1334 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



If an alternating field is applied at right angles to the dc field the 

 magnetization will be driven in precession and when the driving fre- 

 quency coincides with the natural resonance frequency as determined 

 by the strength of the dc field a large amount of power will be absorbed 

 from the driving field. Off resonance the power absorption is small, but 

 the effective permeability seen by the driving field will go through a 

 dispersion such as is exhibited by all resonant systems. With this model 

 in mind we can proceed to discuss the phenomenon of ferromagnetic 

 resonance and the ferromagnetic Faraday effect. 



INFINITE MEDIUM — LONGITUDINAL FIELD 



Polder^ has shown that because of the gyroscopic nature of the mag- 

 netization a tensor permeability is required to relate the magnetic flux 

 density and field intensity vectors in a ferromagnetic medium. At low 

 frequencies the off-diagonal components of this tensor are negligible, 

 and the tensor reduces to the ordinary scalar permeability. At frequencies 

 above about 100 mc. these off -diagonal components can become signifi- 

 cant depending upon the magnetic state of the material. When this 

 tensor permeability is introduced into Maxwell's equations and a wave 

 equation is derived for propagation in the direction of the applied mag- 

 netic field we find that the normal mode solutions to the wave equation 

 are two circularly polarized waves rotating in opposite directions. A 

 solution in terms of linear polarizations is, of course, possible; but the 

 result is more readily interpreted in terms of the circularly polarized 

 waves. Furthermore, the propagation constant for either circular wave 

 contains a simple scalar permeability, instead of the tensor required to 

 describe the medium in general. 



Polder's tensor permeability gives the following relations between 

 b and h when there is a static magnetic field along the positive z axis*. 



^y 



The quantities 



by — jfloKhx + MO/x/ij, (1) 



hz = fidhz 



M = m' - Jm" (2) 



K = k' - jk" (3) 



are (complex relative diagonal and off-diagonal components of the tensor 

 permeability. 



^ D. Polder, Philosophical Mag., 40, p. 99, Jan. 1949. 



* Lower case letters are used for RF magnetic quantities. 



