Effects of Spin-Orbit Interactions in Ferromagnetic Metal Nanoparticles

Abstract: This thesis is a theoretical investigation of the effects of spin-orbit (SO) interactions in ferromagnetic metal nano-particles. Part I of the thesis is devoted to an elementary introduction of the research field, including recent experimental advances which partly motivated the work presented here. At the core of the thesis lie four original papers, collected in Part II, which are presented and summarized at the end of the introduction. In Paper I we introduce a microscopic tight-binding model to study the mesoscopic physics of the nanoparticle magnetocrystalline anisotropy and the hysteresis in the quasiparticle excitation spectra. The model predicts features that agree qualitatively with tunneling spectroscopy experiments, such as large fluctuations in the anisotropy energy per atom when one electron is added to the nanoparticle. Moreover, this model provides a connection between a microscopic Hamiltonian and energy-functional expressions based on classical micromagnetic theory. Paper II presents a theoretical study of the mesoscopic fluctuations of g-tensors in metal nanoparticles. The analysis is based on the tight-binding model of Paper I, and includes both spin and orbital contributions to the g-tensors. The spin contribution is shown to be in agreement with random matrix theory predictions. Furthermore, the orbital contribution in the strong spin-orbit coupling regime depends crucially on the orbital character of the quasi-particle wavefunctions. Paper III is devoted to the essential role played by SO interactions in determining the energies of the collective ferromagnetic resonances and their coupling to low-energy particle-hole excitations. It is argued that a crossover between Landau-damped ferromagnetic resonances and pure-state collective magnetic excitations occurs as the number of atoms in typical ferromagnetic transition metal nanoparticles drops below 10^4. This picture is supported by a RPA-type of calculation based on the model of Paper I. The significance of this picture for the interpretation of recent single-electron tunneling experiments is discussed. Paper IV addresses the regime of ultra small ferromagnetic transition-metal nanoparticles, where particle-hole and collective excitations are separable in energy. It is argued that in this regime a nanoparticle can be described by an effective Hamiltonian with a single giant spin degree of freedom. The total spin S of the effective Hamiltonian is specified by a Berry curvature Chern number that characterizes the topologically non-trivial dependence of the nanoparticle's many-electron wavefunction on magnetization orientation. These ideas are illustrated within the tight-binding model of Paper I.