Localised spin modes of decorated magnetic clusters on a magnetic surface

A method for the calculation of the energies of spin modes of surface magnetic clusters on a magnetic surface, using broken translation symmetry in three dimensions (3D), is employed to determine the spin mode energies for a variety of planar clusters. The cluster is considered to be supported on a magnetically ordered substrate such that the localised spins of the cluster and the substrate interact via magnetic exchange. No electronic effects are considered. The analytical approach solves for the 3D evanescent crystal spin field in the bulk and the surface domains around the cluster. This spin field arises owing to the breakdown of magnetic translation symmetry caused by the surface cluster. The analytical approach can be applied to any cluster configuration, underlying the general character of the calculation. In particular, we consider here a 4-, 5-, and 9-atoms planar clusters supported on the surface of a ferromagnetic simple cubic lattice, the spin order being in the direction normal to surface boundary. The method is applied to calculate the spin mode energies of these planar clusters consisting of Gd atoms interacting via Anti-ferromagnetic exchange with an Fe(100) surface. These results are compared with the calculated energies of the spin modes of the free clusters, and also with those for the same planar clusters when the cluster-substrate exchange is considered hypothetically ferromagnetic. (C) 2002 Elsevier Science B.V. All rights reserved.