Theoretical aspects of demagnetization tensors

A magnetometric demagnetization tensor is defined for uniformly-magnetized samples of arbitrary geometry. It is shown that this is a real symmetric tensor with non-negative diagonal elements and unit trace. Diagonalization of the magnetometric demagnetization tensor yields the Brown-Morrish equivalent ellipsoid and the conclusion that Stoner-Wohlfarth particles of any surface geometry have only two easy directions of magnetization. Transformation of the tensor, subject to periodicity constraints, leads to the conclusion that uniformly-magnetized samples with rotational periodicity, of order about a single axis, have isotropic behavior perpendicular to that axis. It is also shown that if a sample has spherical periodicity with four or more vertices it does not exhibit shape anisotropy. Various methods for determining the numerical values of the tensor elements are presented.