Physics of Magnetism

114 CHAPTER 12. PERMANENT MAGNETS

by any applied field. Generally, the value of the coercivity cannot be further increased
by application of positive fields larger than
After the application of nucleation of reversed domains can occur only in a
negative field H at least equal in size to the nucleation field. Provided is larger than
the propagation field associated with a possible wall pinning at the grain boundaries,
complete magnetization occurs only if meaning that in this case the coercivity
is equal to (see Fig. 12.4.2a).
A slightly different mechanism is also possible. Nucleation may take place at magnetic
inhomogeneities at the grain boundaries where the propagation field associated with the
pinning of walls at these inhomogeneities is larger than the nucleation field
For intermediate field strengths nucleated domains may exist then
but the domain walls will remain pinned at the grain boundary as long as
This mechanism is commonly referred to as inhomogeneous pinning-controlled coercivity.

the magnetization remains very close to saturation in fields

compared to the volume of the total grain. In Fig. 12.4.2b, the corresponding decrease in
magnetization has been strongly exaggerated for clarity.

because

It is difficult to distinguish it from the pure nucleation mechanism owing to the fact that

the volume of the domain nucleated (that has reversed magnetization) is negligibly small

The situation is completely different in pinning-type magnets. Here the Bloch walls can­
not travel freely throughout the whole grain because of magnetic inhomogeneities present
in the grains that act as pinning centers for wall motion. Apart from the change in magneti­
zation associated with some wall bending, this pinning will prevent further magnetization
reversal. Wall displacement (other than bending) can occur only when the force exerted
on the wall becomes sufficiently strong. This is the case when the strength of the external

representation ofthe hysteresis loop associated with such a situation is shown in Fig. 12.4.2c.

field exceeds the pinning field strength that then determines the coercivity. A schematic

The presence of homogeneously distributed pinning centers inside the grain has impor­

tant consequences for the low-field behavior. As illustrated in Fig. 12.4.2c, the low-field

susceptibility is very weak. Saturation requires a field

to surmount the potential barriers associated with the pinning centers. The corresponding

sufficiently high to allow the walls

magnetization process is irreversible and it dominates any other reversible processes that
may be present. The magnetization reversal occurring in a sufficiently high negative field
is subject to the same mechanism that takes place during the initial magnetization.