A fullpotential linearized augmented planewave (FLAPW) electronic structure method was developed to investigate noncollinear magnetism in bulk systems, surfaces, and thin films on the basis of the vector spindensity formulation of the local density approximation (LDA) and the generalized gradient approximation (GGA) to the density functional theory (DFT). To allow the investigation of a large set of relevant magnetic spinstructures, two extensions that go beyond the treatment of periodic and stationary magnetic states were implemented: (i) Arbitrary noncollinear periodic magnetic configurations, which are not the magnetic ground state or a stationary state of the system under consideration, can be treated due to the extension of the density functional equations to constrain the local magnetic moments to any given direction. (ii) Commensurate and incommensurate spiral (or helical) spindensity waves can be treated due the extension of the vector spindensity FLAPW method on the basis of a generalized Bloch theorem. A detailed account of the implementation is given and the importance of various approximations used are discussed. This method was applied to the problem of topological frustration of a twodimensional antiferromagnet on a triangular lattice. We performed selfconsistent calculations for the 3d transitionmetal monolayers V, Cr, Mn, and Fe on the (111) oriented surfaces of Cu and Ag, investigating the magnetism, the interlayer relaxation, and the energetics of a nearly complete set of magnetic states. We found an amazing variety of different magnetic ground states: ferromagnetism for Fe/Cu(111) and Fe/Ag(111); rowwise antiferromagnetism for Mn/Ag(111); a coplanar noncollinear periodic 120° Néel structure for V/Ag(111), Cr/Cu(111) and Cr/Ag(111) ; and for Mn/Cu(111) a new complex threedimensional noncollinear spin structure, a socalled 3Q state, shown on the next page. By comparison with model Hamiltonians we conclude that any realistic description of twodimensional itinerant antiferromagnets on a triangular lattice requires exchange interactions beyond the nearest neighbors and also exchange interactions beyond the Heisenberg model (i.e. 4spin and biquadratic interactions). Bulk and surface calculations for hcp Gd and the Gd(0001) surface were performed. Comparing different methods to treat the localized 4f states, which represent a challenge for firstprinciple theory, we show that it is crucial to remove the unphysical density of states due to the minority 4f electrons at the Fermi energy obtained in both LDA and GGA, in order to predict the magnetic ground state correctly. We carried out spinspiral calculations to model the effect of magnetic excitations, i.e. temperature, on the electronic structure of the Gd(0001) surface. In the ferromagnetic ground state we found a double peak structure in the local density of states, due to the spinsplit d$_{z^{2}}$ surface state of Gd, which is probed by scanning tunneling spectroscopy (STS) experiments. With increasing spinspiral qvector, corresponding to increasing temperature, the splitting of the two peaks decreases and finally vanishes, while the valence magnetic moment remains finite. Hence, the vanishing splitting cannot be taken as support for the applicability of a pure Stoner model.
