Polder Tensor

The Polder tensor is a tensor introduced by Dirk Polder for the description of magnetic permeability of ferrites. The tensor notation needs to be used because ferrimagnetic material becomes anisotropic in the presence of a magnetizing field.

The tensor is described mathematically as:

::$B = \begin \mu & j \kappa & 0 \\ -j \kappa & \mu & 0 \\ 0 & 0 & \mu_0 \end H$

Neglecting the effects of damping, the components of the tensor are given by

:$\mu = \mu_0 \left( 1+ \frac \right)$
:$\kappa = \mu_0 \frac$

where

:$\omega_0 = \gamma \mu_0 H_0 \$
:$\omega_m = \gamma \mu_0 M \$
:$\omega = 2 \pi f$

$\gamma = 1.11 \times 10^5 \cdot g \,\,$ (rad / s) / (A / m) is the effective gyromagnetic ratio and $g$, the so-called effective g-factor (physics), is a ferrite material constant typically in the range of 1.5 - 2.6, depending on the particular ferrite material. $f$ is the frequency of the RF/microwave signal propagating through the ferrite, $H_0$ is the internal magnetic bias field, $M$ is the magnetization of the ferrite material and $\mu_0$ is the magnetic permeability of free space.

To simplify computations, the ''radian'' frequencies of $\omega_0, \, \omega_m, \,$ and $\omega$ can be replaced with frequencies (Hz) in the equations for $\mu$ and $\kappa$ because the $2 \pi$ factor cancels. In this case, $\gamma = 1.76 \times 10^4 \cdot g \,\,$ Hz / (A / m) $= 1.40 \cdot g \,\,$ MHz / Oe. If CGS units are used, computations can be further simplified because the $\mu_0$ factor can be dropped.

References

{{DEFAULTSORT:Polder Tensor
Ferrites
Tensor physical quantities
Ferromagnetic materials
Magnetic ordering