1042 THE HELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1954 



an order-disorder transition in the arrangement of the divalent and 

 trivalent iron ions. M. Fine of Bell Telephone Laboratories has found a 

 remnant of this transition in crystals of the same composition as those 

 studied in the present research, by means of ultrasonic measurements 

 of elastic constants/ We propose that the mechanism which causes the 

 sharp rise in the damping of domain wall motion at low temperatures is a 

 relaxation associated with this transition. Wijn and van der Heide" 

 have explained in this way observations of theirs of losses associated 

 with initial permeability at low frequencies in certain other polycrystal- 

 line ferrites. The time associated with this relaxation should be short 

 because this rearrangement of ions involves only the motion of electrons 

 from one site to another. It should be of the order of the relaxation 

 time associated with the electrical conductivitj^ of Fe304 . Snoek^^ has 

 suggested some time ago that losses in the ferrites were due to an after- 

 effect (relaxation) which, because of the short time constant involved, 

 must be associated with electron migrations. 



It is extremely useful to compare our data with a theory of the damp- 

 ing based on the above relaxation mechanism no matter what assump- 

 tions we make in detail about what it is that relaxes. We shall see that 

 we are led quite generally to the result that v/H '~ 1/r where r is the 

 relaxation time for the process. However, in order to perform this cal- 

 culation explicitly we must make more detailed assumptions about 

 exactly what (quantity relaxes with the relaxation time r. Changes in the 

 direction of the magnetization cause changes in stress in the sample 

 because of magnetostriction. One possible assumption is that the re- 

 sulting strain would lag behind this stress and mechanical energy would 

 be dissipated in the crystal. This mechanism, however, cannot act in 

 our case. The magnetization in the two domains on each side of the wall 

 points in opposite directions, but causes the same strain in both, and 

 they have such a large stifTness that the thin region occupied by the 

 domain wall assumes this same strain even though the direction of the 

 magnetization is different there. Thus regardless of the stresses produced 

 in the wall, the strains remain the same, inside and outside the wall, 

 whether it is moving or not; under these conditions no work is done on 

 the lattice, and no energy can be lost in this way by the mo\'ing wall. A 

 calculation has been made by the author on the assumption that it is 

 the magnetization itself which relaxes with relaxation time r. This 

 assumption leads to the result that wall velocity is not linearl}^ dependent 

 upon {H — II r) ; it is therefore not correct, since the data shows such a 

 linear dependence. A similar result is to be expected if we assume that 

 the dielectric polarization relaxes. 



