24 BELL SYSTEM TECHNICAL JOURNAL 



discussed. But copper would not be ferromagnetic even if the inter- 

 action were large, because the completed shell means that the satura- 

 tion magnetization is zero; in reality copper is diamagnetic. 



A more detailed discussion of the atomic structure of metals, par- 

 ticularly of the band picture of the ferromagnetic metals, is given in a 

 recent article in this journal by W. Shockley.^" 



Interpretation of the Molecular Field 



It was shown by Heisenberg ^^ that the molecular field can be ex- 

 plained in terms of the quantum mechanical forces of exchange acting 

 between electrons in neighboring atoms. Imagine two atoms some 

 distance apart, each atom having a magnetic moment of one Bohr 

 magneton due to the spin moment of one electron. A force of inter- 

 action has been shown to exist between them, in addition to the better- 

 known electrostatic and (much weaker) magnetic forces. It is known 

 that, as one would expect, such forces are negligible when the atoms are 

 two or three times as far apart as they are in crystals. It is supposed 

 also, on the basis of calculations by Bethe,^^ that as two atoms are 

 brought near to each other from a distance these forces cause the elec- 

 tron spins in the two atoms to become parallel (positive interaction). 

 As the atoms are brought nearer together the spin-moments are held 

 parallel more firmly until at a certain distance the force diminishes 

 and then becomes zero, and with still closer approach the spins set 

 themselves antiparallel with relatively strong forces (negative inter- 

 action). In the curve of Fig. 14 the energies corresponding to these 

 forces are shown as a function of the distances between atoms. 



Bethe's curve was drawn originally for atoms with definite shell radii 

 and varying internuclei distances. It may equally well be used for a 

 series of elements if we take account of the different radii of the shell 

 in which the magnetic moment resides. The criterion of overlapping 

 or interaction for the metals of the iron group is the radius, R, of the 

 atom (half the internuclear distance in the crystal) divided by the 

 radius, r, of the ?)d shell. In Fig. 14 this ratio Rjr has been used as 

 abscissa and the elements iron, cobalt and nickel have been given ap- 

 propriate positions on the curve. The recently discovered ferromag- 

 netism of gadolinium ^^ is apparently associated with a large Rjr and 

 small interaction, as compared to nickel. It is placed on the curve 

 accordingly. Slater ^ has shown that the ratio Rjr is larger in the 



low. Shockley, Bell System Technical Journal, 18, 645-723 (1939). 

 " W. Heisenberg, Z.f. Physik, 49, 619-636 (1928). 



12 H. Bethe, Handbuch der Physik, 24, pt. 2, 595-598 (1933). 



13 G. Urbain, P. Weiss, and F. Trombe, Compt. Rend., 200, 2132-2134 (1935). 



