MOTKJN OF INDIVIOIAL DOMAIN WALLS ]{)\'.i 



What seems at present likely to })e the approximate nature of tlK^ 

 mechanism, and what we will assume is tlie nature of tlie meclianism 

 for the purposes of an i 1 lust rati \-e calculation is as follows. As the domain 



wall passes a [)oint in space, and the direction of .1/ chanties, the electrons 

 on tiie (hxalent and ti'ixalent ii'on ions lend to i-eai'rani>;e tiiemselves so 



as to minimize tlie maj;netocrystalline anistropy energy."" If .1/ changes 

 slowly this anistropy en(M-gv is lu^ar tlie minimum possible value (the 

 rwcrsible value) at all times, and the piocess is almost isothermal. As a 

 result of the fact that the process deviates irre\-ersibly from e(|uilihrium, 

 however, net work is done in bringing about the change. If, on the other 



hand, the direction of .1/ changes so suddenly that the electrons have no 

 time to rearrange, the process is adiabatic, and the magnetocrystalline 



anistropy energ}^ varies more \vid(4y with the angular position of M. 



Since our data is taken at low \-elocities and extrai)olated to zero 

 velocity, it seems most appropriate for us to make a calculation of the 

 losses on the assumption that as we increase the veloeity of the wall 

 we are de\'iatiiig from the isothermal condition. Let us define as a ther- 

 modynamical system the part of the magnetic lattice which lies in a 

 small \olnme fixed in space. This volume is a sheet of unit cross-section 

 in which the magnetization is uniform and which is part of the cylinder 

 of unit cross-section normal to the wall mentioned in connection with 

 (11). From the first law of thermodynamics, as the wall passes the small 

 \'olume, we have: 



(hv = dU - clQ - dg, (14) 



where dQ is heat added to the system, dV is a change in internal energy, 

 dw is work done on the system, and g is the anisotropy energy as- 

 sociated with our rearranging electrons. Note that </, is a term in the 

 free energy of the magnetic lattice. The free energy includes other 

 terms in addition to g, and indeed there is in general another t(Mm in 

 the magnetocrystalhne anistropy energy; we will not consider any of 

 these, however, since they also integrate to zero as the domain wall 

 passes our small \()lume. Similarly, there are man}' contributions to 

 dii\ but we will concern ourselves only with the term which does net 

 work on our system, the pressure on the wall times its \-elocity. If we 

 now consider changes in our system with time we have from (14): 



dw da .,_. 



71 = J,- O---^ 



The rate of doing work on luiit area of the wall mu\ing along our 



