Physics of Magnetism

SECTION 12.5. MAGNETIC ANISOTROPY AND EXCHANGE COUPLING 115

Consequently, the coercive field is equal to the propagation field that had shown
up as a jump in the curve of initial magnetization. More details regarding the coercivity
mechanisms described above can be found in reviews published by Zijlstra (1982), Givord
et al. (1990), and Kronmüller (1991).
Permanent-magnet materials like are pinning controlled. At high temper­
atures, the alloy consists of one single phase. Heat treatment of the material at lower
temperatures leads to the occurrence of a finely dispersed precipitate that is able to pin the
Bloch walls and to cause high coercivities. A schematic representation of the microstruc­
ture of such a magnet material is shown in Fig. 12.4.3. In the permanent-magnet materials
and the coercivity is nucleation controlled.
A survey of various magnet materials is given in Table 12.5.1. Extremely high coercivi­
ties are attained in all materials based on rare-earth elements. The reason for this is their high
magnetocrystalline anisotropy discussed in Section 5.6, which leads to high coercivities in
nucleation as well as in pinning controlled permanent magnets.

12.5. MAGNETIC ANISOTROPY AND EXCHANGE COUPLING IN

PERMANENT-MAGNET MATERIALS BASED ON

RARE-EARTH COMPOUNDS

The anisotropy in modern rare-earth-based magnet materials mentioned in the previous
section derives primarily from the sublattice anisotropy of the rare-earth component R. The
anisotropy of the component is much weaker and, in some cases, has even the wrong
sign, that is, it gives rise to an easy-plane magnetization. Generally, one may say that the
rare-earth component in binary and ternary compounds is responsible for the magnetic
anisotropy whereas the component provides a sufficiently high magnetization and Curie
temperature.
It follows from the results given in the previous section that high coercivities can be
reached in materials in which the nucleation fields for domain walls are high or in which
the propagation fields associated with domain-wall pinning are sufficiently high. It can
be shown that both fields are the higher the stronger the magnetocrystalline anisotropy.
A discussion of the crystal field and the concomitant crystal-field-induced anisotropy
has already been given in Chapter 5. We will now go a little further and show how the
crystal-field parameters that reflect the strength and symmetry of the crystal field are
related to the macroscopic anisotropy constants introduced in Chapter 11 in the form