Journal of Magnetism and Magnetic Materials 112 (1992) 146-149 North-Holland Invited paper Basic principles of magnetization processes and origin of losses in soft magnetic materials G. Bertotti ~, F. Fiorillo ~ and P. Mazzetti b "lstituto Elettrotecnico Nazionale Galileo Ferraris and INFM-GNSM, 1-10125 7erino, Italy t, Dipartimento di Fisica del Politecnico, Torino, Italy Domain wall dynamics can be investigated through properly designed experiments in well oriented single crystals, containing one or a few mobile 180 ° walls. Equations of motion are derived which can be specialized to describe extreme cases, such as quasi-static stochastic wall behavior and eddy-current-induced wall bowing. Concepts and results related to single-wall dynamics can then be exploited, through the use of statistical methods, to assess the phenomenology of eddy-current losses in ordinary materials, where complex domain structures exist. It turns out that the conventional concept of loss separation can be physically justified. A general theoretical framework is consequently worked out, which is solidly verified against power-loss experiments in crystalline and amorphous materials. 1. Introduction The origin of power losses in ferromagnetic materials can be described by a simple statement: losses are due to Joule heating produced by the electric currents induced by magnetization changes. If the space and time dependence of the current density j(r, t) is known, then the total power loss per unit volume is P = ( I j(r, t) I 2)/tr, where tr is the electric conductivity and the angu- lar brackets indicate space-time averaging. How- ever, this very general definition does not provide a practical means of calculating losses because of the extremely complex behavior of j(r, t) vs. r and t. A statistical approach to the magnztization process [1] permits one to simplify the whole probtcm, oas~cany providing a pI]yslcai rauonate for loss separation - a long-standing empirical tenet of the literature - in tt-xms of processes taking place over different spatial scales. The Correspondence to: Dr. G. Bertotti, IEN Galileo Ferraris, C.so M. d'Azeglio 42, 10125 Torino, Italy. Tel.: + 39-11-3488933; telefax: + 39-11-6507611. hysteresis loss is associated with very localized Barkhausen jumps of individual wall segments, the classical loss is governed by the specimen geometry, while the excess loss strongly depends on the magnetic domain width and on the scale of microstructural inhomogeneities (e.g. grain di- mension, fluctuations of internal stresses, crystal- lographic texture, etc.). Nevertheless, to describe and clarify in quantitative terms the conaection between excess losses, domain wall (DW) dynam- ics and microstructure remains a difficult task, in spite of its importance and interest from the fundamental and the applicative point of ",~ vl~.w. To tackle this problem, systems characterized oy very simple domain structures have often been consid- ered in the literature. A satisfactory comprehen- sion of the dynamic ..... " of"' " ..... oenav~or lnUlVlUUZ41 L~WS could actually represent a proper basis for treat- ing the complex phenomenology exhibited by or- dinary metallic soft magnetic materials. In this paper, we will briefly review some aspects of this problem, and we will discuss how the results obtained in simple systems can be generalized and applied to materials of applicative interest. 0304-8853/92/$05.00 O 1992 - Elsevier Science Publishers B.V. All rights reserved