172 CHAPTER 16. MAGNETOSTRICTIVE MATERIALSIn this expression, and represent the direction cosines with respect to the x, y
and z crystal axes of the magnetization direction and the length-measurement direction,
respectively. This relation makes it possible to describe the magnetostrictive properties for
any choice of the latter two directions if the two magnetostrictive constants and are
represents the change in length or saturation magnetostriction in the
direction when the magnetization direction is also along the
available. These two magnetostriction constants have the following physicalmeaning:direction after
the material has been cooled through its Curie temperature.
In the following, we will consider the macroscopic properties of a cubic ferromag
netic material for which the preferred magnetization direction is along When a large
single crystal of this material is cooled to below the Curie temperature, it will be in the
unmagnetized state by adopting a magnetic-domain structure that reduces its magnetostatic
energy. The magnetization in each of these domains is along one of the directions
and, if each of these domains is elongated in the corresponding direc
tion. However, no distortion will be observed upon cooling to below the Curie temperature
because the distribution of directions in the domain structure leads to a cancelation
of the distortion. This may be illustrated by means of Fig. 16.1. In this figure, we have
assumed for simplicity that only domains are present in which the preferred direction is
along cubic directions of the type [100] or [010]. The situation changes drastically if we
apply a magnetic field along one of these cubic directions, say [ 100]. The single crystal now
has become one single domain with the magnetization along the field direction. No can
cellation of distortive contributions is possible and the single crystal has become elongated
along the field direction. In other words, when applying a magnetic field along one of the
main crystallographic directions of a magnetically ordered but unmagnetized piece of cubic
material, we can produce an elongation or shrinking. Which of these latter two possibilities
is realized depends on the sign of the magnetostriction constant in this particular direction.
In tetragonal or hexagonal materials, one frequently encounters easy-axis anisotropy,
the preferred magnetization direction being along the crystallographic direction. In that
case, the domain structure will consist of domains separated by 180° walls. Because of