Magnetic skyrmions: structure, stability, and transport phenomena

The pioneering spintronic proposal of a spin field-effect transistor by Datta and Das motivated largely the research of the spin related behavior of electrons propagating in the potentials with structure inversion asymmetry (SIA). Owing to the spin-orbit interaction, inversion asymmetric potentials give rise to a Bychkov-Rashba spin-orbit coupling causing a spin-splitting of a spin-degenerate electron gas. In this article we show that the rich spinorbit driven physics in potentials with SIA is effective also for electrons at metallic surfaces. Carrying out first-principles calculations based on density functional theory (DFT) employed in a film full-potential linearized augmented plane-wave (FLAPW) method in which spinorbit coupling (SOC) is included, we investigate the Rashba spin-splitting of surface electrons at noble-metal surfaces, e.g. Ag(111) and Au(111), at the semimetal surfaces Bi(111) and Bi(110), and the magnetic surfaces Gd(0001) and O/Gd(0001). E.g. on the Bi(110) surface the Rashba spin-splitting is so large that the Fermi surface is considerably altered, so that the scattering of surface electrons becomes fundamentally different. On a magnetic surface, the Rashba splitting depends on the orientation of the surface magnetic moments with respect to the electron wavevector, thus offering a possibility to spectroscopically separate surface from bulk magnetism. Due to the interplay of SIA and SOC effects, magnetic impurities in an electron gas experience spin-spin interactions which arise not only from the common Ruderman-Kittel-Kasuya-Yoshida-type (RKKY) symmetric Heisenberg exchange but in addition also from an Dzyaloshinskii-Moriya-type (DM) antisymmetric exchange. The origin of the latter can be a combination of Moriya-type spin-orbit scattering at the impurities plus kinetic exchange between the impurities and the Fert-Levy type exchange due to relativistic conduction electrons. Assuming that the DM is smaller than the symmetric exchange interaction, we develop a continuum model to explore the rich phase space of possible magnetic structures. Depending on the strength of the DM interaction, we expect in low-dimensional magnets deposited on substrates, such as ultrathin magnetic films, chirality broken two- or three-dimensional magnetic ground-state structures between nanometer and sub-micrometer lateral scale. We present two approaches on how the strength of the DM interaction, the so-called DM vector D, can be calculated from ab initio methods, either using the concept of infinitesimal rotations applicable to Green function type electronic structure methods or using the concept of homogeneous spin-spirals more applicable to a supercell type electronic structure method. We determine D for a doublelayer of Fe on W(110) and show that the quantity is sufficiently large to compete with other interactions. We demonstrate that SOC effects are essential for the understanding of magnetic structures in these ultrathin magnetic films.