11

Magnetic Anisotropy

Phenomenologically, the anisotropy
A magnetic material is said to possess magnetic anisotropy if its internal energy depends
on the direction of its spontaneous magnetization with respect to the crystallographic axes.
energy,
in a material with uniaxial (hexagonal and
tetragonal) symmetry may be described by a series expansion. For tetragonal symmetry,
the lowest order terms are given by
where
and
are the anisotropy constants and where the direction of the spontaneous magnetization relative to the single uniaxial
direction and the
is given
by the polar angles and respectively (see Fig. 11.1).

In most cases, it is sufficient to consider only the

and
terms. The preferred
magnetization direction will be along the
in hexagonal or tetragonal crystal structures
if
predominates and
It will be perpendicular to the
if
If
is not
predominant, the preferred magnetization may point in other directions. In the following,
we will take only
and
into consideration. If one has a situation in which
then one finds that the lowest value of the anisotropy energy is reached for
whereas if
the lowest anisotropy energy is reached for a value given by
A diagram showing the preferred moment directions for different
and
values in a
hexagonal crystal is given in Fig. 11.2.
Experimental values of anisotropy fields,
are commonly obtained by measuring magnetic polarization curves with the field applied parallel and perpendicular to the
easy magnetization direction. The anisotropy field is then obtained as the intersection of
the two magnetization curves mentioned. Illustrative examples of measurements of
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