Journal of Magnetism and Magnetic Materials 272–276 (2004) 681–682 Effects of surface anisotropy and vacancies in ferromagnetic nanoparticles J. Restrepo a,b, *, Y. Labaye a , L. Berger a , J.M. Greneche a a Laboratoire de Physique de l’Etat Condens ! e, CNRS UMR 6087, Universit ! e du Maine, Le Mans Cedex 9 72085, France b Grupo de Estado S ! olido, Instituto de F! ısica, Universidad de Antioquia, A.A. 1226, Medell ! ın, Colombia Abstract The effect of surface anisotropy and vacancies upon the ground magnetic state of ferromagnetic nanoparticles is discussed. Our study is based on a random site-diluted classical Heisenberg Hamiltonian with nearest-neighbor interactions, surface and core anisotropies, and a Monte Carlo–Metropolis approach with simulated annealing for energy minimization. Results reveal severe variations with respect to a single domain phenomenology and wider ranges of metastability resembling a multi-valley energy landscape as vacancies are considered and surface anisotropy increases. r 2003 Elsevier B.V. All rights reserved. PACS: 75.50.Tt; 75.30.Pd; 75.30.Gw Keywords: Nanoparticles; Surface anisotropy; Fe–Pt alloys; Monte Carlo 1. Introduction It is well established for nanoparticles that the average magnetic coordination number is strongly reduced as finite size effects become more pronounced [1]. This fact arises from boundaries and can be even enhanced if dilutor sites are present. Therefore, the presence of vacancies or other defects, impurities, lacking of stoichiometry, non-magnetic dopants, missing atoms or even a non-magnetic constituent element (e.g. Al, Rh, etc. in a nanostructured Fe-based alloy) can play an important role in determining the spin structure of real nanostructured systems where the matrix exhibits ferromagnetic characteristics. In this work we study the effect of including dilutor sites (up to q ¼ 20%) in a random way both in the core and surface upon the spin structure of a nanoparticle whose matrix is ferromag- netic. A comparison with the pure case and the effect of surface anisotropy are presented and discussed. 2. Model and simulation A closely spherical ferromagnetic nanoparticle of radius R ¼ 5a (a is the lattice parameter), simple cubic crystalline structure and a ratio of the number of surface sites to the total one of 50% has been considered. The employed 3D classical Heisenberg Hamiltonian can be written as [2]: H ¼ X /i;jS J ij ~ S i : ~ S j  K V X i ð ~ S i : # zÞ 2  K S X i ð ~ S i : # n i Þ 2 ; ð1Þ where j ~ Sj¼ 1 and the first sum runs over nearest neighbors. Terms dealing with uniaxial anisotropy acting on the core along the z-axis and on the surface have been considered. Dipolar interactions can be neglected at this level [3]. The unitary vector on the ARTICLE IN PRESS *Corresponding author. Laboratoire de Physique de l’Etat Condens ! e, CNRS UMR 6087, Universit ! e du Maine, Le Mans Cedex 9 72085, France. Tel.: +33-2-43833301; fax: +33-2- 43833518. E-mail address: jrestre@univ-lemans.fr, jrestre@fisica. udea.edu.co (J. Restrepo). 0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.719