SECTION 4.2. FERROMAGNETISM 25
exclusively on the form of the Brillouin function It is independent of parameters that
vary from one material to the other such as the atomic moment the number of partic
ipating magnetic atoms N and the actual value of In fact, the variation of the reduced
magnetization with the reduced temperature can be regarded as a law of corresponding
states that should be obeyed by all ferromagnetic materials. This was a major achievement
of the Weiss theory of ferromagnetism, albeit Weiss, instead of using the Brillouin func
tion, obtained this important result by using the classical Langevin function for calculating
M(T):
with
Here represents the classical atomic moment that, in the classical description, is allowed
to adopt any direction with respect to the field H (no directional quantization). The classical
Langevin function is obtained by calculating the statistical average of the moment
in the direction of the field. A derivation of the Langevin function will not be given here.
For more details, the reader is referred to the textbooks of Morrish (1965), Chikazumi and
Charap (1966), Martin (1967), White (1970), and Barbara et al. (1988).
for the ferromagnetic Brillouin functions (Eq. 4.2.11) with
Several curves of the reduced magnetization versus the reduced temperature, calculated
1, and are shown
in Fig. 4.2.2, where they can be compared with experimental results of two materials with
strongly different Curie temperatures: iron and nickel