Derivation of nondiagonal effective dielectric permeability tensors for magnetized granular composites

The effective dielectric-permeability tensors, including off-diagonal terms, for magnetized composites are derived. Based on Bragg and Pippard's average field approximation, the effective tensor is derived for a composite containing an ensemble of oriented ellipsoidal particles embedded in a host medium, which is magnetized along an arbitrary direction. The effective tensor elements are given by the average of the tensor elements of particles and the host medium weighted by ''virtual volume fractions.'' The average electric field at the particle is shown to be a local Lorentz field generalized to ellipsoids. Based on Bruggeman's symmetrized effective-medium theory, the effective permeability tensor is derived self-consistently for the magnetized composite involving n types of ensembles of randomly oriented ellipsoidal particles. The diagonal effective tensor element <(epsilon)over cap> is obtained by solving the equation for <(epsilon)over cap> of order 2n, independently of the off-diagonal effective tensor element <(Gamma)over cap>, while <(Gamma)over cap> is given as the average of the off-diagonal permeabilities of the constituents weighted by ''symmetrized virtual volume fractions.'' Bruggeman's effective permeability tensor, including off-diagonal terms, is calculated for Fe-SiO2 cermet, which falls between the theoretical upper and lower bounds derived by Hashin and Shtrikman.