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Browsing by Author "Matos, Pedro Jorge Andrade"

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  • Numerical simulations in micromagnetism
    Publication . Matos, Pedro Jorge Andrade; Gasche, Thomas Peter, 1939-; Marques, José Pires
    In this thesis we start by reviewing theoretical aspects of micromagnetism. Since many technological applications only depend on the behavior of magnetization of ferromagnets with the applied magnetic field at a macroscopic scale, there is no need to use a highly detailed theory like quantum mechanics. Micromagnetics is the framework that captures at a mesoscopic level the essential dynamical behavior of a magnetization field. It describes the combination of a very fast processional motion and a slower damping toward the magnetic field. The two central relations are the Landau-Lifshitz (LL) and Landau-Lifshit-Gilbert (LLG) equation's. We show how to derive the first assuming two main experimental and theoretical observations: (1) the local magnetization norm is conserved; (2) the equilibrium state that both the magnetic field and magnetization aligned. We then analyze the dynamics implied by four magnetic field contributions: the applied field; the anisotropy field which has a similar behavior to an applied field along the lattice axis; the stray field which depends on all other magnetic moments; the exchange field which is the most relevant term, it tends to smooth out the magnetization direction. We then introduce the LLG equation by representing the damping term by Rayleigh Dissipation. It is an implicit equation of the magnetization. Our goal is to develop a Python code to integrate this equation. We start then by combining it with the Finite Element Method to discretize space and the Implicit Midpoint Rule to discretize time. To avoid meshing the surroundings of the system that was required for introducing the asymptotic boundary conditions for the calculation of stray field potential, we use the Boundary Element Method and a new potential to restrict these calculations to the system. Using the Newton Raphson Method we obtain a linear system of equations that is solved at each time step yielding the evolution of the magnetization. Setting our code to solve a standard problem for permalloy block 120 x 120 x 10nm3 we compare our results of magnetization evolution with those of the OOMMF micromagnetic simulator to validate our code. The results of our code compare very well with those of the OOMMF simulation, specifically the time evolution of y component of magnetization, its Discrete Fourier Transform as well as the spatial distribution of the amplitudes of the Fourier coefficients for two distinct resonance frequencies.
    2017Master thesis Open access Show more