Principles of Electromagnetic Waves and Materials, 2nd Edition

Appendix 11B: Ferrites and Permeability Tensor

In Chapter 11, we discussed the anisotropic properties of a magnetized plasma by modeling it as an anisotropic dielectric whose permittivity is a tensor. Ferrites in the presence of an external static magnetic field behave like an anisotropic magnetic material whose permeability is a tensor. Such material has many applications in microwave engineering. Here we briefly discuss the permeability tensor [1].

Ferrites are magnetic primarily because of the magnetic dipole moment $\overline{m}$ created due to the electron spin. In the presence of a magnetic field $\overline{H}$, torque $\overline{T}$ exerted on the electron is given by

(11B.1)$$\overline{T}={\mathrm{\mu }}_0\overline{m}\times \overline{H}.$$

The equation of angular motion of mechanics is given by

(11B.2)$$\frac{\text{d}\overline{L}}{\text{d}t}=\overline{T},$$

where ...