Page 282 - Electrical Properties of Materials

264 Magnetic materials
28
Taking N m =8 × 10 m –3 and the above-mentioned experimental results,
we get for iron,

~
2
~
λ = 1000 and μ m = 2 × 10 –23 Am . (11.28)
The value for the magnetic dipole moment of an atom seems reasonable. It
would be produced by an electron going round a circle of 0.1 nm radius about
10 15 times per second. One can imagine that, but it is much harder to swal-
low a numerical value of 1000 for λ. It means that the internal field is 1000
times as large as the magnetization. When all the magnetic dipoles line up,
–1
6
M comes to about 10 Am , leading to a value for the internal flux density
3
B int = μ 0 λM =10 T, which is about an order of magnitude higher than the
highest flux density ever produced. Where does such an enormous field come
from? It is a mysterious problem, and we shall leave it at that for the time being.

11.4 Domains and the hysteresis curve
We have managed to explain the spontaneous magnetization of iron, but as
a matter of fact, freshly smelted iron does not act as a magnet. How is this
possible? If, below the Curie temperature, all the magnetic moments line up
spontaneously, how can the outcome be a material exhibiting no external mag-
netic field? Weiss, with remarkable foresight, postulated the existence of a
domain structure. The magnetic moments do line up within a domain, but the
magnetizations of the various domains are randomly oriented relative to each
other, leading to zero net magnetism.
The three most important questions we need to answer are as follows:
1. Why does a domain structure exist at all?
2. How thick are the domain walls?
3. How will the domain structure disappear as the magnetic field increases?

It is relatively easy to answer the first question. The domain structure comes
about because it is energetically unfavourable for all the magnetic moments to
line up in one direction. If it were so then, as shown in Fig. 11.4(a), there
would be large magnetic fields and, consequently, a large amount of energy
outside the material. This magnetic energy would be reduced if the material
would break up into domains as shown in Fig. 11.4(b)–(e). But why would
this process ever stop? Should not the material break up into as many domains
as it possibly could, down to a single atom? The reason why this would not
happen is because domains must have boundaries and, as everyone knows, it is
an expensive business to maintain borders of any kind. Customs officials must
be paid, not mentioning the cost of guard towers and barbed wire, with which
some borders are amply decorated. Thus some compromise is necessary. The
more domains there are, the smaller will be the magnetic energy outside, but
the more energy that will be needed to maintain the boundary walls. When
putting up one more wall needs as much energy as the achieved reduction
of energy outside, an equilibrium is reached, and the energy of the system is
minimized.
We have now managed to provide a reasonable answer to question (1). It is
much more difficult to describe the detailed properties of domains, and their