Physics of Magnetism

SECTION 3.2. THE CURIE LAW 13

Substitution of this result into Eq. (3.1.5) leads to

Since sinh one obtains

After carrying out the differentiation, one finds

with

with

the so-called Brillouin function, given by

It is good to bear in mind that in this expression H is the field responsible for the level

splitting of the 2J + 1 ground-state manifold. In most cases, H is the externally applied

magnetic field. We shall see, however, in one of the following chapters that in some materials

also internal fields are present which may cause the level splitting of the (2J + 1)-mainfold.

Expression (3.1.9) makes it possible to calculate the magnetization for a system of

N atoms with quantum number J at various combinations of applied field and temperature.

Experimental results for the magnetization of several paramagnetic complex salts

containing and ions measured in various field strengths at low temper­

atures are shown in Fig. 3.1.2. The curves through the data points have been calculated

by means of Eq. (3.1.9). There is good agreement between the calculations and the

experimental data.

3.2. THE CURIE LAW

Expression (3.1.9) becomes much simpler in cases where the temperature is higher and

the field strength lower than for most of the data shown in Fig. 3.1.2. In order to see this, we

will assume that we wish to study the magnetization at room temperature of a complex salt

of in an external field which corresponds to an external flux density

more details about units will be discussed