Effective-susceptibility tensor for a composite with ferromagnetic inclusions: Enhancement of effective-media theory and alternative ferromagnetic approach

For calculating magnetic properties of a composite usually effective-medium theories are used. However, we show that for a composite with ferromagnetic inclusions such theories, in particular, Maxwell-Garnett equation, give peculiar and unphysical results, such as significant shift of ferromagnetic-resonance frequency with diminishing volume fraction of ferromagnetic inclusions. Starting from ferromagnetic theory we derive a simple expression for the calculation of the effective magnetic susceptibility of a composite and follow with detailed magnetostatic derivation of tensor equivalent of Maxwell-Garnett equation. By demonstrating the equivalence of both derivations we confirm the validity of the expression which we obtained from the ferromagnetic theory. Furthermore, we identify errors leading to unphysical results of effective-medium theories and show the correct application of these theories.