THE PHYSICAL BASIS OF FERRO MAGNETISM 13 



this becomes therefore the direction of easy magnetization, a situation 

 which is correct for nickel but decidedly not so for iron. The best 

 correspondence between the action of the model and of iron itself is 

 obtained if the model is made by placing a small circular current of 

 electricity, instead of a magnet with finite length, at each lattice point 

 of the space array. In the latter case we can explain the direction of 

 easy magnetization in iron and the variation of magnetic energy with 

 direction in the crystal. 



In considering Ewing's model it is appropriate to estimate the energy 

 of thermal agitation and to compare it with the magnetic potential 

 energy as calculated from the model. Substituting in Eq. (2) the 

 same values of ma and r as were used above, we obtain 10"^® erg per 

 atom for the magnetic potential energy in zero field. This is to be 

 compared with the rotational energy of a single molecule at room 

 temperature, 2 X 10~^'* erg per atom as given by the kinetic theory. 

 Thus the energy of thermal agitation is 200 times as great as the calcu- 

 lated magnetic energy. Even at liquid air temperatures the thermal 

 agitation would prevent the atomic magnets from forming stable con- 

 figurations. Without some additional force the model Ewing used 

 would behave as a paramagnetic rather than a ferromagnetic solid. 



In a real material, however, it is now well established that there are 

 very powerful forces, not contemplated when Ewing made his model 

 and proposed his theory, which maintain parallel the dipole moments 

 of neighboring atoms. These are the electrostatic forces of exchange 

 (see p. 24) which Heisenberg suggested are powerful enough to align the 

 elementary magnets against the disordering forces of thermal agitation, 

 forces much larger than those of magnetic origin. Theory accounts 

 only for the order of magnitude of these forces. Our best estimate of 

 the corresponding energy of magnetization is obtained by assuming 

 that it is equal to the energy of thermal agitation at the Curie point, 

 \ke. For iron {6 = 1043 °K) this gives 7 X lO-^^ erg per atom. 



The Weiss Theory 



In order to understand how atomic forces give rise to ferromagnetism 



it is desirable to review briefly Weiss's theory ^ of ferromagnetism, 



which introduces a so-called "molecular field" that presently will be 



identified with the nature of these forces. This theory is an extension 



of Langevin's theory of a paramagnetic gas. The original Langevin 



theory culminated in a formula relating the magnetization, /, to the 



field-strength, H, and the temperature, T; this is the hyperbolic co- 



« P. Weiss, Jo7ir. de physiqtie (4) 6, 661-690 (1907). P. Weiss and G. Foex, "Le 

 Magnetisme," Colin, Paris (1926). 



