714 BELL SYSTEM TECHNICAL JOURNAL 



trons per atom in the d>d and 4^ bands. The 2)d band with minus 

 spin is supposed full, containing five electrons per atom. The 4^ 

 band (both spins) can contain two electrons per atom, and from 

 Fig. 27 we see that it is about one-fourth full; suppose it contains 

 0.6 electrons per atom; the remaining electrons go to the 2>d band 

 with plus spin which is not quite full but has a "hole" in it of 0.6 

 electrons per atom. There are equal numbers of electrons of each 

 spin in the 4^ band and their magnetic moments cancel. ^^ The net 

 magnetic moment arises from the unbalance of 0.6 electrons per 

 atom between the two parts of the 3)d band. This unbalance will 

 correspond to a magnetization of 0.6 Bohr magnetons. The theory is 

 not capable of predicting the number 0.6 exactly; however, this number 

 is entirely consistent with what can be said about the distribution of 

 levels in the band. In the "atomic" theories of magnetism, it is sup- 

 posed that each atom has a certain magnetic moment. From the 

 results of the gyromagnetic experiments,'® one concludes that the 

 magnetization is due to electron spin. Since an atom whose magnetism 

 is due to electron spin must have a magnetic moment equal to an 

 integral multiple of the Bohr magneton,^'' the "atomic" theory is 

 forced to assume that 40 per cent of the nickel atoms are unmagnetized 

 and that 60 per cent have one Bohr magneton, or else that 70 per cent 

 are unmagnetized and 30 per cent have two Bohr magnetons or at any 

 rate that there are at least two kinds of atoms. These rather awkward 

 assumptions are not required in the band theory, the reason being, as is 

 suggested in Fig. 28, that the electrons are not thought of as belonging 

 to the atoms individually but to the crystal as a whole. 



The intrinsic magnetization of ferromagnetic material decreases with 

 increasing temperature. In the band theory this is explained as fol- 

 lows: at a temperature T some of the electrons are excited from the 

 filled band to the partially filled band; as the temperature is increased 

 more are shifted. Furthermore, if we compare the effects of two equal 

 increments of temperature, one occurring at a higher temperature than 

 the other, the one at the higher temperature will have the greater 

 effect. This is because at the higher temperature more electrons have 

 been shifted; hence the exchange effect displacement of the band of one 

 spin in respect to the band of the other spin is less and electrons need 



^ Actually there will be a slight exchange effect in the 45 band; however, it will be 

 so slight that the magnetic moment produced can be neglected 



"If a piece of iron is suspended so that it can rotate and then is magnetized, it 

 will acquire an angular momentum. The ratio of angular momentum to magnetic 

 moment should be mcje if the magnetization arises from electron spin and 2mc/e if it 

 arises from motion of the electron as a whole. Experiment gives the following 

 fractions of the former value: for iron 1.03, for cobalt 1.23, for nickel 1.05. 



^'' For a discussion of this theorem see K. K. Darrow's article, "Spinning Atoms 

 and Spinning Electrons," Bell Sys. Tech. Jour., XVI, 319 (1937). 



