.MOTION' OF 1M)1\ iDlAI. DOMAIN WALLS 1051 



seriously. Nevertheless, j)laiisil)le assumptions ran be made which make 

 an instructive comparison possible, i/i^ in (31) is equal to the difference 

 in the variation of the anisotropy energy when measured adiabatically 

 and when measured isothermally. At this stage of our knowledge, many 

 assumptions which still retain the symmetry of the crystal are possible 

 concerning the form of (ji^id). For our present purposes we will assume 

 that it is given to within a constant by (34), but we must introduce a 

 minus sign to take account of the fact that the rearranging electrons 

 must ha\e a posilirc anisotropy encM'gy associated with them. Since we 

 differentiate before substituting in (31), we do not need to subtract out 

 the constant. The amplitude of ^i^ is not given by | i^i | of course; we 

 will call this amplitude \ Kr \. When we introduce the minus sign into 

 (34), and calculate the integral in (31), we find: 



_ 1 4.0M, 



"^^!Am/S^"- (38) 



This relation points up the fact that the mechanism we are discussing 

 here is characterized by two parameters, an amplitude factor | Kr \ and 

 a time r. Our experiment tells us nothing about \ Kr\, so we will ar- 

 l)itrarily assume it is about j^ of | T^i | at room temperature, or 20000 

 ergs/cc. I Kr \ can be measured by comparing \'alues of | i^i 1 determined 

 isothermally, say by measuring the torque on a disc, and values of 

 I Ki I determined adiabatically, say by ferromagnetic resonance ex- 

 periments, but this has not been done as yet. To determine r at 77°K, 

 assume that the maximum frequency of rotation of dipoles in the wall is 

 such that ccT = 0.1 when the non-linearity shown in Fig. 9 first occurs 

 (at V = 150 cm/sec). We calculate the thickness of the wall to be 4 X 10~^ 

 cm from standard formulae (see Kittel's review article. Reference 14) 

 and find r = 0.5 X 10"^. These values of r and | Kr | , together ^vith 

 I Ki I from Table II at 77°K and A as calculated above, gii^e v/Ho = 40 

 when in.serted into (38). This is to be compared \\'ith a measured 

 v/(H — He) of 160 at 77°K. In view of the preliminary nature of (31), 

 and the arbitrariness of some of our assumptions, this check is quite sat- 

 isfactory. It would be naive to expect the theoretical result to be closer 

 than an order of magnitude to the experimental one. Inspection of Fig. 

 8 suggests that the mechanism which gives the sharp increase in damp- 

 ing at 77°K is submerged at room temperature in the effects of other 

 mechanisms, perhaps other electronic rearrangements, perhaps exchange 

 effects of the sort recently suggested in metals by Kado.'^ Equation (30) 

 confirms this expectation when we use t = 10^'', as determined either 



