Magnetism of free and supported clusters: a comparative study

The presented work investigates the differences in magnetic properties of free and supported clusters via ab-initio calculations. The electronic structure of the clusters was calculated using a spin polarized relativistic multiple-scattering Green’s function formalism. We focus on Fe clusters of 2–9 atoms, either free or supported by Ni(001), and on Co clusters of 2–7 atoms, either free or supported by Au(111). For the supported clusters, the spin and orbital magnetic moments depend on the cluster size nearly monotonically, while for the free clusters large quasi-oscillations of magnetic moments with the cluster size were observed. Similarly, for supported clusters, the local spin magnetic moments decrease nearly linearly with increasing coordination number, while for free clusters of the same size range the trend is much more complicated. These findings are consistent with the fact that the spectral distribution function contains much sharper features for free clusters than for supported clusters.

THEORY OF THE GOOS-HÄNCHEN DISPLACEMENT IN TOTAL INTERNAL REFLECTION

Since the Goos-Hänchen (GH) effect is the displacement of the totally reflected beam at a dielectric interface from the position prediction by geometrical reflection, the concept of GH displacement is applicable only when the reflected beam retains the shape of the geometrically reflected or incident beam. The necessary and sufficient condition has been advanced for the totally reflected beam to retain the shape of the incident beam. Numerical simulations have been performed to confirm this condition. It has been shown that the GH displacement results from the mechanism of beam reshaping due to the linear dependence of the reflection phase shift upon the parallel component of the wave vector, in the interval in which the angular spectral distribution function of the incident beam is appreciable.