A 2014 study by the US Department of Energy conducted at Lawrence Berkeley National Laboratory estimated that U.S. data centers consumed 70 billion kWh of electricity[1]. This represents about 1.8% of the total U.S. electricity consumption. Putting this in perspective 70 billion kWh of electricity is the equivalent of roughly 8 big nuclear reactors, or around double the nation's solar panel output[2]. Developing new memory technologies capable of reducing this power consumption would be greatly beneficial as our demand for connectivity increases in the future. One newly emerging candidate for an information carrier in low power memory devices is the magnetic skyrmion. This magnetic texture is characterized by its specific non-trivial topology, giving it particle-like characteristics. Recent experimental work has shown that these skyrmions can be stabilized at room temperature and moved with extremely low electrical current densities. This rapidly developing field requires new measurement techniques capable of determining the topology of these textures at greater speed than previous approaches. In this dissertation, I give a brief introduction to the magnetic structures found in Fe/Gd multilayered systems. I then present newly developed techniques that streamline the analysis of Lorentz Transmission Electron Microscopy (LTEM) data. These techniques are then applied to further the understanding of the magnetic properties of these Fe/Gd based multilayered systems. This dissertation includes previously published and unpublished co-authored material.

Neste trabalho,estudamos o índice de Poincaré-Hopf, definido para singularidades isoladas de campos de vetores sobre variedades diferenciáveis. Além disso, investigamos algumas definições de índices de campos de vetores definido sem variedades singulares, como o índice de Schwartz e o índice GSV. Estudaremos estes invariantes no caso específico em que (V; 0) é um germe de uma interseção completa com singularidade isolada na origem / In this work, we study thePoincaré-Hopf index, defined for isolated singularities of vector fields on manifolds. Moreover, we investigate some definitions of indices of vector fields defined on singular varieties, as the Schwartz index and the GSV index. We study these invariants in the case where (V; 0) is a germ of a complete intersection with an isolated singularity at the origin

Neste trabalho,estudamos o índice de Poincaré-Hopf, definido para singularidades isoladas de campos de vetores sobre variedades diferenciáveis. Além disso, investigamos algumas definições de índices de campos de vetores definido sem variedades singulares, como o índice de Schwartz e o índice GSV. Estudaremos estes invariantes no caso específico em que (V; 0) é um germe de uma interseção completa com singularidade isolada na origem / In this work, we study thePoincaré-Hopf index, defined for isolated singularities of vector fields on manifolds. Moreover, we investigate some definitions of indices of vector fields defined on singular varieties, as the Schwartz index and the GSV index. We study these invariants in the case where (V; 0) is a germ of a complete intersection with an isolated singularity at the origin