Métodos em GPU para explorar a estabilidade topológica de nanomagnetos

Abstract

In this thesis, we demonstrate an original methodology for the computational and numerical treatment of micromagnetism, which continuously describes details of the fundamental interactions that govern the dynamics of magnetization in a ferromagnetic material. Using the technology of graphic processing units (GPUs), our algorithm is able to achieve a high degree of efficiency in the simulation of general cases of magnetic materials, with total freedom in the choice of physical parameters and geometry of the samples and with an average improvement of two orders of magnitude in the simulation time for typical problems. This is possible from the integral calculation of the long-range interactions present, without truncations or numerical hypotheses that further restrict the validity domain of the simulations. In addition, we have also developed an original integration method adapted to the nonlinear systems typical of the dynamic micromagnetism equation (the Landau-Lifshitz-Gilbert or LLG equation). The integrator is an adaptation of the spherical midpoint method, recently demonstrated to be symplectic for classical spin systems, analogously to the Verlet method for the Newtonian equation of motion. The use of this integrator depends on a discretized Hamiltonian formulation for the magnetic interactions in materials, which we have shown to be equivalent until second order to the continuous micromagnetic model. We applied this methodology created in several types of problems pertinent to the study of ferromagnetism of complex systems. Our methodology proved to be adequate to deal with phenomena involving topological loads in the magnetization, such as vortices and skyrmions, enabling the study of them in different time scales, which we verified from benchmarking tests. We propose a modified geometry for nanodisks in order to miniaturize devices based on the use of magnetic vortex polarity for their operation. We also used the method to study stochastic effects in systems on the presence of current, showing that thermal noise does not destroy the balance of interesting states for applications at room temperature. Several future applications are also presented, with an emphasis on non-trivial geometries, transformations between topological loads and thermal effects or other external disturbances that hinder the use of previously established methodologies.