The coupling model of relaxation: An alternative for the study of an interacting system of small particles
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Universidad de Santiago de Compostela.
E-15706,
Abstract It is shown that the coupling model of relaxation accounts for the main experimental results of the magnetic relaxation in an assembly of interacting fine particles.
1
Introduction
The coupling model for relaxation in complex systems was first introduced by Ngai in 1979 [1]. Since then, it has been found to offer an accurate description of a wide variety of systems [2]. The theoretical foundation of the model has been given recently [3]. However, its use in magnetism is more recent. See reference [4] and other references therein The fundamental difference between the coupling model and previous models of relaxation is that these earlier models treat the effect of complexity on the relaxation as being essentially static, in the sense that the effect of complexity is to change the relaxation time or to produce a distribution of relaxation times. In contrast to this, in the coupling model, the relaxation in complex systems, is dynamical in nature. From this view-point, according to Ngai [5], a relaxing complex system consists of three parts: i) Individual primary species (PS), which are of interest for the relaxation. ii) A heat-bath, whose interaction with the PS provides a primary mechanism of relaxation. iii) Other relaxing species, X, whose interaction with PS, the PS-X coupling, slows down the relaxation process. This is the main manifestation of complexity. In this paper we propose another application of the coupling model to a magnetic system: namely that of an interacting fine-particle assembly. In this system, the PS are the individual particles whose dipolar coupling with the other particles in the assembly slows down the relaxation process. This is the main difference with preceding attempts to tackle this problem [6,7,8], where the only effect of the presence of inter-particle interactions is a change in the relaxation times. In this paper we show how the model can explain, in a natural way the observed differences for a system of interacting and non-interacting particles via the variation of the inverse of the blocking temperature with the logarithm of the measuring time and the values of the relaxation times (table 1). The organization of the paper is as follows: After a brief review of the coupling model for the relaxation in a complex system (section 2), in section 3 we apply this model to a system of interacting particles and show that their observed behaviour can be accounted for by this model.
247 Mat. Res. Soc. Symp. Proc. Vol. 455 ©01997 Materials Research Society
2
The coupling model
In this section we sumarize briefly the salient features of the coupling model . For more details about the theoretical derivations and the sucessful experimental applications of the model we refer to references [2]-[5]. The coupling model [5] proposes the existence of a temperature-insensitive crossover time, tC, separating two regimes in which the dynamics of the relaxation are different. t,, The relaxation function is a linear exponential exp(-9-)
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