The Polder tensor is a tensor introduced by Dirk Polder[1] for the description of magnetic permeability of ferrites.[2] 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:[3]

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

where

(rad / s) / (A / m) is the effective gyromagnetic ratio and , 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. is the frequency of the RF/microwave signal propagating through the ferrite, is the internal magnetic bias field, is the magnetization of the ferrite material and is the magnetic permeability of free space.

To simplify computations, the radian frequencies of and can be replaced with frequencies (Hz) in the equations for and because the factor cancels. In this case, Hz / (A / m) MHz / Oe. If CGS units are used, computations can be further simplified because the factor can be dropped.

References

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  1. ^ D. Polder, On the theory of ferromagnetic resonance, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 40, 1949 doi:10.1080/14786444908561215
  2. ^ G. G. Robbrecht, J. L. Verhaeghe, Measurements of the Permeability Tensor for Ferroxcube, Letters to Nature, Nature 182, 1080 (18 October 1958), doi:10.1038/1821080a0
  3. ^ Marqués, Ricardo; Martin, Ferran; Sorolla, Mario (2008). Metamaterials with Negative Parameters: Theory, Design, and Microwave Applications. Wiley. p. 93. ISBN 978-0-470-19172-9.