Page 264 - Engineering Electromagnetics, 8th Edition

246 ENGINEERING ELECTROMAGNETICS

When an external field is applied, however, there is a small torque on each atomic
moment, and these moments tend to become aligned with the external field. This
alignment acts to increase the value of B within the material over the external value.
However, the diamagnetic effect is still operating on the orbiting electrons and may
counteract the increase. If the net result is a decrease in B, the material is still called
diamagnetic. However, if there is an increase in B, the material is termed paramag-
netic. Potassium, oxygen, tungsten, and the rare earth elements and many of their salts,
such as erbium chloride, neodymium oxide, and yttrium oxide, one of the materials
used in masers, are examples of paramagnetic substances.
The remaining four classes of material, ferromagnetic, antiferromagnetic, fer-
rimagnetic, and superparamagnetic, all have strong atomic moments. Moreover, the
interaction of adjacent atoms causes an alignment of the magnetic moments of the
atoms in either an aiding or exactly opposing manner.
In ferromagnetic materials, each atom has a relatively large dipole moment,
caused primarily by uncompensated electron spin moments. Interatomic forces cause
these moments to line up in a parallel fashion over regions containing a large number
of atoms. These regions are called domains, and they may have a variety of shapes
and sizes ranging from one micrometer to several centimeters, depending on the size,
shape, material, and magnetic history of the sample. Virgin ferromagnetic materials
will have domains which each have a strong magnetic moment; the domain moments,
however, vary in direction from domain to domain. The overall effect is therefore one
ofcancellation,andthematerialasawholehasnomagneticmoment.Uponapplication
of an external magnetic field, however, those domains which have moments in the
direction of the applied field increase their size at the expense of their neighbors,
and the internal magnetic field increases greatly over that of the external field alone.
When the external field is removed, a completely random domain alignment is not
usually attained, and a residual, or remnant, dipole field remains in the macroscopic
structure. The fact that the magnetic moment of the material is different after the
field has been removed, or that the magnetic state of the material is a function of its
magnetic history, is called hysteresis, a subject which will be discussed again when
magnetic circuits are studied in Section 8.8.
Ferromagnetic materials are not isotropic in single crystals, and we will therefore
limit our discussion to polycrystalline materials, except for mentioning that one of the
characteristics of anisotropic magnetic materials is magnetostriction, or the change
in dimensions of the crystal when a magnetic field is impressed on it.
The only elements that are ferromagnetic at room temperature are iron, nickel,
and cobalt, and they lose all their ferromagnetic characteristics above a temperature
called the Curie temperature, which is 1043 K (770 C) for iron. Some alloys of these
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metals with each other and with other metals are also ferromagnetic, as for example
alnico, an aluminum-nickel-cobalt alloy with a small amount of copper. At lower
temperatures some of the rare earth elements, such as gadolinium and dysprosium,
are ferromagnetic. It is also interesting that some alloys of nonferromagnetic metals
are ferromagnetic, such as bismuth-manganese and copper-manganese-tin.
In antiferromagnetic materials, the forces between adjacent atoms cause the
atomic moments to line up in an antiparallel fashion. The net magnetic moment is