THE PHYSICAL BASIS OF FERROMAGNETISM 29 



copper, indicates that all of these substances should lie to the right of 

 the maximum. It should be expected that iron-cobalt, like iron- 

 nickel, alloys should lie in the region including the maximum. This 

 is not observed; instead, the Curie point continually decreases as iron 

 or nickel is added to cobalt — in this case, however, the change of 

 Curie point with composition is obscured by a change of phase so 

 that no easy test of the theory is possible. 



Sizes of Domains and Widths of Domain Boundaries 



The quantum mechanical interaction in ferromagnetic materials 

 tends to make the magnetic moments of neighboring atoms parallel. 

 One infers that the whole ferromagnetic specimen should be one single 

 large domain; nevertheless in actual fact the parallelism extends over 

 much smaller regions only. This behavior is attributed to strains, 

 crystal boundaries, temperature vibrations, impurities, etc. The fact 

 that a specimen can be demagnetized so that no residual magnetization 

 can be observed by ordinary means, indicates that the domains are 

 not larger than microscopic in size; while the occurrence of heat effects 

 at the Curie point shows that the magnetic unit is larger than a 

 single atom. 



A direct measure of the domain size is obtained from experiments 

 on the Barkhausen effect; ^^ the volume is found to be of the order of 

 10~^ cm.^, so that it contains about 10^* atoms. The Barkhausen 

 data give little information concerning the shape of a domain, but 

 this has been made evident by the powder patterns of Bitter and 

 others; ^ a typical domain is long and slender, either rod-like or plate- 

 like with a thickness of the order of one micron (10"'* cm.) and a 

 length of perhaps 10 microns. The volume thus agrees with the 

 results of the Barkhausen effect within one or two orders of magnitude. 

 No explanation has been given for the occurrence of domains of this 

 particular size. 



There is at present no experimental evidence regarding the nature 

 of the transition region between domains, and in the schematic Fig. 3 

 no transition region is shown. It is believed that the boundary will 

 not be sharp on an atomic scale, but will be spread over a region a 

 considerable number of atoms wide. Calculation indicates that less 

 energy is required if the electron spins change direction gradually from 

 atom to atom as indicated in Fig. 17. The spreading of the transition 

 region over many atoms instead of over one, is analogous to the 

 separation of similar electric charges ; the mutual forces tend to spread 

 them over a region as large as possible and they are held together 



18 R. M. Bozorth and J. F. Dillinger, Phys. Rev., 35, 733-752 (1930). 



