Spin-orbitronics at the nanoscale : from analytical models to real materials

This thesis provides a theoretical description of magnetic nanostructures in inversion asymmetric environments with strong spin-orbit interaction (SOI). The theoretical concepts introduced here can be applied in the field of spin-orbitronics, which consists of exploiting the SOI to manipulate the electron spin without external magnetic fields. The investigated systems display a plethora of interesting phenomena ranging from chiral magnetic interactions to gapped magnetic excitations. In practice, we adopt two different approaches: First, a model-based one relying on the Rashba Hamiltonian, which is employed to demystify and understand magnetic and transport properties of magnetic nanostructure sembedded in a Rashba electron gas. Second, we use a first-principles approach within the framework of the Korringa-Kohn-Rostoker (KKR) Green function method to investigate the ground state properties of magnetic impurities in topologically insulating hosts. This method is suitable to simulate nanostructures in real space. Then, we employed our newly developed code based on time-dependent density functional theory to compute the spin excitation spectra of these magnetic nanostructures embedded in topological insulators. Moreover, the KKR Green function method was used to simulate the electronic structure and ground state properties of large magnetic nanostructures, namely magnetic Skyrmions. In the first part, the analytical Rashba Green function and the scattering matrices modelling the magnetic impurities in the s-wave approximation are employed for the computation of the magnetic interaction tens or which contains: isotropic exchange, Dzyaloshinskii-Moriya (DM) and pseudo-dipolar interactions. The competition between these interactions leads to a rich phase diagram depending on the distance between the magnetic impurities. Next, we consider an external perturbing electric field and investigate the transport properties by computing the residual resistivity tensor within linear response theory. The contribution of SOI is explored. The investigation of arbitrary orientations of the impurity magnetic moment allowed a detailed analysis of contributions from the isotropic magnetoresistance and planar Hall effect. Moreover, we calculate the impurity induced bound currents in the Rashba electron gas, which are used to compute the induced orbital magnetization. For a trimer of impurities with a non-vanishing spin chirality (SC) a finite orbital magnetization is observed when SOI is turned off. Since it emerges from the SC, it was named chiral orbital magnetization. In the second part, we investigate the doping of topological insulators with magnetic impurities, which breaks time-reversal symmetry, leading to the prediction of a gap opening at the Dirac point when the magnetic moments are oriented in the perpendicular direction with respect to the surface of the topological insulator. This could potentially functionalize the topological surface states by enabling the control of the quantum anomalous Hall effect and dissipationless transport. Several experimental investigations obtained conflicting results, generating a lot of controversy on this point. Since the orientation of the magnetic moments depends on their magnetic anisotropy energy, we use the KKRGreen function method to investigate isolated 3d and 4d transition metal impurities on the surfaces and in the bulk of Bi2Te3 and Bi2Se3. We explore the impact of impurity induced in-gap states on the orientation of the magnetic moments, their dynamical spin-excitations and on the zero-point spin-fluctuations affecting the magnetic stability. We propose to use scanning tunneling spectroscopy in the inelastic mode to verify our predictions. In the third part, we focus on magnetic Skyrmions which are topologically protected spin textures. These magnetic entities can be stabilized by the DM interaction. Relying on the KKR method we access the electronic structure of sub-5 nm Skyrmions and propose the spin mixing tunneling magnetoresistance (TXMR) for an all-electrical detection of Skyrmions in devices. Furthermore, we suggest to use X-ray magnetic circular dichroism(XMCD) as a magnetic microscopy technique for optical detection of non-collinear spin textures such as Skyrmions. This can be achieved due to a chiral contribution to the orbital moments, driven by the non-collinear spin texture, and acquiring a topological nature for large Skyrmions