8 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1952 



valid, nevertheless the more complete theory is developed below. The 

 exact theory of this phenomenon should, of course, be approached 

 through quantum mechanics, but since the classical theory, in this 

 particular case, gives a result as satisfactory as the quantum theory 

 and since it lends itself more aptly to a fundamental physical inter- 

 pretation of the phenomenon, it is the classical theory which is developed 

 here. Quantum mechanically, Faraday rotations in the optical region are 

 accounted for by the Zeeman splitting of the spectral lines. 



The classical model which proves quite adequate for the description 

 of ferromagnetic resonance is that illustrated in Figs. 2 and 3 which 

 regards the electrons of the material which contribute to the magnetism 

 as being spinning magnetic tops. The angular momentum of each 

 electron is : 



\J\ = Uh/2ir) (2) 



J = Angular momentum of electron (gm cm /sec) 



h = Planck's constant (6.62 X 10~ erg sec) 



The magnetic moment which arises due to this rotation is: 



where : 



IJLB = Magnetic moment of electron (Bohr magneton) 



e = Charge on electron (4.80 X 10"'" E.S.U.) 



m = Mass of electron (9.10 X 10~"^ gm) 



c = Velocity of light (3 X 10'° cm/sec) 



The so-called gyromagnetic ratio of the electron is the ratio of these 

 quantities and is given by: 



^ = ^24 = ^ ^^) 



If a steady magnetic field is applied to the sample such that the elec- 

 tron sees an effective field H, then a torque will be applied to the electron 

 which tries to turn the electron so that its magnetic moment lies along 

 the field direction. However, as indicated in Fig. 2, the electron will 

 precess around the field direction until damping forces dissipate the 

 energy of precession. The equation of motion of the electron is: 



,,Xi/=^^. =T ^ (5) 



