Physics of Magnetism

148 CHAPTER 14. SOFT-MAGNETIC MATERIALS

Domain theory for rotational processes leads to the following expression for the initial

permeability:

where is the average saturation magnetization of the material and is a dimension­
less prefactor close to unity. The effective anisotropy constant covers all sources of
anisotropy energy such as, for instance, the intrinsic magnetocrystalline anisotropy of
the material considered and the shape anisotropy.
The coercivity is closely related to the initial permeability because both quantities
depend on the effective anisotropy constant :

where is a dimensionless prefactor close to unity.
A domain-wall-motion model in which the grain size is taken into account leads to the
expression:

where A is the exchange constant and D the grain size. Maximization of the initial perme­

ability requires maximization of and minimization of The latter possibility is the

one that is exploited most generally.

The minimization of all sources of anisotropy is important when the attainment of high

initial permeability is the primary objective. However, a finite but small anisotropy is still

desirable for achieving a square or skew hysteresis loop in an assembly of aligned particles.

If the magnetization process is performed with the field applied in the easy direction of the

aligned anisotropic particles, one obtains a high remanence and the hysteresis loop is square.

By contrast, the material exhibits a low remanence and a skew hysteresis loop when it is

magnetized perpendicular to the easy direction. Square-loop materials are commonly used

in magnetic amplifiers, memory devices, inverters, and converters. Skew-loop materials are

primarily used in unipolar pulse transformers.

It will be discussed later that the magnitude and the directional dependence of the

various types of anisotropy depend on the composition and the heat treatment. Magne­

tocrystalline anisotropy has been the most exploited source of anisotropy. Other types are

thermomagnetic anisotropy, slip-induced anisotropy, and shape anisotropy. In practice, one

aims at the dominance of one particular type of anisotropy by excluding all other sources of

anisotropy as far as possible. Of course, this is not necessary if the easy directions originat­

ing from two or more types of anisotropy are parallel. A survey of the anisotropy in various

Fe-based soft-magnetic materials has been presented by Soinski and Moses (1995).

14.2. SURVEY OF MATERIALS

Iron. Electrical-grade steel is the soft-magnetic material employed in the largest

quantities. The annual demand of the electronics industry amounts to several hundred of