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Polder tensor : ウィキペディア英語版
Polder tensor

Polder tensor is a tensor used in description of magnetic permeability of ferrites.〔(G. G. Robbrecht, J. L. Verhaeghe, ''Measurements of the Permeability Tensor for Ferroxcube'', Letters to Nature, ''Nature'' 182, 1080 (18 October 1958), ) 〕 The tensor notation needs to be used because ferrimagnetic materials become anisotropic in the presence of magnetizing field.
The tensor is described mathematically as:〔(Ricardo Marqués, Ferran Martín, Mario Sorolla, ''Metamaterials with negative parameter: theory, design, and microwave applications, Willey, New Jersey, USA, 2009, page 93 ) ISBN 978-0-471-74582-2〕
::B = \begin \mu & j \kappa & 0 \\ -j \kappa & \mu & 0 \\ 0 & 0 & \mu_0 \end H
where:
:\mu = \mu_0 \left( 1+ \frac \right)
:\kappa = \mu_0 \frac^2 - \omega^2}
:\omega_0 = \gamma \mu_0 H_0 \
:\omega_m = \gamma \mu_0 M \
and \gamma = 17.6 \cdot g \ () is a gyromagnetic ratio and ''g'' is a factor between 1.9-2.4 depending on ferrite material. Magnetizing frequency (''f'') is expressed as \omega = 2 \pi f, ''H''0 is a bias field, ''M'' is magnetization and \mu_0 is magnetic permeability of free space.
==References==


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