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Magnetic nanoparticles are of immense current interest because of their possible use in biomedical and technological applications. Here we demonstrate that the large magnetic anisotropy of FePt nanoparticles can be significantly modified by surface design. We employ X-ray absorption spectroscopy offering an element-specific approach to magnetocrystalline anisotropy and the orbital magnetism. Experimental results on oxide-free FePt nanoparticles embedded in Al are compared with large-scale density functional theory calculations of the geometric- and spin-resolved electronic structure, which only recently have become possible on world-leading supercomputer architectures. The combination of both approaches yields a more detailed understanding that may open new ways for a microscopic design of magnetic nanoparticles and allows us to present three rules to achieve desired magnetic properties. In addition, concrete suggestions of capping materials for FePt nanoparticles are given for tailoring both magnetocrystalline anisotropy and magnetic moments.
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ARTICLE
NATURE COMMUNICATIONS | 2:528 | DOI: 10.1038/ncomms1538 | www.nature.com/naturecommunications
© 2011 Macmillan Publishers Limited. All rights reserved.
Received 14 Apr 2011 | Accepted 6 Oct 2011 | Published 8 Nov 2011 DOI: 10.1038/ncomms1538
Magnetic nanoparticles are of immense current interest because of their possible use in
biomedical and technological applications. Here we demonstrate that the large magnetic
anisotropy of FePt nanoparticles can be significantly modified by surface design. We employ
X-ray absorption spectroscopy offering an element-specific approach to magnetocrystalline
anisotropy and the orbital magnetism. Experimental results on oxide-free FePt nanoparticles
embedded in Al are compared with large-scale density functional theory calculations of the
geometric- and spin-resolved electronic structure, which only recently have become possible
on world-leading supercomputer architectures. The combination of both approaches yields a
more detailed understanding that may open new ways for a microscopic design of magnetic
nanoparticles and allows us to present three rules to achieve desired magnetic properties.
In addition, concrete suggestions of capping materials for FePt nanoparticles are given for
tailoring both magnetocrystalline anisotropy and magnetic moments.
1 Fakultät für Physik and Center for Nanointegration Duisburg-Essen (CeNIDE), Universität Duisburg-Essen, Lotharstr. 1, Duisburg D-47048, Germany.
2 Experimentelle Physik IV, Universität Würzburg, Am Hubland, Würzburg D-97074, Germany. 3 Department of Chemistry, Brown University, 324 Brook Street,
Providence, Rhode Island 02912, USA. Correspondence and requests for materials should be addressed to C.A. (email: carolin.antoniak@uni-due.de).
A guideline for atomistic design and understanding
of ultrahard nanomagnets
Carolin Antoniak1, Markus E. Gruner1, Marina Spasova1, Anastasia V. Trunova1, Florian M. Römer1,
Anne Warland1, Bernhard Krumme1, Kai Fauth2, Shouheng Sun3, Peter Entel1, Michael Farle1 & Heiko Wende1
ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms1538
NATURE COMMUNICATIONS | 2:528 | DOI: 10.1038/ncomms1538 | www.nature.com/naturecommunications
© 2011 Macmillan Publishers Limited. All rights reserved.
The small size of magnetic nanoparticles opens new elds of
applications from the technological and biomedical perspec-
tive1,2. ey can be used, for example, as new ultrahigh density
magnetic storage media or as contrast agents in magnetic resonance
imaging techniques, as controllable drug carrier, and as material for
hyperthermia treatment. ese innovative applications based on
ultrasmall magnetic objects in biomedical theranostics, water treat-
ment and multifunctional materials require an atomistic under-
standing and control of magnetic properties like the orientation and
magnitude of the atomic magnetic moment. Current eorts further
concentrate on improving permanent hard magnets, which are
required for future energy-harvesting technologies3, while recently
also exchange-spring composites based on so and hard magnetic
nanoparticles have been discussed for advanced applications of
permanent magnets4. Another example is the combination of cat-
alytic activity with magnetic response5. Designing new types of
bimetallic multifunctional nanoparticles for all of these applications
requires the atomistic understanding of the origin of the particles’
magnetism, for example, if it is dominated by the large surface frac-
tion of the atoms in a lower coordinated electronic state or domi-
nated by intrinsic lattice strains.
For instance, the use of FePt nanoparticles as magnetic stor-
age media, with the magnetization direction of one single particle
representing one bit, has been discussed for more than a decade. A
signicant increase of the storage density requires a drastic decrease
of the nanoparticle size. However, the small size of nanostructures
is boon and bane. In nanoparticles, thermal uctuations may lead to
a decay of the stable magnetization direction, termed as ‘superpara-
magnetism, which inhibits long-term data storage. e coupling of
the magnetization direction to the crystal lattice of the material by
spin-orbit and magnetic dipole interaction is usually described by
the eective magnetic anisotropy energy (MAE) density Ke. e
larger Ke, the smaller the critical particle size for stable magnetiza-
tion at room temperature. As FePt in the chemically ordered L10
state is one of the materials with the highest value of the eective
MAE density, Ke = 6×106 J m − 3 (refs 6–8), it has been considered as
the prime candidate for future data storage media application. Using
this value for FePt nanoparticles and assuming a minimal stability
ratio of stored magnetic information (KeV) to the thermal energy
(kBT), KeV/(kBT)50–70, stable grains down to sizes of about
d(60kBT/Ke)1/32.5 nm are conceivable9. However, for nano-
particles of FePt alloys, Ke is reduced by about one order of magni-
tude10,11, but still large compared with other ferromagnetic materials
like, for example, bcc Fe. One also has to consider that the MAE is
strongly inuenced by lattice parameters and symmetry decreasing
distortions12. In particles, these can be altered with respect to the
bulk case by interlayer relaxation13 due to the presence of facetted
surfaces or surface tension.
For technological applications, particles need to be deposited on
surfaces or embedded in a host material, which may cause struc-
tural deformations leading to an unknown modication of the
desired properties. Also, the particles may have to be exposed to a
more or less reactive atmosphere from which they can be protected
by deliberately covering them with suitable elements. e presence
of a dierent chemical surrounding, however, provides an electronic
environment of the surface (interface) atoms with a tendency to
alter the hybridization of the d states, which are responsible for the
large MAE. In nanoparticles with a nearly balanced surface-to-vol-
ume ratio, both eects on the MAE, structural and electronic, will
be signicant. It is the purpose of this work to quantify these con-
tributions in atomistic detail by means of a combined experimental
and theoretical investigation.
We present the results on the inuence of surface modications
on the MAE and the magnetic moments by capping FePt nano-
particles with Al, Au or Cu studied by large-scale rst-principles
calculations within the framework of density functional theory
(DFT) and X-ray absorption spectroscopy and its associated mag-
netic circular dichroism (XMCD). is combined eort provides
the unique possibility to simultaneously determine the MAE and
microscopic magnetic properties like the spin and orbital magnetic
moments. While the spectroscopic investigations rather provide
averaged values per atom deduced from nanoparticle ensembles,
the DFT ideally complements the experiment by allowing the
quantitative calculations of structural and electronic properties on
the atomistic level for individual particles. e link to the electronic
structure helps to understand the relevant properties and to design
guidelines for improved materials.
Orbital magnetism of ultrathin lms or nanostructures has been
a topic of intense theoretical research for more than two decades14–17.
Up to now, the main eorts have gone into understanding the
intriguing properties of ultrathin magnetic layers on non-magnetic
substrates18,19, while the inverse problem, the inuence of non-
magnetic layers on magnetic substrates, has attracted much less
attention. e presence of several non-equivalent surfaces and the
possibility of surface-related relaxation eects aecting the particle
core, however, call for a new integral approach, paying attention to
the inuence of all relevant interfaces at the same time. e merit
of such an approach is demonstrated in the present investigation.
Furthermore, our atomistic approach allows the evaluation and pre-
diction of articial structures that do not exist in nature. We will
demonstrate below that this can be used to separate hybridization
eects with capping materials from the inuence of intrinsic distor-
tions of the particle itself.
Results
Orbital and spin magnetic moments. Site-specic magnetic
moments were calculated within DFT for chemically ordered
Fe67Pt8 0 and Fe80Pt67 cuboctahedra in the L10 structure covered by
an additional layer of Al, Cu or Au. Aer geometrical relaxation
by minimization of the total energy, it can be clearly seen that the
morphology of the FePt nanoparticle is almost unaected by Cu
and Au layers, while Al coverage causes severe changes of shape
and crystal structure (Fig. 1). e spin-orbit contribution of an
electron to the Hamiltonian is generally expressed by the relation
HSOC =
ξ
σ
, where
σ
and l refer to spin and orbital momenta,
respectively, and
ξ
is the spin-orbit-coupling parameter. e
latter is about one order of magnitude larger for the 5d elements
like Pt, while the opposite holds for the exchange splitting
of the 3d component Fe. us, for FePt none of the elemental
contributions may be neglected a priori. A detailed inspection
of the individual spin and orbital moments of the FePt core,
as presented in Figure 2, will therefore be necessary to identify
the relevant trends. As the particle shape is close to spherical,
the quantities are presented site-resolved with respect to their
distance to the particle centre.
Fe80Pt67Al162 Fe80Pt67Cu162 Fe80Pt67Au162
Figure 1 | Morphology of capped FePt nanoparticles. L10 Fe80Pt67 nano-
particles terminated with a monolayer of Al, Cu and Au after structural
relaxation. Blue spheres refer to Fe, reddish spheres to Pt atoms and the
other colours to the respective covering element. The foreground shows
the nanoparticles in cross-section.
ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms1538
NATURE COMMUNICATIONS | 2:528 | DOI: 10.1038/ncomms1538 | www.nature.com/naturecommunications
© 2011 Macmillan Publishers Limited. All rights reserved.
e presence of an Al cap leads to a signicant reduction of the
Fe spin polarization in the interface region, which induces a simul-
taneous breakdown of the Pt spin and orbital moments. is strong
eect of the hybridization of the Fe 3d states with additional (s, p)
electrons suggests that elements of the Au group may be a better
alternative to minimize the impact of the matrix on the magnetic
properties of the particle, while reducing the tendency of interdiu-
sion of particle and matrix elements. Indeed, our calculations con-
cerning Cu-covered particles reveal no impact on the magnetism
of the Fe atoms, only a moderate reduction of the Pt spin magnetic
moment. In the case of Au capping, solely the Fe orbital moment
is aected. is suggests that in the rst case the Pt-terminated
while in the second case the Fe-terminated surface should rather be
avoided, respectively, in order to get magnetic moments close to the
values of uncapped FePt nanoparticles. is clearly shows that not
only the choice of the appropriate covering element is important,
but also the termination at the particle interface can have a major
impact on spin-orbit-related properties, which consequently should
be accounted for during the fabrication process of the particle itself.
For all ternary systems, we nd that the characteristic site-depend-
ent variation of the Pt spin moments is accompanied by a likewise
pattern shown by the respective orbital moments. is demonstrates
that in accordance with previous considerations for the bulk case20,21,
the orbital magnetism of Pt is dominated by single-site contributions
due to the large spin-orbit-coupling parameter, even close to the
interface. is leads to the primary guideline that preserving a large
Pt spin magnetic moment at the interface is crucial for maintaining
the desired hard magnetic properties. A similar correspondence is
not encountered for the 3d species, which is aected via hybridiza-
tion by the strong spin-orbit coupling to the 5d sites22.
In order to prove the calculated results experimentally, we focus
on the determination of element-specic magnetic moments and
MAE of FePt nanoparticles with dierent sizes (6 and 2 nm) capped
with Al. ese should show the strongest modication on structure
and magnetism compared with the uncapped case. Light elements
like Al and its passivating surface oxides do not impose technical
problems in measuring the X-ray absorption near-edge structure
(XANES) by total electron yield as discussed in the Supplementary
Information. e wet-chemically synthesized FePt nanoparticles23
were deposited onto a naturally oxidized Si substrate as depicted in
Figure 3. A typical scanning electron microscopy image is shown
in Figure 4a. By an oxygen and subsequent hydrogen plasma treat-
ment24, all organic ligands (oleic acid and oleylamine) surrounding
the particles in the as-prepared state are removed completely and
oxides are reduced. Aer this cleaning procedure, the particles were
annealed in order to obtain the chemically ordered L10 state and
capped with Al. In order to avoid interface alloying, the sample was
allowed to reach room temperature again aer annealing and before
evaporation of Al was started. However, some interdiusion at the
interface cannot be excluded entirely. More details on the sample
preparation can be found in the Supplementary Information. e
thickness of the Al was chosen to be 2 nm larger than the mean
diameter of FePt nanoparticles to prevent the particles from oxida-
tion, that is, 4 nm for the particles with 2 nm in diameter and 8 nm
for the particles with 6 nm in diameter, respectively. As Al forms a
passivating oxide layer that is only about 1 nm thick when exposed
to air, the thickness of Al capping is sucient to ensure a pure, that
is, non-oxidized FePt/Al interface.
3.0
2.5
2.0
Fe80Pt67:Al162
(Fe terminated)
Fe80Pt67:Cu162
(Fe terminated)
Fe80Pt67:Au162
(Fe terminated)
1.5
0.10
0.08
0.06
Fe orbital moment (B) Fe spin moment (B)
0.04
0.02
0.00
0.10
0.0
0.2
Pt spin moment (B)Pt orbital moment (B)
0.4
0.6
0.8
0.08
0.06
0.04
0.02
0.00
0
NFe 1 2 4 8 16 32 NPt 1 2 4 8 16 32
Distance from center (Å)
24680246802468
Figure 2 | Calculated orbital and spin magnetic moments of Fe and Pt atoms in capped FePt nanoparticles. Spatially resolved spin (top) and orbital
(bottom) moments of the Fe and Pt atoms for Al-, Cu- and Au-covered Fe80Pt67 nanoparticles, with (001) surfaces of Fe. The moments are shown as a
function of their distance from the particle centre. Blue circles denote position and moments of Fe atoms, while reddish squares depict Pt. The intensity
of the colour refers on a logarithmic scale to the number of overlapping symbols, that is, the frequency of atoms with a given moment and distance
from centre. The dashed lines connect the averages of distances and moments over all atoms of the respective species, which belong to the same fcc
coordination shell; the arrow heads at the left and right axis denote the respective nanoparticle averages of Fe and Pt moments.
Spin coating
Plasma cleaning
and annealing
Al evaporation
Si substrate
FePt nanoparticles
dispersed in n-hexane
Al thickness:
particle diameter + 2 nm
Figure 3 | Preparation steps. Schematic overview of sample preparation
of pure metallic, that is, oxygen-free and ligand-free, FePt nanoparticles
capped with Al.
ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms1538
NATURE COMMUNICATIONS | 2:528 | DOI: 10.1038/ncomms1538 | www.nature.com/naturecommunications
© 2011 Macmillan Publishers Limited. All rights reserved.
An example of XANES and XMCD measured at the Fe L3,2
absorption edges of an ensemble of pure metallic 6 nm FePt nano-
particles covered with Al is shown in Figure 4b. A small shoulder
that is visible above the L3 absorption edge around 710 eV could be
assigned to a hybridization between Fe d-states and Al sp-states as
it is known, for example, for the similar case of Fe d-states and Si
sp-states in Fe3Si25. Evidence for this can be found in the electronic
density of states. is hybridization yields also a reduction of the
XMCD in the energy range between 710 and 715 eV compared with
Fe bulk material, which is also useful to distinguish between the
changes in the spectral shape of the XANES caused by hybridization
with Al states and the formation of Fe oxides that show a dierent
XMCD signal (see for example, ref. 26).
By integration of the XMCD, the total magnetic moment per
unoccupied nal states at the Fe sites can be separated into spin
and orbital contribution according to the so-called sum rules27–29.
e values are listed in Table 1 using a number of unoccupied
d-states nh = 3.41 obtained from band structure calculations. Note
that the values taken from ref. 30 have been recalculated with the
same number of unoccupied d-states. As predicted by theory, the
magnetic moments at the Fe sites of Al-capped FePt particles with
diameters around 6 nm are signicantly reduced with respect to the
ones of uncapped nanoparticles of the same size30. Increasing the
fraction of surface atoms by reducing the particle diameter yields a
further decrease of spin and orbital magnetic moments indicating
that the magnetic moments of Fe atoms at the interface to the Al cap
layer are signicantly reduced as it was already expected from our
theoretical investigations. e total magnetization can be estimated
by summing up the experimentally determined spin and orbital mag-
netic moments per unit cell volume, V(0.386 nm)3. For uncapped
particles, both Fe and Pt magnetic moments were determined as
reported elsewhere31 yielding a magnetization M106 A m1. For Al-
capped particles, the Pt moments are assumed to be reduced with
respect to the ones measured for uncapped FePt nanoparticles by the
same factor as the Fe magnetic moments, that is, about 10% for 6 nm
particles yielding a total magnetization M9×105 A m1, and about
25% for 2 nm particles yielding M7.5×105 A m − 1, respectively.
Note that the ratio of orbital-to-spin magnetic moment remains
unchanged within experimental error. Compared with our theo-
retical results, this may indicate a Fe-terminated surface of the wet-
chemically synthesized nanoparticles.
Magnetic anisotropy. e proportionality between the anisotropy
of orbital magnetic moments and MAE proposed by Bruno14 for ele-
mentary metals was put into question for binary 3d–5d systems22,31.
Consequently, for FePt it is necessary to determine the MAE inde-
pendently, for example, by recording the eld-dependent XMCD as
a measure of magnetization32 at various temperatures. Examples at
three dierent temperatures can be seen in Figure 5a. For ensem-
bles of non-interacting nanoparticles with diameter d, uniaxial
anisotropy Ke and randomly oriented easy axes of magnetization,
the temperature dependence of coercivity can be described by Shar-
rock’s equation33:
H T K
M
k T
Kd
Ceff B
eff
( )
/
≈ −
125 6
3
2 3
p
Simulation of the experimental data as shown in Figure 5b yields an
eective anisotropy of Ke = 6–7×105 J m − 3 corresponding to a mean
blocking temperature of about 220 K. is approximately agrees with
earlier experiments on uncapped nanoparticles10,34. For the simu-
lations, the magnetization was varied around the value estimated
from the magnetic moments as described above. e non-vanishing
coercivity above the mean blocking temperature is related to nano-
particles with larger diameters than the mean value of 6 nm.
From theory, the inuence of capping layers on the MAE can
be determined by the dierences in the band energies obtained by
changing the magnetization direction away from the easy axis para-
llel to the shortened c axis of the L10 lattice to the (intermediate) hard
axis perpendicular to it. e results for the dierent possibilities of
surface termination (Fig. 6) indicate in fact a large inuence of the
capping species, and corroborate the trends obtained from the orbital
moments above. While Al capping leads to a signicant decrease of
the MAE regardless of the termination of the FePt (001) facets, the
elements with the lled d shell, Cu and Au, yield encouraging results
coming close to the values obtained for uncapped nanoparticles.
Cu and Au are iso-electronic, they only dier by size and the loca-
tion of the centre of the d-band with respect to the Fermi energy as
well as magnitude of the spin-orbit-coupling parameter. Computer
experiments oer full control of the congurational arrangements
and thus provide a straightforward possibility to estimate the con-
tribution from matrix-induced geometrical changes, which will, for
(1)(1)
Table 1 | Fe XMCD results*.
Sample
m
Seff (
m
B)
m
L (
m
B)
m
tot (
m
B)
m
L/
m
Seff (%)
FePt, uncapped30, 6 nm 2.38 ± 0.26 0.20 ± 0.02 2.58 ± 0.28 8 ± 1
FePt + Al cap, 6 nm 2.14 ± 0.22 0.15 ± 0.02 2.29 ± 0.24 7 ± 1
FePt + Al cap, 2 nm 1.78 ± 0.19 0.13 ± 0.02 1.91 ± 0.21 7 ± 1
XMCD, X-ray magnetic circular dichroism.
*The error bar was estimated to be slightly more than 10% for the effective spin and orbital magnetic moment, including inaccuracies of the sum-rule-based analyses, the error in calculated number of
unoccupied final states and—as smallest effect here—the error due to the small overlap in energy of L3 and L2 absorption edge of Fe. For each sample, eight spectra have been averaged to obtain these
results.
6
4
2
0
p
q
XANES, XMCD intensity (arb. units)
–2
700 720 740
Photon energy, E (eV)
760
–4
0
4
Integral of XMCD signal (arb. units)
8
12
Figure 4 | Experimental X-ray absorption data of an FePt nanoparticle
ensemble capped with Al. (a) Exemplary scanning electron microscopy
image of uncapped 6 nm FePt nanoparticles on a naturally oxidized Si
wafer. (b) X-ray absorption near edge structure (reddish line) and its
associated magnetic circular dichroism (black line) at the Fe L3,2 absorption
edges. Integrating the dichroic spectrum (blue line) yields the element-
specific magnetic moments at the Fe sites.
ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms1538
NATURE COMMUNICATIONS | 2:528 | DOI: 10.1038/ncomms1538 | www.nature.com/naturecommunications
© 2011 Macmillan Publishers Limited. All rights reserved.
example, arise from a variation of the tetragonal distortion of the
particle core35. We can estimate such contributions by removing all
covering atoms but leaving the Fe and Pt atoms exactly in place.
e MAE of the stripped nanoparticles is for all cases signicantly
larger than the MAE of the original decorated isomers, which can
be naturally traced back to the released quenching of orbital mag-
netism of the surface atoms. e MAE of the stripped nanoparticles
can signicantly exceed the values obtained for the fully relaxed iso-
mers with clean surfaces, whereas the electronic interaction with
the atoms of the capping layer generally leads to a reduction of the
MAE. ese results demonstrate clearly that both structural modi-
cations due to additional layers of surface atoms and changes in
the electronic environment, yield equally important contributions,
which need to be taken into account explicitly when comparing
experimental results on free nanoparticles, embedded nanoparticles
and nanoparticles supported by dierent substrates.
In the case of Au coverage, the change of the interface termina-
tion from Fe to Pt is connected with a strong increase of the MAE,
which—following ref. 33—can be related to contributions from
o-site spin-orbit scattering of the Fe states, which seem also to be
responsible for the quenching of the interfacial orbital magnetic
moments of Fe as shown in the upper panel of Figure 2. us, the
type of the particles surface termination can be deemed of particular
importance if the protective shell consists of heavy elements, which
possess a large spin-orbit-coupling parameter. Note that also other
coverages have been considered in our calculations, such as carbon,
as presented in the Supplementary Information. In that case, the
hybridization of the (s, p) states of C with the d states of FePt is
presumably strong, and the magnetism of the FePt nanoparticle fur-
ther suers from the diusion of C into the FePt particle matrix. We
expect that this negative aspect of C capping will survive for other
covalently bonding materials as well.
Discussion
Our combined approach allows us to disentangle the dierent con-
tributions that strain and surface modications have on the magnetic
properties of free and covered magnetic nanoparticles by correlat-
ing detailed experimental and ab initio large-scale DFT calcula-
tions. From our results, we will deduce basic fabrication guidelines
to appropriately modify the magnetic properties, that is, MAE and
magnetic moments, by capping FePt nanoparticles in L10 symmetry:
in order to obtain protected hard magnetic nanostructures with
large MAE, one must ensure in the rst place that the spin moment
of the Pt interface atoms will not be aected by the capping—neither
directly, nor indirectly by quenching of the inducing Fe moments,
unless the presence of a so magnetic shell (or possibly even a dead
layer) is desired. Exactly this is the case if the protective cover allows
for hybridization with (s, p) electrons. Unaected by experimen-
tal diculties in the XANES measurements, the DFT approach
straightforwardly allows us to inspect site-resolved orbital magnet-
ism of particles capped with heavier elements, as the late elements of
the d series. Indeed, Cu and Au present alternatives preserving the
0.05 ∆µFe (Pt-term.)
∆µFe (Fe-term.)
∆µPt (Pt-term.)
∆µPt (Fe-term.)
0.00
∆µorb (µB/atom)
150 Pt-terminated
Fe-terminated
100
MAE (meV/particle)
50
Fe67Pt80:X162
Fe80Pt67:X162
0Al Cu Au Free
Surface
Figure 6 | Calculated magnetocrystalline anisotropies for capped
FePt nanoparticles. Comparison of the calculated magnetocrystalline
anisotropy energy (MAE) in meV per atom for different cappings and
termination of the (001) surfaces. The small circles refer to 147 atom
particles with stripped decorations but retained atomic positions and
clean nanoparticles. The values have been calculated relying on the
magnetic force theorem from the difference in band energy between
the easy and intermediate axis orientations of collinear magnetic
arrangements in [001] and [100] directions. The upper panel shows the
difference
µ
orb =
µ
stripped
µ
decorated between the average orbital moment
between stripped and decorated configurations (magnetization [001]).
Note that a value of 100 meV per particle corresponds to ~7×106 J m3.
0.04
a
b
0.02
0
–0.02
T = 30 K
T = 150 K
T = 300 K
XMCD signal (arb. units)
–0.04
–2 –1 0
External magnetic field, µ0H (T)
12
0.8
0.6
Keff = 6.2×105 J m–3, M = 0.8×106 A m–1
Keff = 6.4×105 J m–3, M = 0.9×106 A m–1
Keff = 7.3×105 J m–3, M = 1.1×106 A m–1
0.4
Coercive field, µ0Hc(T)
0.2
0
0 50 100 150
Temperature, T (K)
200 250 300
Figure 5 | Field- and temperature-dependent XMCD measurements for
the estimation of magnetocrystalline anisotropy. (a) Field-dependent
X-ray magnetic circular dichroism as a measure of magnetization at the Fe
sites of Al capped FePt nanoparticles for three different temperatures. (b)
Extracted temperature dependence of the coercive field (filled symbols)
and simulations using Sharrock’s equation with different parameters
(lines). Note that for FePt, 1×106 J m3 corresponds to ~0.1 meV per atom
(0.2 meV per Fe atom, respectively).
ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms1538
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© 2011 Macmillan Publishers Limited. All rights reserved.
hard magnetic properties of the FePt core. In the case of Au, how-
ever, additional attention must be paid to the specic interface con-
tributions to the MAE according to the interaction with the dierent
facets of the magnetic core. Decoration of carefully selected facets
with sixth row elements can thus provide a signicant improvement
over a mere minimization of anisotropy losses. e corresponding
interactions are, however, not easily predictable a priori, and the
magnetic properties of such nanocompounds can decisively depend
on the fabrication conditions. An interesting option for a further
systematic investigation may also be capping with elements of the
5f series as their degree of electron localization increases with the
atomic number from itinerant (taking part in the chemical bond)
to strongly localized (comparable, for example, with rare earth met-
als) while large orbital magnetic moments are present. Our nd-
ings can be condensed into three key observations, which form
the basic ingredients to construct guidelines for the design of FePt
nanoparticles with special magnetic properties. First, as not only the
choice of the appropriate covering element is important, but also
the termination at the particle interface can have major impact on
the MAE, it is necessary to select the appropriate surface termina-
tion within the fabrication process. Second, preserving a large spin
magnetic moment at the Pt sites at the interface is crucial for main-
taining the hard magnetic properties of FePt (as the hybridization
of the 5d states with the strongly spin polarized 3d states of Fe is
essential for a large magnetocrystalline anisotropy). ird, struc-
tural modications due to additional layers of surface atoms and
changes in the electronic environment are equally important for the
magnetic properties.
ese observations imply that it is possible to design nano-
particular systems with the desired magnetic properties by
choosing the right capping material from a technological perspec-
tive or for basic research. e origin of these dierent magnetic
properties for dierent capping materials is due to both electronic
hybridization eects and structural distortions of the nanoparticle
itself, which can be separated by means of state-of-the art rst-
principles calculations. Consequently, our combined approach
allows us to formulate three design rules for L10 FePt nanoparticles
with optimized magnetic properties. First, for hard magnetic FePt
nanoparticles: to maintain the large MAE of uncapped FePt nano-
particles and their magnetic moments, covering with an element
from the late d series like Cu is advised. For FePt nanoparticles
with Pt-terminated surfaces, capping with Au gives the possibility
to even exceed the MAE of the uncapped particles. Second, for
so magnetic FePt nanoparticles with large saturation magneti-
zation: FePt nanoparticles with Fe-terminated surfaces should be
capped with heavy elements with large spin-orbit coupling like Au,
which yield largely unchanged magnetic moments with respect
to the uncapped particles, but a signicant decrease of the MAE.
ird, for so magnetic FePt nanoparticles with reduced satura-
tion magnetization: capping with Al yields to a signicant reduc-
tion of both MAE and magnetic moments. Lighter elements like C
show enhanced diusion into the particle and yield to a complete
breakdown of the net magnetization.
Methods
Calculations. Structural relaxations were carried out in the framework of DFT
and the Vienna Ab-initio Simulation Package36. e wavefunctions of the valence
electrons (3d74s1 for Fe, 5d96s1 for Pt, 3s23p1 for Al, 3d104s1 for Cu and 5d106s1 for
Au) were expanded within a plane wave basis set (cuto Ecut = 335…450 eV) in
combination with the PAW method for the interaction with nuclei and core
electrons37. We used the generalized gradient approximation exchange correla-
tion functional in the formulation of Perdew and Wang38,39 together with the spin
interpolation formula of Vosko, Wilk and Nusair40. Spin-orbit interaction can be
included in the non-collinear version of the code41–43.
For each of the core-shell particles (FePt/Al, FePt/Cu and FePt/Au), we
considered 147 atom FePt clusters (consisting of 67 Fe atoms and 80 Pt atoms,
and vice versa), with perfect L10 layering, capped with 162 atoms of Al, Cu or Au.
e particles were placed in a cubic supercell with an edge length of 28 Å to avoid
interactions between the periodic images. Geometrical optimizations were carried
out on the Born–Oppenheimer surface without any symmetry constraints on
charge density and forces using a conjugate gradient algorithm, in a similar manner
as in previous investigations of the authors (for further details, see, for example,
refs 12,44). As the problem is non-periodic, Brillouin zone sampling was restricted
to the Γ-point with a Gaussian-type nite temperature smearing of the occupancies
near the Fermi surface.
For the calculation of spin-orbit-related properties extremely well-converged
wave functions and charge distributions on the one hand, and a sharp denition of
the energy levels close to the Fermi surface on the other are mandatory. To ensure
this, the nite temperature smearing was reduced in three consecutive scalar-
relativistic calculations with collinear spin alignment with respective widths of
σ
= 50, 20 and 10 meV, the latter initialized by the converged charge density and
wave functions of the previous run with larger smearing. e resulting wave
functions and charge densities have been used to initialize fully self-consistent
calculations of spin and orbital moments with magnetization aligned in the
easy axis direction (Ecut = 335 eV). ese calculations were allowing for possible
non-collinear arrangements. However, only minor directional deviations of the
spin moments from the easy direction were encountered, which are not signicant
for the present study.
e accurate calculation of the magnetocrystalline anisotropy energy (MAE)
requires increased numerical eorts compared with the orbital moments. In
agreement with the experience of Błon´ski and Hafner43, an increased energy cuto
of Ecut = 450 eV and in addition a denser Fourier grid has been chosen. Calcula-
tions of this kind are extremely demanding with respect to computation time and
memory, and can—so far—for large systems of 300 magnetic transition metal
atoms (and beyond) only be performed on world-leading supercomputers as the
IBM Blue Gene/P installation JUGENE at Forschungszentrum Jülich, which gave
us the possibility to distribute one single calculation on 1,024 compute nodes
(or more), simultaneously.
A fully self-consistent non-collinear calculation for hard magnetic materials as
FePt may yield spurious results as the spin moments are allowed to rotate towards
their easy axis. To prevent this, our calculations were carried out in terms of the
magnetic force theorem45,46. Here, non-self-consistent calculations of the relativistic
energies are performed for dierent orientations of the spin quantization axis
depending on charge densities and wavefunctions obtained from self-consistent
collinear scalar-relativistic runs. e MAE is obtained from the dierence in band
energies between hard and easy axis (in the present case [001] and [100], the
MAE with respect to [110] are in agreement within numerical error). e orbital
moments obtained from the non-self-consistent calculations with easy axis
alignment were found in close agreement with the above-described fully self-
consistent approach.
In the main manuscript, spatially relsoved spin and orbital moments were
only shown for Fe80Pt67 particles with Fe-terminated (001) surfaces. e results
for the Pt-terminated Fe67Pt80 particles are completely analogous and shown for
completeness in the Supplementary Figure S1. In addition to the metallic elements
Al, Cu and Au, we also considered an alternative coating of the Fe–Pt clusters with
carbon. During the relaxations, we encountered very severe structural distortions,
which included (energetically downhill) diusion of carbon atoms into subsurface
positions of the comparatively open [100] and [001] surfaces. Furthermore, we
also encountered a dramatic disturbance of surface/interface magnetism, including
antiferromagnetic admixtures on the Fe sites, and a nearly complete breakdown
of the spin polarization of the interface Pt atoms, as shown in the Supplementary
Figure S2. We attribute, as in the case of Al, this degradation of the magnetic
properties to the increased hybridization between d and (s, p) electrons due to the
presence of carbon.
Sample preparation. FePt nanoparticles were synthesized by thermal
decomposition of Fe(CO)5 and Pt(acac)2 as described elsewhere23. e particles
are in the chemically disordered state as the formation of the chemically ordered
state—which is the equilibrium state at room temperature—is kinetically sup-
pressed. e size distribution was determined by analysis of transmission electron
microscopy images. e mean diameters and the standard deviation of the log-nor-
mal size distributions of the two samples investigated in this work are d = 6 nm with
σ
= 0.15, and d = 2 nm with
σ
= 0.17, respectively. In the as-prepared state,
the particles are surrounded by organic ligands, oleic acid and oleyl amine.
is prevents agglomeration of the particles while deposited onto a naturally
oxidized Si substrate using the spin-coating technique.
In order to remove the organic ligands, the sample was cleaned by a radio
frequency (13.6 MHz) oxygen plasma treatment for 15 min with a power of 30 W at
an oxygen pressure of 5 Pa (0.05 mbar). e oxidized Fe was reduced subsequently
by a hydrogen plasma treatment for 40 min with a power of 30 W at a pressure of
8 Pa (0.08 mbar). Note that during the oxygen plasma treatment, a small amount of
Cu from the Cu electrode may be sputtered and deposited onto the sample.
In order to avoid agglomeration of the particles during thermal treatment,
the annealing was performed at quite low temperatures of 575 °C at maximum.
e annealing procedure under UHV conditions is the following: heating up the
sample from room temperature to 575 °C in 2 h and hold the maximum tempera-
ture of 575 °C for 7 h, cool down to 475 °C in 30 min and hold 475 °C for 1 h, cool
ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms1538
NATURE COMMUNICATIONS | 2:528 | DOI: 10.1038/ncomms1538 | www.nature.com/naturecommunications
© 2011 Macmillan Publishers Limited. All rights reserved.
down to 410 °C in 30 min and hold 410 °C for 1 h, cool down to 360 °C in 30 min
and hold 360 °C for 1 h, switch o heating. Aer annealing, the sample was allowed
to reach room temperature again before evaporation of Al was started at rates of
0.1–0.2 nm min − 1 to avoid alloying.
X-ray absorption experiments. X-ray absorption measurements were carried out
at the PM3 bending magnet beamline of the BESSYII synchrotron radiation source
in magnetic elds up to
µ
0H = ± 2.8T in total electron yield mode by detecting the
sample drain current. XMCD was measured by reversing the direction of magnetic
eld or helicity of X-rays aer each scan varying the energy from 680 to 790 eV.
Magnetic hystereses were recorded by detection of the eld-dependent X-ray
absorption signal at the energy of maximum dichroism (708.6 eV) normalized
to the eld-dependent absorption in the pre-edge region (700 eV). e sample
temperature was stabilized at dierent temperatures between 11 and 300 K.
Details on data analysis can be found in the Supplementary Information.
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Acknowledgements
We would like to thank the HZB-BESSY II sta, in particular T. Kachel and H. Pfau for
their kind support during beamtimes, and T. Umbach and A. Amyan (U. Würzburg)
for help in the measurements. e calculations were carried out on the supercomputers
of the John von Neumann Institute of Computing at Forschungszentrum Jülich.
We thank the sta of the Jülich Supercomputing Center, and P. Vezolle of IBM for
their kind support. is work was funded by the BMBF (05 ES3XBA/5) and the DFG
(SFB445, SPP1239).
Author contributions
C.A. and M.E.G. equally contributed to this work. C.A. procured beamtime, K.F. provided
experimental setup, C.A., B.K., M.S. and A.W. performed the experiment, S.S. synthesized
nanoparticles, F.M.R. and A.V.T. prepared the samples. C.A. analysed the XAS data,
M.E.G. performed and analysed the DFT calculations. C.A., M.E., M.F., P.E. and H.W.
wrote the paper. All authors discussed the results and commented on the manuscript.
Additional information
Supplementary Information accompanies this paper at http://www.nature.com/
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doi: 10.1038/ncomms1538 (2011).
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Citation: Nguyen Trong, D.; Cao Long, V.; Ţȃlu, Ş. The Structure and Crystallizing Process of NiAu Alloy: A Molecular Dynamics Simulation Method. Publisher's Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Abstract: This paper studies the influence of factors such as heating rate, atomic number, temperature, and annealing time on the structure and the crystallization process of NiAu alloy. Increasing the heating rate leads to the moving process from the crystalline state to the amorphous state; increasing the temperature (T) also leads to a changing process into the liquid state; when the atomic number (N), and t increase, it leads to an increased crystalline process. As a result, the dependence between size (l) and atomic number (N), the total energy of the system (E tot) with N as l~N −1/3 , and −E tot always creates a linear function of N, glass temperature (T g) of the NiAu alloy, which is T g = 600 K. During the study, the number of the structural units was determined by the Common Neighborhood Analysis (CNA) method, radial distribution function (RDF), size (l), and E tot. The result shows that the influencing factors to the structure of NiAu alloy are considerable.
... Initially, the ratio between NiAu alloy and Ni:Au is 1:1, as in 2048 NiAu atoms, there are 1024 Ni atoms, 1024 Au atoms (NiAu 2048 ), 2916 atoms (NiAu 2916 ), 4000 atoms (NiAu 4000 ), 5324 atoms (NiAu 5324 ), 6912 atoms (NiAu 6912 ); all samples are studied by molecular dynamics (MD) simulation method [85][86][87][88][89][90][91][92][93][94][95] with embedded Sutton-Chen (SC) interaction [39,[96][97][98][99] and boundary conditions recirculating with the Equation (1): ...
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This paper studies the influence of factors such as heating rate, atomic number, temperature, and annealing time on the structure and the crystallization process of NiAu alloy. Increasing the heating rate leads to the moving process from the crystalline state to the amorphous state; increasing the temperature (T) also leads to a changing process into the liquid state; when the atomic number (N), and t increase, it leads to an increased crystalline process. As a result, the dependence between size (l) and atomic number (N), the total energy of the system (Etot) with N as l~N 1/3, and Etot always creates a linear function of N, glass temperature (Tg) of the NiAu alloy, which is Tg = 600 K. During the study, the number of the structural units was determined by the Common Neighborhood Analysis (CNA) method, radial distribution function (RDF), size (l), and Etot. The result shows that the influencing factors to the structure of NiAu alloy are considerable.
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