Magnetic Materials Review

Matt’s Quick Guide to Magnetism in Materials
Matt Jordan
October 12, 2012
1 Introduction
• Where does magnetism come from
• Why are some materials magnets and others not
• How do magnetic materials behave in a magnetic field
1.1 Origins of Magnetism
Magnetism is one part of electromagnetism which is one of the four fundamental
forces (gravity, strong, and weak nuclear forces being the other three).
It is wrong to say that electrical fields or charges “cause” the magnetism since
really magnetism is a manifestation of the electromagnetic force. Yet these
qualities are inseparably linked. We know from Ampere’s Law that magnetic
fields arise when there are changing electric fields and moving charges (current).
Also the field points in a peculiar direction that follows the so called
”right-hand-rule” and is thus perpendicular to the electric field at all times.
The magnetic fields for currents flowing through wires and bent into loops
are depicted in figure 1.
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Figure 1: Magnetic fields: (a) Around a wire (b) in a loop of wire (c) a
another view of a loop of wire
It is safe to say that wherever there are changing electric fields and/or
currents there is also a magnetic field. This is where magnetic properties
come from.
1.2 Magnetic Moments
Just as the electric and magnetic fields are useful constructs for understanding
the electromagnetic force, the magnetic moment is useful in understanding
the strength of a magnetic material. For instance, consider a magnetic
rod of length l in a uniform magnetic field, H, and pole strength p. The
torque on the rod can be written:
2

Figure 2: A magnetic rod in a uniform magnetic field
pH sin θ l 2 + pH sin θ l = pHl sin θ (1)
2
And we can define the magnetic moment as:
m = pl (2)
The magnetic moment can be interpreted as the maximum moment of
torque applied to a magnetic material of pole strength p and length l in a
field H. If one were to calculate this for a loop of wire like the one in figure
1 (b) and (c) they would find:
m = πR2 i
10 = Ai
10
Where R is the radius of the wire and i is the current. The factor of 10
arrises from converting between SI and cgs units.
(3)
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2 Magnetism in materials
2.1 The Bohr Magneton
Magnetic moments of wires are great, but what about the magnetic moment
of something interesting like iron or magnetite Well, let’s simplify this
problem a bit by considering the electrons surrounding a single atom. If we
use the Bohr model of the atom we have electrons orbiting a positive nucleus.
These electrons have orbital angular momentum and also intrinsic angular
momentum or spin. Let’s consider the magnetic moment of electrons due
to the orbital angular momentum (Note for atomic magnetic moments it is
customary to use the greek letter µ rather than m). Similarly to the loop of
wire:
( ev
)
µ orbit = πr 2 2πr
= evr in SI units (4)
2
(5)
The momentum of the electron will be an integral multiple of the reduced
Plank constant, . So for the first orbit, n=1:
µ orbit = e
2m
Incidentally the angular momentum due to spin is /2.
magnetic moment due to spin of:
(6)
This leads to a
µ spin = e
2m
These are the same! In fact this value is considered fundamental and so is
given a special name, the Bohr magneton.
2.2 Magnetics of atoms
Lets assume that the magnetic moment of atoms arises solely from the electrons.
We can picture two situations:
(7)
4

1. All the electron magnetic moments cancel out and leave a net magnetic
moment of 0.
2. The cancellation of magnetic moments is only partial leaving a residual
atomic magnetic moment.
The first case results in non-magnetic materials like copper, bismuth, and
graphite. The other case results in magnetic materials. Magnetic materials
may be classified by the relationship between their atomic magnetic moments
and their crystal structures. These emergent properties result in para-, ferro-,
antiferro-, and ferrimagnetism.
2.2.1 Paramagnetism
In a paramagnet the atomic magnetic moments are randomly distributed.
By applying a magnetic one can cause them to preferentially align to the
magnetic field. This is a linear relationship, thus the stronger the magnetic
field the more the moments are aligned and the larger the bulk magnetization,
or sum of magnetic moments is. There is also a randomizing element,
temperature. Higher temperatures lead to higher disorder and tend to lessen
the magnetization of a paramagnet.
2.2.2 Ferromagnetism
The atomic magnetic moments in a ferromagnet, on the other hand, are
strongly coupled to one another. Thus, large sections of the magnet are
aligned in a single direction. A section that is aligned in one direction is
called a magnetic domain. Random fluctuations can lead to multiple domains
within a single ferromagnetic material. In a steady state the net
magnetization is 0, but if one were to apply a magnetic field the atomic
magnetic moments opposing the field near the domain wall will experience a
torque and flip to regain equilibrium. This leads to a shift of the domain wall.
Eventually a ferromagnetic material will consist of a single domain. Continued
application of stronger magnetic fields will cause the atomic magnetic
moments to rotate leading to saturation magnetization. This is depicted
schematically in figure 3.
5

Figure 3: Domain wall motion followed by moment rotation
The change caused by this type of magnetization can be displayed in a
hysteresis loop, which you described in the pre-lab. An example hysteresis
loop is displayed in figure 4.
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Figure 4: Domain wall motion followed by moment rotation
If the loop is wide the magnet is said to be hard or permanent because it
takes a large applied magnetic field to switch it’s magnetization. If the loop
is narrow and tall the material is said to be soft. Soft magnets are useful
because you can get a large magnetic flux out of them after putting in a
small field.
Again temperature tends to counteract magnetization of a ferromagnet.
Above a certain temperature, called the Currie temperature or T C , a ferromagnet
is randomized and acts like a paramagnet.
2.2.3 Antiferromagnets
Like ferromagnets, antiferromagnets consist of materials whose atomic magnetic
moments are strongly coupled. Only in this case adjacent atomic planes
are coupled anti-parallel to each other. Thus at low temperatures they have
only a small magnetic susceptibility. Again like ferromagnets at a certain
temperature, called the Ne’el temperature or T N , antiferromagnets are randomized
and act like paramagnets.
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2.2.4 Ferrimagnets
We do not use ferrimagnets, also called ferrites, in this lab, but for completeness
I’ll describe them here. A ferrite is like an antiferromagnet in that the
adjacent atomic planes are antiparallel to each other. The difference here is
that the planes contain different materials and thus have different magnetic
moments leading to larger reminance magnetizations than antiferromagnetics.
Ferrites can also be made out of ceramic materials and other materials
that do not conduct electricity meaning that they are not susceptible to eddy
currents, one of the main sources of resistance for ferromagnetic materials. In
structures like transformers where they need the properties of ferromagnetics
without eddy currents a combination of ferrites and ferromagnets is used.
Also similar to ferromagnets, above the curie temperature the magnetization
is randomized and they act like paramagnets.
3 Overview
• Where does magnetism come from
Magnetism is part of the electromagnetic force and is present whenever
there are changing electric fields or moving charges.
• Why are some materials magnets and others not
Depending on the arrangement of electron magnetic moments the overall
atomic magnetic moment either cancels completely (non- or diamagnetic)
or cancels only partially leading to magnetic materials.
• How do magnetic materials behave in a magnetic field
Depending on the coupling of atomic magnetic moments different magnetic
materials react differently to magnetic fields and temperatures.
The effect of temperature and the alignments are summarized in figure
5.
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Figure 5: Saturation Magnetization and Susceptibility vs. Temperature
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