Failure of the Local-Field Concept for Hysteresis Calculations

The ``local field'' is the electric or magnetic field of external sources and of all molecules or particles except the one under examination, at the position of that one. The concept is useful in the molecular theory of dielectrics, where the basic relations are linear. It has also been applied, however, to magnetically interacting single-domain particles in a ferromagnetic powder; here the relations not only are nonlinear but involve discontinuous irreversible jumps, for which instability conditions are decisive. The local-field concept is then unreliable. In a two-particle system, for example, the local-field method examines the stability of one moment with respect to rotation in a fixed field due to the other moment and to external sources; this procedure imposes a constraint, for in the actual system the two moments may rotate simulatneously and independently. The incorrectness of the local-field method is demonstrated here by calculations for two-and three-particle chains of spheres and for two- and three-part composite cylinders. The concept of an interaction field that merely displaces the hysteresis loops of the particles without changing their widths, as in a common interpretation of the Preisach model, is thus erroneous.