A REVIEW OF NEW MAGNETIC PHENOMENA 1163 



The walls have been found to exhibit properties of mass and stiffness 

 and to be subject to damping. Thus it is possible to write an equation 

 which describes the motion of a wall under the influence of an alternating 

 field. ' If x is the displacement of the wall from its equilibrium posi- 

 tion, then 



m^,+Pj^ + ax=^ M.He'"', (2) 



where m = mass/unit length of wall, 



jS = damping coefficient, 



a — stiffness parameter, 



Mg = saturation moment of sample, 



He^"^ = applied field, 



This equation should look familiar to electrical engineers. It has the same 

 form as that for an RLC circuit subject to a sinusoidal applied voltage.^^ 

 If the damping constant is not too great, we would expect the wall 

 motion to have a resonance at a frequency, /o, for which 



Fig. 4 shows the expected variations of jjl' and m'' in the vicinity of reso- 

 nance under these conditions. 



If, however, the mass of the wall is negligible, the situation is some- 

 what different. In this case, /z" has a maximum at a frequency for which 

 0) = a/^, while m' decreased monotonically from its low frequency value, 

 reaching 3-^ this value at a; = a//?. It is apparent that this behavior is 

 analogous to that of an RC circuit. It is commonly known by the term 

 ''relaxation". We see, therefore, that, depending upon wall mass, there 

 are two possible ways in which wall motion may contribute to the be- 

 havior shown in Region A of Figure 3; namely, through domain wall 

 resonance and through domain wall relaxation. 



VII. DIMENSIONAL RESONANCE 



The second phenomenon which may aid in accounting for the behavior 

 indicated in Region A is dimensional resonance. In 1950, Brockman, 

 Dowling, and Steneck^^ reported the results of some experiments on a 

 manganese-zinc ferrite known commercially as Ferroxcube III. Using 

 blocks of this material, they built a closed rectangular core. Measure- 

 ments on a winding placed on this core showed behavior like that of 

 region A with /i lying between 1 and 2 mc. When they decreased the 



