On the electromagnetic characterization of ferromagnetic media: Permeability tensors and spin wave equations

Abstract
Various constitutive equations applicable to ferromagnetic and ferrimagnetic media are discussed systematically, the emphasis being on a formulation and analysis of the underlying assumptions. A distinction is made between the "ordinary" (Maxwellian) and certain "average" field vectors. The latter are useful in the presence of domain structure; they include appropriately defined spatial averages,\langle\overrightarrow{b}\rangleand\langle\overrightarrow{h}\rangle, of the time-dependent components of the ordinary\overrightarrow{B}and\overrightarrow{H}, respectively. In cases where\langle\overrightarrow{b}\rangleand\langle\overrightarrow{h}\rangleare connected by a "point relation", the general form of Polder's permeability tensor is extended to nonsaturated media; the special tensors due to Polder, the writer, and Wangsness, are then reviewed. In cases where\langle\overrightarrow{b}\rangleand\langle\overrightarrow{h}\rangleare not so connected, the "exchange effect" and the "spin wave equation" are discussed. Following Ament and Rado, three consequences of this equation are treated: the new boundary conditions, and the triple refraction and "equivalent isotropic permeability" in metals.