Demagnetization factors of the general ellipsoid: An alternative to the Maxwell approach

Abstract

A transparent, exhaustive, and self-contained method for the calculation of the demagnetization tensor of the uniformly magnetized ellipsoid is presented. The method is an alternative to the established Maxwell derivation and is based on a Fourier-space approach to the micromagnetics of magnetized bodies. The key to the success of the procedure lies in the convenient treatment of shape effects through the Fourier representation. The scaled form of the demagnetization factors which depends on two dimensionless aspect ratios is argued to be their natural integral representation. Amongst other advantages, it allows for the immediate implementation of symmetry arguments such that only one of the principal factors needs to be computed. The oblate and prolate ellipsoids of revolution are examined from the same general point of view. The demagnetization factors for these distinct types of spheroid are seen to be related by analytic continuation of well-known Gaussian hypergeometric functions.

Acknowledgements

Financial support by the US Department of Energy (Basic Energy Sciences) under contract numbers DE-AC02-98CH10886 and DE-FG02-01ER45893 are gratefully acknowledged by MB and MDG.

Notes

¹ Below, we choose to use magnetostatic terminology, but the discussion is relevant to the electrostatic counterpart throughout.