Physics of Magnetism

SECTION 12.3. DOMAINS AND DOMAIN WALLS 109

relevant parameter here is the maximum amount of mechanical work that can be obtained in
a reversible way from a well-designed configuration with a given magnet and a magnetizable
object. It is well known that this maximum mechanical work (available per unit volume
during a change in configuration) is equal to in the case of an ideal magnet in which
the complete (linear) hysteresis branch in the second quadrant is traversed reversibly.
There are also applications of permanent-magnet materials in which temporary or even
cyclic excursions to elevated temperatures are required. In such cases, the suitability of a
given magnet material will depend to some extent on the temperature dependence of its
remanence and on the temperature dependence of its coercivity in the temperature range
of interest. For many industrial applications, it is required to have stable coercivities and
magnetizations up to at least 150°C. If both quantities decrease significantly with increasing
temperature, one will be faced with a corresponding loss in magnet performance upon
increasing the temperature. In the most favorable cases, these losses in magnet performance
are only temporary and the original values of remanence and coercivity are recovered
after returning to room temperature. Unfortunately, for some types of materials the loss in
performance is irreversible. Reversible temperature coefficients ofcoercivity and remanence
can usually be dealt with by designing a machine according to a given specification in a
manner that the magnets are sized to be sufficiently strong at the highest temperature when
they are most prone to demagnetization effects.
The corrosion resistance, the chemical and mechanical stability, the ease of mechanical
processing, the weight per unit of energy product, and the electrical resistance are suitability
criteria of a different kind that also have to be considered. Furthermore, one has to bear in
mind that it is always necessary to magnetize magnets at some point in the manufacturing
cycle. In favorable cases, this can conveniently be done with the magnets in situ in a partially
or fully assembled machine, as with Alnico- and ferrite-type magnets. The production of
machines in which premagnetized magnets are used may present severe problems. One
of these is the attraction of magnetic dust during surface grinding. For this reason, it is
sometimes desirable to employ magnets having coercivities that are sufficiently high for the
purpose, but that are not so high as to make in situ magnetizing of the assembled magnet
impossible. This means that the applicability of a magnetic material may require a lower
as well as a higher limit for the coercivity. For more details, the reader is referred to the
survey published by McCaig and Clegg (1987).

12.3. DOMAINS AND DOMAIN WALLS

It was mentioned already that not only a large maximum energy product but

also a high intrinsic coercivity is needed in some applications. Moreover, the maximum

energy product itself depends on the coercivity and, if falls appreciably below the value

it may become lower than the theoretical limit

For this reason, it is desirable to look somewhat more closely at the mechanisms that govern

the magnitude of the coercivity in permanent-magnet materials.