Physics of Magnetism

SECTION 4.2. FERROMAGNETISM 23

all the steps from Eq. (3.1.4) to Eq. (3.2.2). This means that Eq. (3.2.2) should actually be

written in the form

Introducing the magnetic susceptibility we may rewrite Eq. (4.2.3) into

where is called the asymptotic or paramagnetic Curie temperature.
Relation (4.2.4) is known as the Curie–Weiss law. It describes the temperature depen­
dence of the magnetic susceptibility for temperatures above The reciprocal susceptibility
when plotted versus T is again a straight line. However, this time it does not pass through
the origin (as for the Curie law) but intersects the temperature axis at Plots of
versus T for an ideal paramagnet and a ferromagnetic material above
are compared with each other in Fig. 4.2.1.
One notices that at the susceptibility diverges which implies that one may have
a nonzero magnetization in a zero applied field. This exactly corresponds to the definition
of the Curie temperature, being the upper limit for having a spontaneous magnetization.
We can, therefore, write for a ferromagnet

This relation offers the possibility to determine the magnitude of the Weiss constant

from the experimental value of or obtained by plotting the spontaneous magnetization

versus T or by plotting the reciprocal susceptibility versus T, respectively (see Fig. 4.2.1c).

We now come to the important question of how to describe the magnetization of a ferro­

magnetic material below its Curie temperature. Ofcourse, when the temperature approaches

zero kelvin only the lowest level of the (2J + 1)-manifold will be populated and we have

In order to find the magnetization between T = 0 and we have to return to

Eq. (3.1.9) which we will write now in the form

with

where is the total field responsible for the level splitting of the 2J + 1 ground-state
manifold.
The total magnetic field experienced by the atomic moments in a ferromagnet is
and, since we are interested in the spontaneous magnetization (at H = 0), we
have to use (Eq. 4.1.7), or rather This means
that y in Eq. (4.2.8) is now given by