716 BELL SYSTEM TECHNICAL JOURNAL 



this paper we shall use the fact that the magnetism changes with the 

 temperature to explain the anomalous expansion of ferromagnetic 

 materials. In Fig. 29 we show the variation in intrinsic magnetization 

 with temperature as observed for iron, cobalt and nickel. 



Variation of Intrinsic Magnetization with Composition 



Let us consider how the intrinsic magnetization should vary from 

 element to element in the transition series, supposing always that the 

 temperature is so low that thermal effects can be neglected. The ele- 

 ment next to nickel is cobalt; cobalt has one less electron than nickel 

 so that the Zd band and partially filled 4^ band for it will have one 

 less electron in them. Because of the relatively small number of 

 quantum of states in the 45 as compared to the 2>d band, this deficit 

 will be made up mainly by the 3rf band which will therefore contain 

 not 4.4 as for nickel but instead 3.4 electrons leading to an unbalance 

 of 1.6 Bohr magnetons per atom. The observed ^ for cobalt is 1.7 in 

 good agreement with this. 



One can obtain electron atom ratios intermediate between cobalt 

 and nickel by forming alloys. We shall speak of the electron concen- 

 tration, C, of these and other alloys, meaning by this term the total 

 number of electrons available for the 3>d and 4^ bands divided by the 

 total number of atoms. So long as the minus spin half of the Zd band 

 remains full and so long as the number of electrons in the 45 band does 

 not vary much, the value of /S will be a linear function of the electron 

 concentration varying from ~ 1.6 to ~ 0.6 as the concentration varies 

 from 9 for cobalt to 10 for nickel. In Fig. 30 are given the intrinsic 

 magnetizations plotted against electron concentration for a series of 

 alloys. It is seen that from cobalt to about halfway between nickel 

 and copper, an increase in C produces, very nearly, a numerically equal 

 decrease in /S. This means that the increase in C goes toward filling 

 up the holes in the Zd band and reducing the unbalance and hence jS. 

 Some alloys are included in Fig. 30 for which the two elements are not 

 adjacent in the periodic table; their values of /S also conform to the 

 values predicted from their electron concentrations. 



The very natural way in which the band theory accounts for the 

 results shown on Fig. 30 is its principal success in the theory of fer- 

 romagnetism. 



The bend in the curve between iron and cobalt is not very satis- 

 factorily explained at present. One theory is that for iron neither Zd 

 band is entirely full; but this explanation is said to be inconsistent with 

 the observed dependence of magnetization upon temperature at low 



