1162 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER, 1953 



For convenience in the following discussion, Fig. 3 has been divided 

 into three regions as indicated. It will be observed that there are two 

 peaks in the curve of ix" versus frequency, one in Region A and the other 

 in Region B. The frequencies at which these occur are those at which 

 relatively large amounts of energy are absorbed by the material. These 

 two absorption peaks are due to entirely different mechanisms within the 

 ferrite and it is, therefore, of interest to consider them separately. We 

 begin with Region A. 



The behavior indicated in Region A is typical of polycrystalline 

 samples of ferrite (as distinguished from single crystals which will not 

 be considered here), yl rises somewhat above its constant low frequency 

 value and then decreases rather suddenly. If /i denotes the frequency at 

 which the peak in \i" occurs, we find that in general a high value of ii' 

 at low frequency is associated with a low value of /i, and vice versa. 



At the present time, we are not sure which of two experimentally ob- 

 served effects in the ferrite is responsible for the behavior shown in 

 Region A. It is quite likely that what one observes in a given sample is 

 actually a combination of the two effects, domain wall motion and 

 dimensional resonance, each of which will now be described. 



VI. DOMAIN WALL MOTION 



The basic unit of magnetism is the spinning electron. In an atom of 

 ferromagnetic material, there is an excess of electrons with spins in one 

 particular direction. As a result, the atom has a net magnetic moment. 

 Any ordinary sample of ferromagnetic material consists of many small, 

 irregular volumes called domains, each of which may contain many 

 atoms. Each domain is completely magnetized along some direction. 

 Both the size of the domains and the directions of their magnetizations 

 vary from point to point throughout a sample. In an unmagnetized 

 material, the random orientation of individual domain magnetizations 

 results in a mutual cancellation of their effects. However, if a magnetic 

 field is applied, certain domains will be in a preferred orientation, having 

 their magnetic moments more nearly in the direction of the applied field 

 than others. These will grow at the expense of less favorably oriented 

 domains by a process of motion of the walls separating adjacent do- 

 mains. When an alternating field is applied, the walls will be subject to 

 an alternating force which will tend to move them first in one direction 

 and then in the opposite direction. Now it has been shown^^ that, under 

 these conditions, the permeability of the material is proportional to the 

 ease of displacement of the domain walls. Therefore, if we can predict 

 how a wall will move as the frequency of the applied field changes, we 

 can predict how the permeability will change with frequency. 



