434 THE BELL SYSTEM TECHNICAL JOURXAL, MARCH 1957 



Equation (10) luijs a pole at %,„ ± k = —3 which simply indicates the 

 resonance condition for a sphere as derived by Kittel.^° This can be 

 verified from (2) : 



Xn.±K = -^ (11) 



cr rb 1 



Xote that p and o- are either both positive or both negative, hence, only 

 one of the two ciuantities (xm + a) or (xm — k) goes through resonance 

 at I 0- I = 1. A similar situation exists for Xms ± Ks expressed in terms 

 of (11) 



^""^ "^ "' ^ V+W±T) ^^^^ 



One of the two quantities (xms ± Ks) goes through resonance at 



U l« = 1 - I P 1/3 (13) 



Observing that the field in the sphere is given bj^ (9) this may be written 

 as 



= H. + MJZ = H,' (14) 



ItI 



(Kittel's resonance frequencj^ of a ferrite sphere) 



It is easily seen that this resonance of the spherical sample makes the 

 evaluation of Xm and k from (10) rather unattractive because one would 

 expect inaccurate results for Xm and k in the vicinity of the sphere reso- 

 nance as . Furthermore, for all numerical computations (10) must be 

 separated into real and imaginary parts 



/ , ' _ Q (Xm' ± k' + 3)(xm' ± li') + iXm" + k") /, -^ 



"""" ^'' -'^ (x.' ±k' + 3y + ixr." ± K'y ^^^^ 



■V " -I- '" 



/ ' _. / ' Q Xm ^t li (I r\ 



Xma ± Ks —if , , / , qN" r / 'ii~^ vy) ^^^! 



yXm ± K + 3j- + \Xm ± K )- 



In general higher order terms of Xm" and k" ma}' be neglected, but in the 

 vicinity of sphere resonance these terms predominate as the term 

 Xm ± k' + 3 vanishes. It can be seen from the preceding discussion 

 that the determination of Xm', Xm", «', and k" from Xms and k^ has its 

 difficulties. Fortunately, there is an easier way to the interpretation of 

 Xms and Ks in terms of the intrinsic parameters Xm and k. "We use (9) to 

 define a new quantity <j' in terms of the applied magnetic field. 



cr' = cr + p/3 = I 7 \ii^l^ (17) 



