THE PHYSICAL BASIS OF FERROMAGNETISM 15 



where C is a constant. This relation, known as Curie's Law, is obeyed 

 by some paramagnetic though not by ferromagnetic substances. It is 

 usually written with IjH denoted by the symbol %> representing 

 susceptibility : 



Many more paramagnetic substances obey the similar "Curie-Weiss 

 Law ' ' : 



1= ^^ . • (4) 



Weiss pointed out the significance of 6 in this equation: it means that 

 the material behaves magnetically as if there were an additional field, 

 NI, aiding the true field H. This equivalence is shown mathematic- 

 ally by putting 6 = NC in Eq. (4) with the result 



C(H±NI) 

 T 



The quantity represented by NI is called the "molecular field" and 

 that by N the " molecular field constant." It is interpreted by suppos- 

 ing that the elementary magnet does have an influence on its neighbors, 

 contrary to the assumptions of the simple Langevin theory. 



The significance of the molecular field for ferromagnetism is now ap- 

 parent if we replace the Hhy H -{- NI in the more general Eq. (3) and 

 examine the resulting equation : 



| = ,,„h^^i(^L+^. (5) 



h kT 



This equation is perhaps the most important in the theory of ferro- 

 magnetism. It indicates that even in zero field there is still a mag- 

 netization of considerable magnitude, provided the temperature is not 

 too high. Putting II = and 



Eq. (5) reduces to 



e - ixANhIk, 



This purports to specify the magnetization at zero applied field by a 

 function that is the same for all materials, when the magnetization is 

 expressed as a fraction of its value at absolute zero and the temperature 

 as a fraction of the Curie temperature on the absolute scale. This 

 magnetization vs. temperature relation, plotted as the solid line of Fig. 



