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JOURNAL OF APPLIED PHYSICS 99, 08G706 共2006兲 Nanostructure calculation of CoAg core-shell clusters F. Dorfbauera兲 Institute for Solid State Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, Wien, 1040 Austria T. Schrefl Department of Engineering Materials, University of Sheffield, Sheffield, S1 3JD United Kingdom M. Kirschner, G. Hrkac, D. Suess, O. Ertl, and J. Fidler Institute for Solid State Physics, Vienna University of Technology, Vienna, 1040 Austria 共Presented on 1 November 2005; published online 27 April 2006兲 Detailed studies of the structure of magnetic nanoclusters are crucial for understanding their magnetic properties. We have investigated the structure of CoxAg1−x nanoparticles by means of molecular dynamics simulations utilizing the embedded atom method. Starting from a completely random distribution of Co and Ag atoms, the clusters were heated up to 1300 K and subsequently cooled down. The size of the resulting particles was 2.8 nm 共864 atoms兲. A clear segregation of the Ag atoms on the surface of the Co core was obtained. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2176107兴 INTRODUCTION Magnetic nanoclusters will play a crucial role in future nanomagnetic materials. The rapid growth of the areal storage density in information storage technology naturally results in smaller magnetic structures. Knowing the crystalline configuration of such structures is important to understand their peculiar magnetic behavior and is necessary for both developing high density information storage materials and spintronic devices. Experimentally, arrays of self-assembled particles such as FePt clusters can be prepared by a solution phase chemical procedure.1 Another possibility to prepare such clusters is to use laser vaporization with a gas phase condensation source 关low energy cluster beam deposition 共LECBD兲兴. Dupuis et al.2 recently investigated the magnetic properties of single CoM 共M = Ag, Pt兲 clusters by means of the microsuperconducting quantum interference device 共micro-SQUID兲 technique. Compared to bulk magnetic materials, nanoscale magnetic clusters exhibit strong contributions to the magnetic anisotropy from the surface. Moreover, interfacial effects between the surface and a surrounding matrix result in a change of the magnetic properties. Due to their miscibility, Co clusters embedded in a Nb matrix exhibit magnetically dead interface layers, resulting in a decrease of the effective magnetic core.3 In contrast, the sharp interface of the core-shell formation of CoAg does not influence the magnetic core. Consequently, the blocking temperature of CoAg is higher 共30 K兲 compared to CoNb 共12 K兲. materials or metals. Although such simple approaches can deliver the right ground-state energy, specific properties, such as elastic constants of metals cannot be reproduced.4 To overcome these problems, more elaborate potentials were developed: Daw and Baskes introduced the embedded atom method,5 an approach based on the idea of quasiatoms.6 A quasiatom is defined as a unit consisting of the ion and its electronic screening cloud. Considering this unit as impurity in an electronic system, the energy of this quasiatom only depends on the electron density of the host. The main feature of the embedded atom method is based on the idea of quasiatoms: every single atom in a system is now considered as being an impurity in the host. The energy of the embedded atom i is now calculated via an embedding function Fi, dependent on the electronic density caused by the host at the position of the impurity, = Fi共host Vemb i i 兲, 共1兲 whereas the electronic density host is just the sum over all i electron density functions of all other atoms, host = 兺 atom 共rij兲. i j 共2兲 j⫽i Combining the embedding potential with a pair potential, = Vpair i 1 兺 ij共rij兲, 2 j⫽ì 共3兲 yields the total embedding atom potential function, + 兺 Vpair V = 兺 Vemb i i . i 共4兲 i SIMULATION METHOD Molecular dynamics simulations using empirical twobody potentials, such as the Lennard-Jones potential type, are not suitable for applications involving chemical active a兲 Electronic mail: [email protected] 0021-8979/2006/99共8兲/08G706/3/$23.00 In practice, the embedding function Fi is fitted to obtain reasonable bulk material parameters such as the lattice constants, elastic constants, or vacancy free energies. For the only electron orbits outside electronic density function atom i the screening regime of an atom have to be considered. They can be either calculated by a simple Hartree-Fock approxi- 99, 08G706-1 © 2006 American Institute of Physics Downloaded 28 Mar 2007 to 128.130.45.110. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp 08G706-2 J. Appl. Phys. 99, 08G706 共2006兲 Dorfbauer et al. FIG. 1. Atomic concentration of a CoAg cluster measured from the center. A sharp transition between the Co core and the Ag shell occurs at 1.2 nm from the center. The inset on the right shows a Co70Ag30 cluster sliced along a perfect 共111兲 plane. The light spheres represent the silver atoms, whereas the dark spheres depict the cobalt core. 7 mation, or other functional shapes are fitted to the desired density.8 In order to simulate metallic alloys, the pair potential between different species of atoms has to be defined. Following the alloy model of Johnson,9 the alloy pair potential is defined as a combination of monoatomic pair potentials, weighted by the electron density functions, ab共r兲 = 冋 册 1 b共r兲 aa a共r兲 bb 共r兲 + 共r兲 . 2 a共r兲 b共r兲 共5兲 The calculation of Eqs. 共2兲 and 共3兲 are performed only within a certain cutoff radius. Potential functions for monoatomic calculations are not suitable for simulations of alloys due to their possibly different choice of the cutoff distance. Zhou et al.10 have developed a consistent set of potential functions for sixteen metals by designing monoatomic pair potentials suitable for alloy simulation. The specific design of those functions intrinsically forces the potentials to be zero within the cutoff distance. The potentials presented in Ref. 10 have been successfully used to simulate nanoscale magnetic multilayers used in giant magnetoresistive 共GMR兲-sensor elements. To simulate the core-shell formation of CoxAg1−x nanoclusters, the Co and Ag atoms were distributed randomly on a face-centered-cubic grid. The initial temperature was set to 1300 K and subsequently decreased in 20 K steps towards 100 K. At each temperature step 6 ⫻ 104 verlet-integration steps 共time step= 1 fs兲 were performed. FIG. 2. Left: stacking order of the Co core 共without the Ag shell兲 of a Co70Ag30 cluster. Right: the arrow indicates the line of sight in respect to the depiction on the left side. Whereas each plane A, B, and C itself are perfect 共111兲 planes, the vertical stacking order does neither follow the fcc stacking ABC nor does it follow a plain hcp stacking AB 共see Fig. 3兲. concentration of 70% Co, the whole surface is covered with a monolayer Ag. By increasing the initial cobalt concentration to values above 70%, the Ag shell starts to be perforated along the edges of the Co core. For clusters with a diameter of about 2.8 nm, the mi nimum silver concentration to cover the whole Co surface is thus given by about 30%. In order to determine the crystal structure of the Co core, the stacking order has been investigated. Whereas a fcc structure shows an ABC stacking order and a hcp structure exhibits an AB order; the cobalt core of the investigated coreshell systems exhibit no clear stacking order 共Fig. 2兲. To analyze this feature in more detail, the radial distribution function 共RDF兲 of bulk fcc Co, bulk hcp Co, and the cobalt core has been calculated. Figure 3 shows clearly the appearance of a typical hcp peak at 4.1 and 4.8 Å, which are missing in the fcc RDF of fcc-bulk cobalt. Compared to the hcpbulk RDF, the ratio between the peaks at 4.8 and 5.0 Å of the Co core is 1:1, whereas the bulk-hcp RDF exhibits a ratio of 2.5:1. This indicates a partial hcp-like structure in the calculated core-shell systems. RESULTS AND DISCUSSION Simulations were made at different Co–Ag ratios with a constant total number of atoms 共864兲. After the calculation of the annealing process, the clusters exhibited a shape similar to a truncated octahedron. Annealing always resulted in a clear Co core and a Ag shell. The segregation of Ag can be explained with the lower surface energy of silver 共1.2 J / m2兲 compared to cobalt 共2.6 J / m2兲 共Ref. 2兲 and was found for similar systems as well.11 Figure 1 shows the atomic concentration of Co and Ag in dependence of the radial distance from the center. Below a FIG. 3. Calculated radial distribution function 共RDF兲 of the core of a Co75Ag25 cluster at 100 K. Compared to the RDF of fcc Co, two additional peaks at 4.1 and 4.8 Å arise 共see arrows兲. This indicates a partial hcp stacking in the core. Downloaded 28 Mar 2007 to 128.130.45.110. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp 08G706-3 J. Appl. Phys. 99, 08G706 共2006兲 Dorfbauer et al. The coexistence of both hcp-like and fcc-like stackings may result in a different magnetic behavior compared to plain fcc cores. Experimentally, the crystalline structure of the core of CoAg cluster was determined to be fcc.2 Due to the fact that clusters in an experimental setup are prepared in a gas phase adsorption, the relaxation times and the atomic coalescence of such processes can be considered as being different from the simulation setup presented in this work. Moreover, the initial temperature used in the simulations 共1300 K兲 is below the melting point of Co 共1768 K兲 which may result in an imperfect rearrangement of the core. Thus a direct comparison of a gas-phase-adsorption method and the results presented here is not valid. Nevertheless, the theoretical approach to simulate an annealing process with a relatively low initial temperature reveals the possibility of coexisting fcc- and hcp-like crystal phases. Moreover, the pure Co core 共without the Co atoms forming the interface with Ag兲 exhibits a mean cohesive energy per atom of −4.38 eV at 100 K, which is comparable to the mean cohesive energy of fcc Co. SUMMARY AND OUTLOOK Molecular dynamics simulations using the embedded atom method have been successfully used to simulate the crystal structure of binary magnetic nanoclusters. The peculiarities of such systems, including stacking faults and inter- facial contribution to the magnetic anisotropy have to be taken into account for the design of future application of such clusters. Molecular dynamics 共MD兲 studies can provide quantitative inputs for multiscale magnetic simulations. Magnetic properties like the crystal phase distribution derived from the MD simulations can be used as input for hysteresis simulations on a mesoscopic length scale. ACKNOWLEDGMENTS The author thanks Wolfgang Wernsdorfer and Gregory Grochola for inspiring discussions. 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Pellarin, J. Phys. Chem. B 104, 5430 共2000兲. Downloaded 28 Mar 2007 to 128.130.45.110. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp