CHAPTER 16. MAGNETOSTRICTIVE MATERIALS 173the equivalence of the positive and negative c direction, domains on either side of the
domain wall will experience the same type of deformation in the magnetically ordered
state. This means that no special effect will be observed when applying a magnetic field in
one of these directions, causing the disappearance of domains that have their magnetization
in the opposite direction. Therefore, cubic materials are generally considered to be more
appropriate for obtaining magnetostriction effects generated by domain-wall motion. The
magnetostriction constant of several cubic materials can be compared with each other in
Table 16.1.
In polycrystalline materials, the situation is more complex than in single crystals
because one has to relate the magnetostriction of the whole piece of material to the mag
netoelastic and elastic properties of the individual grains. This problem cannot be solved
by an averaging procedure. For this reason, it is assumed that the material is composed of
a large number of domains with the strain uniform in all directions. It can be shown that,
for a material in which there is no preferred grain orientation, this leads to the expression
(Chikazumi, 1966):
Inspection of the data listed in Table 16.1 shows that in particular the cubic compound
(also called Terfenol) has quite outstanding magnetostrictive properties. For this
reason, this compound has found applications in magneto-mechanical transducers. It can,
for instance be used to generate field-induced acoustic waves at low frequencies in the
kHz range (Sonar). Alternatively, its changes in magnetic properties under external stresses
have led to applications in sensors for force or torque. A variety of other magnetostrictive
materials and their properties are discussed in the reviews of Cullen et al. (1994) and
Andreev (1995).
The microscopic origin of magnetostrictive effects has sometimes been attributed to
dependencies of the exchange energy or the magnetic dipolar energy on interatomic spacing.
However, these approaches proved less satisfactory because they were not able to account
for the magnitude of the observed magnetostriction. As discussed in more detail by Morrish
(1965), it is more likely that magnetostriction has the same origin as the magnetocrystalline
anisotropy. In that case, magnetostriction can be viewed as arising because the spontaneous
straining of the lattice lowers the magnetocrystalline energy more than it raises the elastic
energy. Indeed, the analysis of modern magnetostrictive materials based on rare earths (R)
and 3d metals (T) has shown that there is an intimate connection between magnetostriction
and crystal-field-induced anisotropy, as is explained in more detail in the treatments of
Clark (1980), Morin and Schmitt (1990), and Cullen et al. (1994). Generally, the theoretical