Spin-fluctuation spectra in magnetic systems: a novel approach based on TDDFT

Magnetism at the micro- and nano-scale level is a well-established research field, by virtue of its relentless technological impact and astounding variety of structures it can shape in condensed-matter systems. The characterization of most of these structures has become possible in the last fifty years thanks to the development and refinement of magnetic spectroscopies, most notably neutron scattering for bulk magnetism, and electron spectroscopies for surfaces and thin films. A fundamental outcome of the most recent experiments is the need to address magnetism in its full non-collinear nature also at the theoretical level, i.e. by treating the magnetization density as a true vector field, allowed to vary its direction at each point in space. This paves the way to the study of chiral topological magnetic structures such as skyrmions, or of the effect of Spin-Orbit Coupling (SOC) on the ground-state con- figuration and on the excited-state dynamics. Handling non-collinearity however, a far-from-trivial task on its own, proves to be particularly demanding in ab-initio calculations, where, at present, it is far from being a standard tool in the study of excited states. In this thesis we shall focus on the development of a method to study the dynamical spin-fluctuations of magnetic systems in a fully non-collinear framework, within Time-Dependent Density Function Theory (TDDFT). The outline of the thesis follows. In Ch. 1 the technological framework and the main experimental findings which have inspired our work are presented; a link between the experiments and the relevant physical quantities, namely the magnetic susceptibility, will also be shown. In Ch. 2 and 3 the theoretical framework in which we move will be introduced, namely Time-Dependent Density Functional Theory (TDDFT) and linear response. In Ch. 4 and Ch. 5 original work is presented: in the former, we devise a computational approach for the study of magnetic excitations via TDDFT, in a fully non-collinear framework. In the latter, we discuss the implementation and compute the spin-wave dispersion for BCC Iron. The final chapter is devoted to the conclusions.