Caracterización del caos e hipercaos en sistemas magnéticos clásicos

Abstract

The aim of the present thesis is to study the dynamics of magnetic systems out of equilibrium. That is, systems where there is a competition between the injection and the dissipation of energy. In particular, the thesis focuses on classic magnetic systems where each magnetic element can be described by a mono-domain, such that the domain does not have spatial inhomogeneities. We study the case of one element (or particle) as well as the case of two interacting particles. The effects of the shape and composition are considered through the magnetic anisotropy energy. We will use homogeneous external fields and time dependent ones.

The first two chapters of the thesis are focused on addressing the basic concepts of magnetism as the theoretical framework. Firstly, a brief history of magnetism is given and the types of magnetic materials are presented. Subsequently the equations that govern the dynamics of classical magnetic moments and their fundamental properties are introduced. The scenarios where the system has constants of motion are shown. In addition, a special case of one magnetic particle is studied when a homogeneous external magnetic field is applied.

The third chapter deals with the dynamics of a particle with multiple axes of anisotropy in the presence of a time-dependent external field. Regular and chaotic phases are characterized using the Largest Lyapunov exponent within two-dimensional diagrams. Refining the resolution of the diagrams we found regular islands inside of chaotic regions with form of shrimps.

In the fourth and fiKh chapters the dynamics of two coupled particles with uniaxial anisotropy is studied. First, the case of exchange interaction with homogeneous external magnetic field is analyzed. The laLer case focuses on dipolar interaction between the particles, such that they are in the presence of a time-dependent field. In both cases, two-dimensional phase diagrams of Lyapunov exponents are using to discriminate the regular phases respect to the chaotic (or hyperchao)c) ones. Furthermore, different types of synchroniza)on between the par)cles are measured.

Finally, in the sixth chapter the conclusions and prospects are presented.