First-Principles Simulations of Atomic Structure and Magnetism in Fe Nanoparticles
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First-principles Simulations of Atomic Structure and Magnetism in Fe nanoparticles 1
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A. V. Postnikov , P. Entel and José M. Soler 1 Theoretical Low-Temperature Physics, FB10, Gerhard Mercator University Duisburg, D-47048 Duisburg, Germany 2 Department of Physics, University of Illinois, Urbana, Illinois 61801, USA and Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
ABSTRACT The properties of small clusters Fe3 and Fe5, in which the non-collinearity of magnetic density is expected to be important, and of larger nanoparticles (consisting of up to 62 atoms) are studied from first principles making use of density functional theory, norm-conserving pseudopotential and numerical local orbitals method, as implemented in the SIESTA code. We concentrate on the interplay of lattice relaxation, mostly pronounced near the surface of particles, and the particles' magnetic characteristics. Previously obtained theoretical findings of enhanced magnetic moments in outer shells of nanoparticles are confirmed. These results are refined by taking structure relaxation into account and by considering more representative bcc- and fcc-related particles; moreover, we allowed antiferromagnetic ordering along with ferromagnetic one. INTRODUCTION In view of growing interest for the magnetic properties of nanoparticles, there is a demand for the systematic study of morphology and electronic structure of Fe clusters, depending on their size. Previous studies of Fe clusters are quite numerous, but they addressed either ground-state structure of selected small clusters, or electronic structure of some larger clusters without the structural relaxation taken into account. The aim of the present study in twofold: we provide some results on the morphology and magnetism in two small clusters (Fe3 and Fe5) where noncollinear orientation of magnetic moments supposedly plays a role. Moreover, we look into interplay of structure relaxation and magnetic properties in larger nanoparticles, having essentially bcc or fcc inner structure, but with full structure relaxation allowed. The corresponding first-principle calculations (of electronic structure, total energy and forces driving the structure relaxation) have been performed with the SIESTA method. CALCULATION METHOD The overview of backgrounds, practical implementation and performance of the SIESTA method may be found in several recent publications [1]. The method uses norm-conserving pseudopotentials and a compact basis set of localized functions. It allows to treat periodic systems and finite molecules/clusters on the same footing, using supercell geometry for finite systems but suppressing spurious effects of interaction between repeated fragments. The reason for the use of supercell geometry is a possibility it implies to solve the Poisson equation with a smooth (non-local) part of the charge density by Fourier transformation on a regular grid. The W8.9.1
plane-wave cutoff in this charge density representation becomes a controllably conv
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