Physics of Magnetism

112 CHAPTER 12. PERMANENT MAGNETS

In iron metal, one has and a = 0.3nm. The value of may be

calculated by means of Eq. (4.4.14), using Z = 8, and S = 1.1. This leads

to J. By means of Eq. (12.3.6), one now finds

which is about 200 lattice spacings, and

This may be compared with the situation in a strongly anisotropic material like the tetragonal

compound for which and where the wall width is one order of

magnitude smaller than in Fe metal.

12.4. COERCIVITY MECHANISMS

Already in 1948, Stoner and Wohlfarth showed that for a magnetization-reversal process

proceeding by means of uniform rotation of the magnetic moments in spheroid particles, in

which the major axis coincides with the easy direction of the magnetization, the coercivity

is given by

where and are the demagnetizing factors corresponding to the two extreme directions
of the spheroid particles. The first term is the normal anisotropy field that determines the
easy magnetization direction when there is only magnetocrystalline anisotropy. The second
term takes account of the fact that, even in the absence of magnetocrystalline anisotropy,
the moments would align in the direction of the lowest demagnetizing factor. As already
mentioned, the coercivity as expressed in Eq. (12.4.1) is based on a magnetization-reversal
mechanism in which all moments retain their parallel arrangement during magnetization
reversal (uniform rotation).
In practice, the coercivities obtained for most hard-magnetic materials are substantially
lower, often by more than a factor of 10. This behavior is illustrated in Fig. 12.4.1, where
deviations from the corresponding values of the nucleation field to be defined shortly,
are shown, the latter representing the values of the first term of Eq. (12.4.1).
The reason for this is that there exists another magnetization-reversal mechanism that
can proceed via considerably lower energy expenditure. The latter mechanism is based on
nucleation of Bloch walls and growth of reversed domains. If, somewhere in a large single
crystal, a tiny region with a less perfect magnetic-moment arrangement is present, it can
serve to generate a Bloch wall. The Bloch wall will subsequently spread into the crystal
and move across the whole crystal until magnetization reversal has been established over
the whole crystal. Note that the energy required for this process is only equal to the wall
energy taken over the whole surface of the wall and hence will involve only a very small
volume compared to the total volume of the crystal. For the uniform-rotation process, the
anisotropy energy taken over the whole volume of the crystal would be required.
Bloch walls and reversed domains can be generated near all types of defect regions
where the local values of the exchange field and anisotropy field have become sufficiently