Hysteresis and after-effects in massive substances. From spin-glasses to the sand hill

Abstract

We discuss the problem of magnetic hysteresis in the framework of a model of a distribution of thermally activated double well potentials. Having shown the equivalence, at T = 0, of this description with the classical picture of Preisach and Néel we consider specifically the effects associated with the fact that the width of the distribution of the barrier-heights is necessarily finite. We show how this limit can be introduced in the classical Preisach construction and how it opens the door to the description of after-effects (in terms of time and of temperature) as well as to the description of the effect of the field beyond the Rayleigh domain. We describe in detail the evolution of the different hysteresis loops of the remanences and susceptibilities in terms of field, time and temperature. A particular reference is made to the spin-glass case. The magnetization relaxations at different temperatures (S(T) curves) and the Fulcher law are discussed We finally attempt a justification of the Preisach construction within a language more adapted to the great generality of this construction which successfully applies to magnetic as well as to mechanical hysteresis or to the weight of a sand hill !!... This could be viewed as a first-order approach of non ergodic problems