THE QUANTUM PHYSICS OF SOLIDS 713 



theory must be regarded as representing great progress over non -wave- 

 mechanical theories. The reason is this: in older theories of ferro- 

 magnetism the energy was supposed to come from the magnetic inter- 

 action between the magnetic dipoles, and it turned out that the ener- 

 gies calculated in this way were at least a thousandfold too small. 

 The energies calculated in the new theory are adequate in magnitude 

 but have nothing to do with the magnetic moment of the electron; 

 they arise from the exchange energy, which is, as we have said before, 

 an electrostatic energy resulting from the wave-mechanical treatment 

 of Pauli's principle. It is the laws governing the spin quantum num- 

 ber of the electron, not the magnetic moment, which are responsible 

 for the energy of magnetization; the externally observed magnetic 

 field of a ferromagnetic material is merely a superficial indication of 

 more fundamental electrostatic forces. 



Intrinsic Magnetization 



According to our theory, the low energy state and therefore the 

 stable state of metallic nickel is a magnetized one. If one picks up a 

 piece of nickel at random, however, it may not appear to be magnetized. 

 This apparent absence of magnetism is due to the presence of "do- 

 mains." According to the domain theory — which is a very well estab- 

 lished branch of magnetic theory — a block of nickel will consist of a 

 number of microscopic domains, each highly magnetized, but having 

 their magnetic moments pointing at random in a number of directions 

 so that on the average there is no magnetism. The application of a 

 magnetic field aligns the magnetic moments of these domains and, 

 since they are then all parallel, one can measure the total magnetization 

 of the sample. A field strong enough to line up all the domains is said 

 to produce "saturation" because a further increase in field will give no 

 further increase in magnetization. It is customary and convenient to 

 divide the total or saturation magnetic moment of the material by 

 the total number of atoms, thus finding the average magnetic moment 

 per atom, and to express this value in Bohr magnetons. The resultant 

 value is called the intrinsic magnetization per atom and is denoted by 

 /3.'^ For example, if a crystal had one electron per atom and all the 

 electrons had their spins parallel, then all their magnetic moments 

 would be parallel, too, and the intrinsic magnetization would be 

 unity, /S = 1. 



For nickel the intrinsic magnetization is 0.6 Bohr magnetons per 



atom. The following argument shows how easily such a fractional 



number can be accounted for by our theory. Nickel has 10 elec- 



^ The "intrinsic magnetization" is customarily defined as the magnetic moment 

 per unit volume when the moments of the domains are parallel. 



