SECTION 4.3. ANTIFERROMAGNETISM 31
and hence the susceptibility by
In a polycrystalline sample, one has crystallites with all orientations relative to the field.
Since the number of orientations lying within of the inclination is proportional to
we have for the susceptibility of a piece of polycrystalline material or for a powder sample
with
and
This leads to
The above results for the magnetic susceptibilities are generally found to be in qualitative
agreement with the properties observed for polycrystalline samples of several simple anti
ferromagnetic compounds. A sharp maximum in the susceptibility at the Néel temperature,
or, equivalently, a sharp minimum in the reciprocal susceptibility, are generally consid
ered as experimental evidence for the occurrence of antiferromagnetic ordering in a given
material.
Let us consider the effect of an external field H on a magnetic material for which the
magnetization is equal to zero before a magnetic field is applied. The work necessary to
generate an infinitesimal magnetization is given by
The total work required to magnetize a unit volume of the material is
For antiferromagnetic materials and comparatively low magnetic fields, we may substitute
into this equation. After carrying out the integration, one finds for the free energy
change of the system
It can be seen in Fig. 4.3.2 that below the Néel temperature This means
that the application of a magnetic field to a single crystal of an antiferromagnetic material
will always lead to a situation in which the two sublattice moments orient themselves
perpendicular to the direction of the applied field or nearly so, as shown in the right part of
Fig. 4.3.2. With increasing field strength, the bending of the two sublattice moments into
the field direction becomes stronger until both sublattice moments are aligned parallel to
the field direction and further increase of the total magnetization is no longer possible. The