electromagnetic interaction(force) being one of the four fundamental forces in
physics. They are characterized by magnetic field H and magnetic induction B. All the magnetic phenomena are a consequence of moving
electric charges (electric currents) whereas electrostatics describes the forces between unmoved electric charges. Electrodynamics finally
deals with the connection of electric and magnetic fields varying with time.
With the magnetism of matter an orientation of magnetic moments (colloquial elementary magnets)is defined by polarization J. These moments
are composed of the orbital moment of electrons moving around the nucleus of the atom and the so called electron spin moment which is
caused by the rotation of the electron around its own axis. If all these moments are compensated the material is called diamagnetic.
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Concerning para- ferro- antiferro- and ferrimagnetic materials the sum of these moments is different from zero. They differ by the kinds of
coupling of adjoining atomic moments: In the case paramagnetic materials there is no coupling; with ferromagnetic materials adjacent atomic
moments are parallel; with antiferromagnetic materials they are adjusted antiparallel. If the antiparallel adjusted atomic moments do not
compensate each other completely and a resulting magnetization remains it is called ferrimagnetism.
Magnetomotive Force: Q Term for the line-integral of field strength H along any path. For the case of a closed path the magneto motive force is
the sum of the electrical currents enclosed within the curve :.
Unit: 1 A = 1,256 Oe cm = 1,256 Gilbert.
Magneto resistive sensor: (MR)-sensor using the change of electric resistance in a magnet field to measure it. Because of recent developments
of thin layers showing extremely high magneto resistive effects we have a renaissance of MR-sensors. ( see also XMR-effect )
Magnet Pole: Part of the surface of a magnet where the magnetization is rectangular to the surface. This part corresponds to the regions where
the magnetic flux leaves the magnet.
Maxwell: Former unit of magnetic flux
1 Maxwell = 10-8 Wb = 10-8 Vs.
Melt spin process: Method of an extremely fast cooling of a melting charge being sprayed on a rotating cylinder which leads to alloys with
different physical properties than melting charges cooled down under normal conditions. This method is used to produce the basic powder of
Neofer p ®.
Moment (magnetic), (dipolar moment): Product of polarization J and Volume V of a homogeneously magnetized magnet. The moment in units
of Vsm corresponds to the mechanic torque in Nm of the magnet in a magnetic field perpendicular to the magnetization of 1 A/m. The moment
is designated by m, better by mCoul (Coulomb's magnetic moment ) to not confuse it with mAmp ( Ampers's magnetic moment ) the formerly
often used quantity.
mAmp = mCoul / m0 is the product of Magnetization M and Volume V.
Multicomponent injection moulding: Injection moulding process where two or more different materials are injected one after another for example
a non-magnetic material is injected on top of a magnetic compound.
Neofer â: Permanent magnet material based on neodymium, iron and boron.
Neofer p â: Permanent magnet material based on neodymium, iron and boron with a bonding agent.
Oersted: Former unit of magnetic field strength 1 Oersted = 79,6 A/m = 0,796 A/cm = 0,0796kA/m.
Oerstedmeter: Instrument for measuring the magnetic field strength H (also known as Gaußmeter).
Oxide Magnet: Hard ferrite, ceramic magnet material, e.g. composed of iron oxide and barium oxide (Ba0 x 6 Fe2 03).
Paramagnetism: Magnetic property of materials with permeability m > 1. All ferromagnetic materials exhibit paramagnetism above the Curie
temperature.
Permagraph: Measuring instrument for plotting the entire hysteresis loop of a magnet. It consists of an electromagnetic yoke to apply an
external field measuring instruments for measuring field strength H and induction B and a calculator or a chart recorder to describe the curve.
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Glossary of Magnetism: 5
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Permeability: m = B/H; relationship between induction B and the magnetic field H. In permanent magnet technology permanent
permeability is important as this gives the change in B when small changes in H take place (dp = dB/dH) especially in the proximity
of the optimal working point. Unit: 1 Tm / A.
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The permeability of the vacuum (magnetic field constant) is m0 = 1,256-10-6 T m / A = 1,256- 10-6 \/s / Am.
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Permeance: Ratio of magnetic flux to magnetic potential difference ( in the case of an air gap surface : length)
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Plastic bonded magnet material: If a magnet powder is blended with plastic material it is possible to apply methods of plastic
industry (injection moulding, rolling etc.) to produce magnets of very complex shapes. The advantages: cheap manufacturing
processes, small tolerances and many kinds of shapes must be compared with the disadvantages: expensive tools and lower
magnetic properties.
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Polarization J: Grade of magnetic orientation in a magnetic material (magnetization multiplied by field constant). It is J = m0 M =
B - m0 H.
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Potential, magnetic: Physical quantity of which the gradient gives the magnetic field H. Only a potential difference can be measured
(magnetic tension between two points) as an integral of the field strength over any path between these two points, provided this
path does not enclose an current-carrying conductor.
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Prac Ò: Pressed magnet composed of AlNiCo powder and bonding agent.
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Preferred Direction: Direction in a permanent magnet in which magnetic properties are at a maximum. This direction is determined
by the manufacturing process.
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Pressed Magnet: A magnet manufactured by a pressing process from powdered magnet material and a bonding agent.
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Prox Ò: Pressed magnet composed of oxide powder and a bonding agent.
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Rare earth magnet materials: The rare earth metals Nd and Sm are applied to different alloys for manufacturing permanent
magnets with very high magnetic properties. The nowadays commercially exploited materials Seco and Neofer are based on the
compositions SmCo5, Sm2(FeCo)17 and Nd2Fe14B.
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Radial magnetization: Magnetizing a ring magnet between two coils carrying currents of opposite directions
leads to a radial magnetization. One pole is on the inner circumference of the magnet the other pole on the
outer circumference.
Reed switch: Magnetomechanic switch where two metal reeds in a inert gas get into contact by applying a
magnetic field actuating the switch. The unit of the sensitivity of the switch is ampere windings.
Remanence BR: Residual induction in a solid which has been subjected to a magnetizing field (true
remanence in the case of a closed magnetic circuit, apparent remanence in the case of an open magnetic
circuit).
Residual magnetism: Because of the manufacturing process delivered magnets show more or less a residual
magnetism. This can only be reduced by a demagnetization process.
Saturation: Better termed saturation polarization
Saturation Polarization: Highest practically achievable magnetic polarization of a material when exposed to a
sufficient strong magnetic field..
Seco Ò: A magnet material composed of an alloy of rare earths and cobalt.
Seco P Ò: A magnet material composed of a rare earth cobalt alloy and a plastic bonding agent
Sintered Magnet: A permanent magnet pressed from a mixture of metallic or ceramic powders and solidified
by heating below the melting point (burning).
SI-units: Physical units according to the System International (SI) which is based on the units kilogram, meter
second and ampere. All other units are a product, a quotient or a power of these four basic units. The
traditional cgs-units resp. the Gauß-units in magnetism are still in use but have to be adapted by law. The
following table shows some magnetic units and their conversion.
REFERENCE: http://www.magnetfabrik.de/english/abc/service.htm