400 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1960 



and that this is constant per unit area. As we increased the number 

 of ribbon domains, we would increase the total wall energy. Some- 

 where there is an optimum spacing where the total energy is a mini- 

 mum, and tliis is the stable spacing. In these crystals the spacing 

 depends on the thickness, and on the magnetization. If we decrease 

 the thickness, the ribbons become narrower; if we increase the mag- 

 netization, the ribbons become narrower. Suppose the magnetization 

 were decreased to zero. Then there would be no fields associated with 

 a configuration such as that in figure 8(a), and it would be the stable 

 domain configuration. Referring back to figure 1, we see that for 

 gadolinium iron garnet there is a compensation point just a little 

 below room temperature. It is merely necessary to cool the sample 

 about 10° C. to get so close to the compensation point that the mag- 

 netization is negligible, and very large areas replace the ribbon 

 domains. 



The part of the energy of which we have just been speaking is 

 often termed the "demagnetizing energy," since its minimization al- 

 ways tends to demagnetize magnetic bodies. The fields are "demag- 

 netizing fields." The effect obviously has a great deal to do with the 

 shape of a sample, and with the direction within the sample along 

 which the magnetization chooses to lie. 



DOMAIN WALLS 



Let us change our frame of reference slightly and consider the 

 domain walls as entities. Of what do they consist, what are their 

 energies, and what is their importance? Figure 9 is a schematic 

 representation of the magnetization distribution on passing through 

 a 180° domain wall; that is, a wall on one side of wliich the magneti- 

 zation is antiparallel to that on the other side. In the domains on 

 each side of the wall the magnetization lies along an easy direction, 

 and neighboring volumes have their magnetization parallel. But 

 within the wall there is a volume of material which has its magnetiza- 

 tion along other than easy directions ; thus the wall must have asso- 

 ciated with it a certain amount of anisotropy energy. This part of 

 the energy could be reduced by making the wall thinner, for then the 

 total volume of magnetization out of an easy direction would be 

 reduced. If the wall had no thickness, it would have no anisotropy 

 energy. But we remarked much earlier that if it had no thickness, 

 the net magnetic moment of neighboring cells would be antiparallel 

 and would have a prohibitive exchange energy. The total exchange 

 energy can be reduced by making the angle between tlie magnetiza- 

 tion of adjacent volume elements as small as possible. Thus the 

 exchange energy would be a minimum for an infinitely thick wall. 

 Here we have two energy conditions, one forcing the wall to be 



