100 CHAPTER 11. MAGNETIC ANISOTROPY
where is the remanence in the hard direction and where the factor
has been introduced to simulate perfect magnetic alignment of the powder particles.
An example of a modified Sucksmith–Thompson plot, obtained on a single crystal of
and
derived from the intercept and slope in this plot are equal to 1.5 and 3.9
respectively.
by Durst and Kronmüller (1986), is shown in Fig. 11.4. The values of
The variation of the anisotropy energy with the direction of the magnetization in cubic
materials is commonly expressed in terms of direction cosines. Let OA, OB, OC be the
cube edges of a crystal and let the magnetization be in the direction of OP. Furthermore,
and The anisotropy energy per unit volume
of the material, if it is magnetized in the direction OP, is given by
The constant K has been included for completeness, although it is rarely used. In many
textbooks, the constants and are represented as and Note that odd powers
of are absent in Eq. (11.9) because a change in sign of any of the αs should bring the
magnetization vector into a direction that is equivalent to the original direction. Furthermore,
the second-order terms can be left out of consideration since
of magnetization
The anisotropy constants can most conveniently be determined by measuring the energy
along different crystal axes of a single crystal. These determina
tions include measurements of the J(H) curve, starting from the demagnetized state up to
magnetic saturation. Subsequently, the area between this curve and the is determined.
Examples of such measurements were already displayed in Fig. 8.3.
The energies required for magnetizing cubic materials to saturation in the various
crystallographic directions can be derived from Eq. (11.9). For the [100] direction, one