* Corresponding author. Fax: #56-32-797656. E-mail address: pvargas@"s.utfsm.cl (P. Vargas). Journal of Magnetism and Magnetic Materials 226}230 (2001) 603}605 Magnetism of nanosized metallic Co-clusters P. Vargas*, D. Altbir,J.d'Albuquerque e Castro Departamento de Fn& sica, Universidad Te& cnica Federico Santa Marn& a, Casilla 110-V, Valparan& so, Chile Departamento de Fn& sica, Universidad de Santiago de Chile, Casilla 307, Santiago 2, Chile Instituto de Fn& sica, Universidade Federal do Rio de Janeiro, Cx. Postal 68.528, 21945-970, RJ, Brazil Abstract Themagnetizationofasmallferromagneticparticleasafunctionofthetemperatureisinvestigated.Thepossibilityof occurrence of vortex-like excitations within the cluster, giving rise to a non-saturated magnetization even at low temperatures, is pointed out.  2001 Elsevier Science B.V. All rights reserved. Keywords: Nanostructured materials; Granular magnetic systems Interest in the study of small magnetic structures has increased in recent years because of their properties, which make them appropriate for applications. In par- ticular, granular materials consisting of nanosized clus- ters of a magnetic metal embedded in a non-magnetic metallic matrix have potential applications as media for data storage. It has been shown that the shape and dimensions of the particles [1}4], the grain size distribu- tionandgrainboundarycompositioncanstronglyin#u- ence the magnetic properties of these materials. Interest has also been focused on magnetization curves of granu- lar metals, from which information on the cluster size distribution can be obtained [4,5]. It is generally accepted that a small ferromagnetic particle, with diameter less than 10 nm, is always mag- netized to saturation as a single domain [6]. This as- sumptionisbasedonthefactthatparticlesinsuchasize rangearenotbigenoughtoaccommodateadomainwall [6]; hence, they cannot be broken into domains. Since the average size of the clusters in metal spun samples is between 3 and 6nm [5], it may seem natural to regard themassaturatedsingledomains.However,someexperi- mental results give evidence for the existence of single vortexstateinmagneticdots[7}9],andnumericalsimu- lationsintwo-dimensionalsystemsshowsuchvortex-like structures [10]. Thus, a proper theoretical description of themagneticstructureofasmallthree-dimensionalgrain is in order. In this work, we study the dependence on temperature of the equilibrium magnetization of a Co- cluster and look at some magnetic excitations that are present in the grain. In order to investigate the magnetic structure of mag- netic granules, we have considered a simple system con- sisting of a three-dimensional arrangement of magnetic moments with dipolar and exchange interactions be- tween them. We have also included in our model a cry- stalline anisotropy. Results for the temperature dependence of the cluster magnetization are presented, andtheoccurrenceofvortex-likeexcitationsisdiscussed. We consider a compact array of 603 magnetic atoms (21 closed shells in an FCC structure). The atoms carry magnetic moments   , and are located at the sites of an FCC lattice with lattice parameter a  . The magnetic moments are coupled by both a short-ranged exchange interaction and the classical dipolar interaction. The lat- ter is given by E  "   )   !3(  ) n(  )(  n(  ) r  , (1) where r  is the distance between the magnetic moments   and   and n(  denotes the unit vector along the direction that connects both magnetic moments. The sumiscarriedoutoverallpairsofmagneticatomsinthe cluster.Thus,thetotalenergyofthesystem,includingthe 0304-8853/01/$-see front matter  2001 Elsevier Science B.V. All rights reserved. PII:S0304-8853(00)00691-0