Vector spin chirality is one of the fundamental characteristics of complex magnets. For a one-dimensional spin-spiral state it can be interpreted as the handedness, or rotational sense of the spiral. Here, using spin-polarized scanning tunneling microscopy, we demonstrate the occurrence of an atomic-scale spin spiral in finite individual bi-atomic Fe chains on the (5×1)-Ir(001) surface. We show that the broken inversion symmetry at the surface promotes one direction of the vector spin chirality, leading to a unique rotational sense of the spiral in all chains. Correspondingly, changes in the spin direction of one chain end can be probed tens of nanometers away, suggesting a new way of transmitting information about the state of magnetic objects on the nanoscale.

The motion of domain walls in ferromagnetic, cylindrical nanowires is investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a classical spin model in which energy contributions from exchange, crystalline anisotropy, dipole-dipole interaction, and a driving magnetic field are considered. Depending on the diameter, either transverse domain walls or vortex walls are found. The transverse domain wall is observed for diameters smaller than the exchange length of the given material. Here, the system behaves effectively one-dimensional and the domain wall mobility agrees with a result derived for a one-dimensional wall by Slonczewski. For low damping the domain wall mobility decreases with decreasing damping constant. With increasing diameter, a crossover to a vortex wall sets in which enhances the domain wall mobility drastically. For a vortex wall the domain wall mobility is described by the Walker-formula, with a domain wall width depending on the diameter of the wire. The main difference is the dependence on damping: for a vortex wall the domain wall mobility can be drastically increased for small values of the damping constant up to a factor of 1/α 2 .

A variety of methods have been used to investigate the empirical relationship between research and development (R&D) spending and the productivity of firms. The most widely employed frameworks are the production function and the associated productivity framework. In these settings, productivity growth is related to expenditures on R&D, and an attempt is made to estimate statistically the part of productivity growth that can be attributed to R&D activities. This article surveys the expansive body of empirical literature on this subject and finds a large and significant impact of R&D on firm performance on average. However, the estimated returns vary considerably between the different studies due to differences across data samples and econometric models, as well as methodological and conceptual issues. A meta-analysis on the studies surveyed reveals that the estimated rates of return do not significantly differ between countries, whereas the estimated elasticities do. Furthermore, the estimated elasticities are significantly higher in the 1980s and consistently higher in the 1990s compared with the 1970s. Hence, contrary to a widely held belief, we find no convincing evidence of an exhaustion of R&D opportunities in the last two decades.

Current driven motions of domain walls in ferromagnetic, cylindrical nanowires are investigated by solving the Landau-Lifshitz-Gilbert equation including the adiabatic and nonadiabatic spin torque terms. Depending on the type of domain wall ͑transverse or vortex͒ and on the nonadiabaticity parameter ␤ different behavior of the domain wall motion has been found. A transverse domain wall shows a linear motion accompanied by a clockor anticlockwise precession of the wall depending on the relation between the nonadiabaticity parameter ␤ and the Gilbert damping ␣. For ␣ = ␤ no rotation occurs. Further, an easy way to derive the velocity equation is presented. In the case of the vortex domain wall an unexpected chirality effect has been found. Depending on the sense of rotation either a straight motion or a reversal of the rotation followed by a straight motion can be seen. Furthermore, due to the impossibility of a Walker breakdown the averaged velocity of the domain wall v is zero for all currents with ␤ = 0 while the motion is damped by the emission of spin waves for higher currents and ␤ Ͼ ␣.

An investigation of thermally induced spin dynamics of magnetic nanoparticles is presented. We use an atomistic model for the magnetic interactions within an effective, classical spin Hamiltonian constructed on the basis of first-principles calculations for L1 0 FePt. Using Langevin dynamics we investigate how the internal degrees of freedom affect the switching behavior at elevated temperatures. We find significant deviations from a single-spin model, arising from the temperature dependence of the intrinsic properties, from longitudinal magnetization fluctuations, and from both thermal and athermal finite-size effects. These findings underline the importance of atomistic simulations for the understanding of fast magnetization dynamics.