Download Nanostructure calculation of CoAg core

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
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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.
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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. This work was supported
by the Austrian Science Fund 共Y132-N02兲.
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