Physics of Magnetism

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 sponta­

neous 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 measur­
ing 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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