# Interaction potential of FePt with the MgO(001) surface

R. Cuadrado  Department of Physics, University of York, York YO10 5DD, United
Kingdom  R. W. Chantrell  Department of Physics, University of York, York YO10
5DD, United Kingdom

###### Abstract

By means of density functional theory we have undertaken a structural,
electronic and magnetic survey of the adsorption of the FexPty ($x,y\leq 4$)
clusters on MgO(001) surface under the generalized gradient approximation. We
have tested different atomic adsorption geometries with the aim of scan a
wider range of adsorption sites in order to determine the preferential surface
covering. Our main conclusion in this respect is that the FePt wets the
surface. The $intracluster$ (before and after the adsorption) and
cluster–to–surface binding mechanisms were investigated via the adsorption
energy, charge transfer, density of states and hybridization analysis. The
adsorption energy values increased for those geometries in which keeping the
Fe or Pt atom @$top$–O, the outermost species was moved to $cover$ the
surface. In general the unsupported clusters present higher $intracluster$
energies than the adsorbed ones being the average difference of 1.5 eV. In
this regard there was a small reduction in the net magnetic moment of the
supported clusters due to an internal and external rearrangement of the
spin–up/–down charge. Furthermore, a complex and subtle charge transfer
between different species takes place having an increasing the Pt and O
population at the expense of the lost Fe charge.

##  I Introduction

During the past two decades, continuous miniaturization has driven data-
storage technology to the nanometer scale and consequently, the study of
magnetism in low-dimensional systems is currently attracting a great deal of
interest shou ; hans . The interaction of metallic clusters and alloys with
supporting metal–-oxide surfaces is a subject of great current interest,
because of their numerous technological applications. musolino ; ricci
Important objectives of these studies are to understand how the atomic and
electronic structure of both subsystems are modified through their
interaction, as well as the properties of the resulting interface. Due to its
high uniaxial magnetocrystalline anisotropy energy (MAE) of $7\times 10^{7}$
ergs/cm3, the FePt–L10 alloy is a promising candidate for the next generation
for the fabrication of ultrahigh density data-recording devices. FePt in the
disordered state has a face–centered cubic ($fcc$) crystal structure and is
magnetically soft. In contrast, the ordered face–centered tetragonal ($fct$)
L10 phase of the FePt alloy has Fe and Pt atomic planes stacked alternatively
along the $c$ axis in the equiatomic composition. In this phase it exhibits
exceptional magnetic properties including high uniaxial (MAE), high
coercivity, high saturation magnetization, and good chemical stability. weller
There have been a number of studies looking at the magnetic properties of
FePt–L10, for example, in films or multilayers, thin ; multi  slabs
Chepulskii2012  and more recently in doped bulk phases. ramon2

However, during the last decade the possibility to use clusters deposited on
surfaces to increase the recording density. dieguez ; cuadrado1 ; gambardella
; medina  has emerged. These clusters or nanoparticles (NPs) have different
properties from bulk counterparts due to their reduced surface atomic
coordination. In particular, binary 3$d$–5$d$ NPs formed by transition metals
(TM) such as Fe or Co, together with 5$d$ noble metals such as Au or Pt allow
the possibility to tune the magnetic properties based on an in–depth knowledge
of their geometrical and magnetic behavior. rollman ; seivane ; chen  The high
MAE also permits the use of smaller particles before the onset of
superparamagnetism, which may translate into potentially larger recording
densities. Hence, the primary motivation to synthesize and study
perpendicularly oriented FePt nanoparticles dispersed in a nonmagnetic matrix
is to combine favorable properties, which accompany size reduction, with
superior magnetic properties of FePt and arrive at a system that is highly
suitable for high-density perpendicular magnetic recording.

Wettability and material spreading are of key importance for many
applications. At large scales, wetting or non–wetting plays an important role
in, for example, oil recovery bertrand  and on a smaller scale, wetting
solutions have been proposed to solve technological problems in microfluidics
and nanoprinting, inkjet printing, etc. tabeling  All these phenomena are
governed by the surface and interfacial interactions, acting usually at small
(a few nanometers for van der Waals or electronic interactions) or very small
molecular distances. These length scales are now being probed with relatively
new experimental techniques, such as atomic force microscopy, or theoretical
tools, such as molecular dynamics. musolino  In such surface–anchored
cluster/alloy systems it would be highly desirable to find ways to control and
tune the properties of the adsorbed clusters through manipulation of the
supporting substrate and the deposited clusters. The properties that may be
influenced via substrate manipulation include: adsorption energies, cluster
geometries and dimensionalities, cluster diffusion barriers, charge
distributions, and chemical reactivities.

The magnetic properties of gas–phase metal clusters have been the subject of
both experimental and theoretical investigations as we have pointed out,
however, to the best of our knowledge there have been no studies about the
wettability of the FePt–L10 alloy onto an MgO surface. The growth of FePt on
MgO has been predicted to be one of the possible candidates for for the
fabrication of ultrahigh density data recording media. Thus, in this study, we
have performed detailed density functional theory (DFT) computations to study
the adsorption of bimetallic FexPty clusters on MgO, where $x+y\leq 4$. We
present the study of the structural, electronic and magnetic properties of
these ultrasmall clusters regarding different adsorption sites for the Fe or
Pt species, namely, @$top$–O/–Mg and @$hollow$ sites. Even though the size of
these small agregates is far from the real structures currently used as a
recording magnetic media, the look into the complicated bonding mechanism at
the atomic level between Fe or Pt species with the MgO surface will elucidate
the still unclear interplay between these ferromagnetic–oxide systems. The
importance of how FePt–L10 grows onto MgO is of vital importance in magnetism
because of the following questions: (1) what are the stable configurations for
the adsorption of these FexPty clusters on MgO? (2) How do the electronic and
magnetic properties of the adsorbed clusters vary with the sizes? (3) How does
the chemical activity of these functionalized MgO by FexPty clusters?

The paper is structured as follows. In section II we describe the theoretical
tools to perform all the calculations as well as the set of geometries studied
in the present work. Convergence tests are presented in Sec. III.1. The
energetic and structural analysis after the relaxation of the $dimers$,
$trimers$ and $tetramers$ will be explained in III.2. The $intracluster$ and
the cluster–to–surface charge transfer study are described in subsection III.3
together with the local magnetic moments analysis. Finally, Sec. IV summarizes
the main results.

##  II Theoretical Methods

Our density functional based calculations have been performed using the code
SIESTA siesta  within the generalized gradient approximation (GGA) for the
exchange correlation (XC) potential pbe . We used norm-conserving
pseudopotentials in the separate Kleinman-Bylander kb  form under the
Troullier-Martins parametrization tm  and to address a better description of
the magnetic behaviour, nonlinear corrections were included in the XC terms cc
. The valence reference electronic configuration for the pseudopotentials are
4$s^{2}$4$p^{0}$3$d^{6}$ (Fe), 6$s^{1}$6$p^{0}$5$d^{9}$ (Pt),
3$s^{2}$3$p^{0}$3$d^{0}$ (Mg) and 2$s^{2}$2$p^{0}$3$s^{2}$ (O) with $s/p/d$
cutoff radii 2.0/2.5/0.6 a.u. (Fe), 2.0/2.75/1.25 a.u. (Pt), 2.6/2.6/2.6 a.u.
(Mg) and 0.75/0.75/1.75 a.u. (O), respectively. The geometry optimizations
were carried out using the conjugate gradient (CG) method at a spin-polarized
scalar relativistic level. As a basis set, we have employed double-$\zeta$
polarized (DZP) with strictly localized numerical atomic orbitals, and, the
electronic temperature –kT in the Fermi-Dirac distribution– was set to 50 meV.
After the relaxation process the forces per atom were less than 3 meV/Å.

The adsorption of the FexPty clusters onto a MgO surface has been modeled as a
two–dimensional periodic slab comprising of four MgO(001) layers. We first
consider $dimer$ structures as illustrated schematically in Fig. 1, followed
by more complex FePt clusters as depicted in Fig. 2. The Magnesium oxide
structure can be described as two interpenetrating fcc lattices displaced by
$a/2(111)$ along the body diagonal of the conventional cube and the bulk
experimental value for its lattice parameter is $a$=4.22Å. We optimized the
MgO lattice constant $a$ for the GGA–XC functional obtaining the lattice value
of 4.30Å. To converge the physical quantities and minimize the out–of–plane
and in–plane interactions between nearest cells, a total of subtract32
in–plane MgO atoms was chosen, as we will point out in the section III.1.

In this work, the adsorption energies, Eads, were evaluated after subtracting
from the total energy of each configuration of the energy of the clean MgO
surface and those of the clusters following the equation:

$E_{ads}=-(E^{T}-E_{C}^{T}-E^{at/clus}),$

where $E^{T}$ is the total energy of the whole system, the $E_{C}^{T}$ is the
energy of the clean MgO surface and the $E^{at/clus}$ is the energy if either
one Fe/Pt atom or FexPty clusters are adsorbed.

##  III Results and discussion

We performed the energetic study of different size FePt clusters adsorption on
MgO(001) surface. Several adsorption sites and clusters orientations with
respect to the MgO surface were taken into account. The optimized geometric
configurations were obtained by means of the conjugate gradient method
allowing that the clusters and the first two MgO layers moved freely. In the
following we present the sistematic analysis of the geometric, electronic and
magnetic properties of these optimized configurations checking previously the
feasibility of the calculations with a convergency test for two unit cell
sizes.

###  III.1 Convergence test

Table 1: Adsorption energies, Eads, heights of the Fe/Pt adatoms with respect to the first MgO plane, $z_{Fe/Pt}$, for the $top$–O/–Mg and $hollow$ adsorption sites for different number of support MgO planes, $N_{l}$, and for two sizes of the unit cell: c18 and c32. The energies are in eV and the heights in Å.  |  |  | Fe adatom |  |  | Pt adatom
---|---|---|---|---|---|---
cell | Fe/Pt site | Nl | Eads |  | zFe |  |  | Eads |  | zPt
c18 |  $top$–O | 2 | 2.26 |  | 1.99 |  |  | 3.54 |  | 2.00
|  | 3 | 2.10 |  | 1.92 |  |  | 3.64 |  | 2.00
|  | 4 | 2.25 |  | 1.93 |  |  | 3.50 |  | 2.00
|  | 5 | 2.32 |  | 1.97 |  |  | 3.35 |  | 2.00
|  $top$–Mg | 2 | 0.69 |  | 2.87 |  |  | 1.63 |  | 2.64
|  | 3 | 0.87 |  | 2.70 |  |  | 1.44 |  | 2.60
|  | 4 | 0.71 |  | 2.73 |  |  | 1.91 |  | 2.65
|  | 5 | 0.67 |  | 2.75 |  |  | 1.16 |  | 2.64
| $hollow$ | 2 | 1.74 |  | 1.96 |  |  | 2.67 |  | 2.05
|  | 3 | 1.88 |  | 1.90 |  |  | 2.70 |  | 2.03
|  | 4 | 1.56 |  | 1.96 |  |  | 2.65 |  | 1.98
|  | 5 | 1.50 |  | 1.95 |  |  | 2.71 |  | 1.98
c32 |  $top$–O | 2 | 2.40 |  | 1.93 |  |  | 3.51 |  | 2.00
|  | 3 | 2.17 |  | 1.92 |  |  | 3.56 |  | 2.01
|  | 4 | 2.29 |  | 1.93 |  |  | 3.62 |  | 2.00
|  | 5 | 2.28 |  | 1.93 |  |  | 3.70 |  | 2.01
|  $top$–Mg | 2 | 0.84 |  | 2.97 |  |  | 1.35 |  | 2.57
|  | 3 | 0.87 |  | 2.92 |  |  | 1.86 |  | 2.67
|  | 4 | 0.88 |  | 2.94 |  |  | 1.53 |  | 2.64
|  | 5 | 0.88 |  | 2.91 |  |  | 1.53 |  | 2.66
| $hollow$ | 2 | 1.26 |  | 1.95 |  |  | 2.70 |  | 1.99
|  | 3 | 1.75 |  | 1.94 |  |  | 2.72 |  | 1.95
|  | 4 | 1.64 |  | 1.96 |  |  | 2.80 |  | 1.99
|  | 5 | 1.49 |  | 1.95 |  |  | 2.53 |  | 2.00

In order to use the best geometric configuration to avoid the spurious
interaction between adjacent in–plane and out–of–plane cells due to the
periodic boundary conditions, we have calculated the adsorption energy of one
Fe and Pt atom on the @$top$–O, @$top$–Mg and @$hollow$ sites as well as the
vertical distances between these atoms and the MgO surface. In order to ensure
that our model systems were sufficiently large we have investigated the effect
of increasing the MgO system size. Specifically, we have chosen two supercell
sizes labeled as $c18$ and $c32$ with 18 and 32 MgO atoms at the surface
respectively, and varied the thickness of the supported MgO layer by varying
the number of atomic planes from 2 to 5. Each configuration was optimized
using the conjugate gradient (CG) method until the forces between atoms were
less than 0.03 eV/Å. The relaxations were undertaken allowing the Fe or Pt
atoms and the first two MgO planes move freely, keeping the atoms belonging to
the last MgO layers fixed to their bulk sites. Only for the configurations in
which the number of MgO planes were two or three, i.e., $c18/32$–2/3, only the
first MgO layer was allowed to move together with the adsorbed atoms. In table
1 we can see the values of the adsorption energies (Eads) and the heights
between the Fe/Pt atoms and the surface ($z_{Fe/Pt}$). These values were
computed as the difference in the $z$ coordinate between the Fe/Pt and the
O/Mg species, depending on whether the adsorption site was @$top$–O or
@$top$–Mg, respectively. The perpendicular distances for atoms situated on
@$hollow$ sites were calculated as the difference of the $z$ coordinate of the
Fe/Pt and the average $z$ coordinate of O and Mg.

Detailed analysis of table 1 is not germane to the aim of the paper, so here
we only discuss the main results in order to discriminate the less accurate
geometric configurations and define the best geometry for accurate and CPU
efficient calculations of the properties of FePt clusters on MgO. We expect
that a bigger supercell together with a higher number of MgO layers will
provide more accurate calculations. The reason is clear after inspection of
the differences in the Eads as we move from two to five MgO layers and after
we compare the values between the $c18$ and $c32$ supercells. As an example,
in $c18$–Fe@$top$–O configurations the Eads converges to 2.32 eV as the MgO
thickness increases. Almost the same value is achieved when the $c32$ was used
(2.28 eV). This suggests that the use of the $c32$ configuration composed of 4
or 5 MgO layers is sufficient to study the adsorption of the FePt clusters
onto MgO(001) surface. Beyond this there are no significant changes in the
distances between the atoms and the surfaces, only around $\pm$0.05 Å, in
moving to the higher thickness and sizes.

It is interesting to note that the Pt atoms prefer to lie @$top$–O as shown in
the adsorption energies in comparison with the other adsorption positions and
species in the table 1. This is surprising because, as shown in FePtOnMgO ,
the Fe atoms of a FePt–L10 alloy prefer to lie @$top$–O rather than having a
Pt-termination. Clearly the behavior of individual Fe and Pt atoms is very
different from that of a FePt alloy on MgO(001). However, we will show later
that as the size of the FePt clusters increases the preferential adsorption of
the Fe species returns to the @$top$–O site after adding one Pt atom to the
cluster.

###  III.2 DFT structural relaxations

The main purpose of this work is to shed light on whether the magnetic
FePt–L10 alloy prefers to grow vertically or horizontally when it is supported
by the MgO(001) surface. If the magnetic alloy grows, covering the whole
surface, it is said that the FePt wets the MgO surface. In the other case the
L10–like structure will cover remain localised to region on the MgO surface
forming FePt–L10 “drops”. The most obvious means of determining whether the
FePt wets the MgO would be to simulate large extended structures to determine
the preferential growth. However, such calculations would be extremely
computationally expensive and beyond the scope of this paper. Instead, we have
used only a representative number of ultrasmall FexPty clusters with different
sizes and structures, ranging $x$ and $y$ from 1 to 2. As we will see, we will
fix some atoms of the clusters @$top$–O on the MgO surface and will move
others in order to scan different adsorption positions, keeping the same
number of the total atoms in the cluster. As we pointed out in section III.1
we have used four MgO planes and the $c32$ supercell for all the calculations.
The FexPty clusters and the first two MgO planes were allowed to move freely
during the optimization, keeping the atoms of the last two planes fixed to
their bulk positions. The final forces on the atoms involved were less than
0.03 eV/Å.

####  III.2.1 Dimers on MgO

Figure 1: (Color online) Variation of the total energy of an FePt dimer
supported on an MgO surface with the angle of the dimer bond, $\theta$
(measured from the normal to the MgO plane). In (A) the Fe side of the dimer
is closer to the MgO surface and the dimer is initially placed vertically. The
scans take place in two different planes: (011) (full blue triangles) and on
(101) (empty green circles). In (B) the Pt atoms are placed closer to the
surface and the scans are carried out as in (A). In both figures the total
energies are plotted relative to the minimum energy for each arrangement (E0A
and E0B). The solid lines are a guide for the eye.

Figure 1 summarizes the total energy profile of the FePt dimer adsorbed onto
the MgO surface as a function of the angle $\theta$. As the schematic
adsorption geometries insets show in the figure, the $\theta=0^{\circ}$
corresponds to the first configuration, that is when the dimer lies just
out–of–plane with respect to the MgO surface; the following total energy
values were calculated at $10^{\circ}$ intervals along a circular trajectories
on the (011) and (101) rotation planes, depending on whether the farthest Fe
or Pt atom was conducted to lie @$top$–O (green empty circles) or @$top$–Mg
(blue full triangles), respectively. This ensures that we checked two possible
adsorption sites for the outermost atoms. In addition, and based on the
convergence test in section III.1, we calculated two possible adsorption
configurations depending on whether the Fe or Pt atoms lie @$top$–O, Fig. 1(A)
and (B), respectively. Each calculation fixes the dimer bond value and only
the angle is changed at each step. To construct the $\theta=0^{\circ}$
configuration, the distance between the O and Fe or Pt atom was optimized
moving away and approaching the dimer to the surface. The minimum of the
quadratic energy curve gives the Fe/Pt bond distance between the atoms and the
O site.

Figure 2: Schematic representation of the initial configurations for the
different adsorption positions of the Fe2Pt and Fe2Pt2 clusters on MgO(001)
surface, left (A–E) and right (A–E), respectively. The side (top) views are
depicted in the upper (lower) row. In this schematic picture of the adsorption
of the FexPty clusters on MgO surface only the Fe species are directly in
contact with the surface via the O atoms. However, along the text, the study
of the Pt species on the MgO surface have also taken into account.

Consider first the A arrangement, where the Fe is situated on @$top$–O. The
dependence of $E$ on angle is shown for the cases of Pt moving towards Mg and
O sites. The rotation toward the @$top$–O site gives generally a monotonic
increase, albeit with a local minimum close to 90 deg. The global minimum
occurs for Pt rotating toward the top Mg site at an angle of around 60 deg. In
comparison, the case B arrangement has a local minimum at 0∘, i.e with the
dimer oriented perpendicular to the MgO plane. We note that the energies are
plotted relative to the minimum energy, and that E${}_{0A}<$ E0B. Thus the
global minimum for all configurations occurs for the A arrangement with Pt
rotated toward the Mg site.

In general, although in this case we only have a dimer on MgO and we are far
from the FePt bulk phase, we note that the angle is close to the FePt–L10 bulk
phase ($\approx 46^{\circ}$). This is a first attempt to discriminate how the
FePt–L10 grows onto the MgO alloy.

####  III.2.2 Trimers and tetramers on MgO

In the next step we increase the number of atoms in the FePt cluster to three,
four and so on. Figure 2 shows the schematic configurations of the initial
Fe2Pt (left) and Fe2Pt2 (right) adsorbed clusters onto the MgO(001) surface.
In both cases we have labeled them from A to E, though it should be noted that
they appear in no particular order. In the picture we only show the
configurations in which the Fe atoms are fixed to the O sites. Those in which
the Pt atoms are fixed in the same way as the Fe have also been studied, but
they are not shown in figure 2. The furthest Fe(Pt) atom from the surface in
Fe2Pt(Fe2Pt2) was placed at several adsorption sites on the surface in order
to scan the total energy dispersion and enable us to discriminate the
preferential growth type of the FePt–L10 onto MgO alloy.

Among all the configurations, A would represent a vertical growth, whilst the
others correspond to the FePt atoms wetting the MgO. Within the four B–E
geometries we will discriminate how far the Fe/Pt species prefer to lie from
each other while the FePt alloy grows. For instance, in the Fe2Pt B and C
geometries, the Pt atom is located @$top$–Mg or @$hollow$ site, respectively.
The remaining two settings accommodate the second Fe closer (D) or farther (E)
from the first Fe fixed @$top$–O. Similar situations are depicted for
tetramers (B–E). The starting configurations for the trimer were constructed
as follows: keeping the best dimer geometry, i.e., $60^{\circ}$ we added one
more atom further away from the surface in A and at different sites for the
remaining places (B–E). It is worth mentioning that, as we showed earlier in
III.2.1, when the Pt atom was closer to the O site the best configuration was
vertical, so we would expect the lowest energy to be obtained by adding the
next Pt to this dimer. However, since we want to compare quantitatively the
total energies of similar geometries, initially we placed this additional Pt
atom at the same position as the previous one. In the case of the tetramer we
had to proceed more carefully because more initial configurations were
possible. In order to reduce them we just inspected some. In Fg. 2(left)
configuration (A), we added one Fe/Pt, atom following the usual construction
of a hypothetical FePt–L10 unit cell. In the remainder we only placed the
Fe/Pt in different sites. Again it must be pointed out that additional
possibilities will arise when the number of atoms increases, but the aim of
the present study is to have an initial indication of how the FePt “covers”
the MgO so that a few reasonable geometries would in principle be enough.

After the relaxation, the shapes of all the initial geometries were kept, just
some of the atoms in FePt2–C and Fe2Pt2–A (Fe-terminated) moved away from
their initial sites. These structures are marked in Fig. 3 with black arrows.
In the first case, the Fe located @$hollow$ initially, moved to lie just
@$top$–Mg, and in the second, the initial geometry is broken having finally
each Pt atom @$top$–O/Mg keeping the Fe atoms @$top$–O.

In principle, the higher the adsorption energy, the more stable the structure.
In this respect, we observe that the FePt2/Fe2Pt–E geometries correspond to
the highest Eads and they should be the most stable. However, we have to take
into acount that in the $trimer$–E cases one of the Fe/Pt atom is located
farther away with respect to the other FePt structure and it could be treated
as an “isolated” atom added to the $dimers$. So, as we pointed out in table 1,
whether one Fe or Pt atom is adsorbed onto a $c32$ supercell using four MgO
planes the Eads takes the value 2.29 eV for Fe and 3.62 eV for Pt. Roughly, we
can subtract these values from those in Fig. 3 and we would get the values of
$\approx$2.0 eV for FePt2 and $\approx$1.5 eV for Fe2Pt. This immediately
would indicate that these configurations would not belong to those
preferential geometries for the FePt on MgO and we can discard them from the
preferential growth modes. We justify this conclusion by comparing the
distances between Fe/Pt pairs in E and the other configurations. In E, the
Fe–Fe distance is 4.3 Å and 4.71 Å for Pt–Pt. The calculated Fe–Fe bond
distance for the other geometries is around 2.4Å and 2.8Å for the Pt–Pt.
Furthermore, if we focus on, for example, the B configuration that has a
mediated Fe or Pt atom, the distances are 4.1Å and 3.7Å, for Fe–Fe and Pt–Pt,
respectively. In Fig. 3 the blue and green dashed lines represent the
connection between the D and E adsorption energies in the case that we would
assume the previous behaviour. It is then interesting to note that the three
B, C and D geometries have almost a similar adsorption energy values
indicating that the $trimers$ preferentially spread on MgO instead of growing
vertically. As we pointed out, the preferential adsortion is when Fe atoms are
closer to the MgO as the blue line shows.

The Eads for the $tetramers$ shown in Fig. 3(right) tends to corroborate our
argument from the previous paragraph, namely, that from B up to E geometries
the adsorption energies increases with respect to A, indicating a
predisposition of the Fe/Pt atomic species to lie onto MgO, covering the
surface. It is worth nothing that the E configuration for $trimers$ is not
present for $tetramers$ due to the fact that we scanned a limited number of
geometries as we pointed out before. The blue line in figure 3(right) shows
that the $tetramers$ follow the same trend as the $trimers$, having the higher
adsorption energies to those which the Fe atoms are in contact with the Mg
surface. We observe in B, C, D and E an oscillation in the Eads but its
dispersion is only about 0.5 eV. An additional study of the geometry, as for
example the bond and angle distances, would explain the origin of this
oscilation, but this study is beyond the scope of the current work. However,
we will compare the cohesive energy of the clusters in their gas phases with
respect to those adsorbed onto the MgO surface in order to check the
stability.

Figure 3: (Color online) Diferent adsorption positions prior to the adsorption
energy. Left: Fe2Pt and FePt2 $trimers$, blue empty and filled green diamonds,
respectively. The blue and green dashed lines represent the hypothetical link
between the D and E configurations after subtracting the adsorption energy of
the isolated Fe or Pt atom; Right: Fe2Pt2 $tetramers$, blue empty and green
filled squares whether the first contact atoms is Fe or Pt, respectively. The
black arrows show two configurations that changed substantially after the
relaxations.

In Fig. 4 is shown the cohesive and $intracluster$ binding energy of each
cluster adsorbed at different $i$ sites before and after the adsorption onto
the MgO surface, empty and filled symbols, respectively. The comparison of
these binding values will give an idea of the stability of the clusters upon
the adsorption and also which of them presents more stability at the surface.
The binding energies were calculated following the equations:

$E_{coh}^{G}(i)=-[E_{G,i}^{T}-n_{Fe}E_{Fe,i}^{T,G}-n_{Pt}E^{T,G}_{Pt,i}]/N,$

for the gas phases (G), and by:

$E_{intra}^{A}(i)=-[E^{T}_{A,i}+(N-1)E_{C,i}^{T}-n_{Fe}E_{Fe,i}^{T,A}-n_{Pt}E^{T,A}_{Pt,i}]/N$

after the adsorption (A). $E_{G,i}^{T}$ is the total energy of the free
cluster, $E^{T}_{A,i}$ is the total energy of the system upon the adsorption,
$E_{C,i}^{T}$ is the total energy of the clean MgO surface,
$E_{Fe/Pt,i}^{T,G}$ is the total energy for an isolated Fe or Pt atom,
$E_{Fe/Pt,i}^{T,A}$ is the total energy for the surface on which the Fe or Pt
atom is adsorbed, $n_{Fe,Pt}$ are the number of each specie in the cluster and
$N=n_{Fe}+n_{Pt}$ is the total number of atoms in the cluster. The values of
the $E^{T,A}_{Fe/Pt,i}$ were calculated after performing a self consistent
(SC) calculation and keeping the closest Fe or Pt atom @$top$–O/–Mg as they
were in the final relaxed configuration in the $trimers$ and $tetramers$. The
total energy of the clean surfaces, $E_{C,i}^{T}$, was calculated by removing
the cluster from the relaxed structures.

Figure 4: (Color online) Cohesive (gas phases) and $intracluster$ binding
energies (supported) as a function of the different adsorption positions for
the $trimers$ and $tetramers$, left and right graphs, repectively. Empty
symbols depict the Ecoh for the clusters after remove them from the MgO
surface and the filled ones the $intracluster$ energy after the adsorption.

It is clear that the clusters in their gas phases are more stable than those
adsorbed onto the MgO surface since the energy has reduced by an average value
of 1.5 eV for the $trimers$ and 2.0 eV for the $tetramers$. In this respect
the $tetramers$ present a slightly higher stability as indicated by the fact
that the bigger the cluster, the more stable the structure. There is no
significant difference in the cohesive and binding energy depending on whether
the Fe or Pt atom is in contact with the surface. In general, the most stable
configurations after the adsorption, are B and C for $trimers$ and
$tetramers$. As we pointed out, these geometries would correspond to an
initial covering of the MgO (See Fig. 2). However it is worth mentioning that
the competition between the adsorption on the surface and cohesion among the
atoms in the clusters is an important feature of the FexPty/MgO system.

###  III.3 Charge analysis and Magnetic Moments

Figure 5: Left: Reduction of the magnetic moment, $\Delta MM=MM^{G}-MM^{A}$,
per atom (black squares) and charge transfer per atom (grey circles) as a
function of the A to E geometries for $trimers$ (first row) and $tetramers$
(second row). Right: Spin-up (down) projected density of states, DOS↑(↓), for
the Fe2Pt-C and Fe2Pt2(Fe-term)-C configurations, upper and lower two figures,
respectively. Thick solid line represents the projected DOS for the adsorbed
clusters and the thin solid lines those in gas phases. The DOS units are as
usual in states/eV.

In this section we address the Mulliken population analysis of each
configuration to identify any charge transfer between the cluster and the
surface atoms. The magnetic moment values (MM) were obtained by subtracting
the spin–up from spin–down populations. As we will see, upon adsoprtion, the
net MM values of the $dimers$ and $trimers$ are reduced compared to the gas
phases. The mechanisms that promote this change have two different origins:
geometric and electronic. A rearrangement of the atoms in space after the
ionic relaxation would imply a variation in the population of the cluster’s
states changing the net MM values. However, after comparing the initial and
final geometries there were no significant changes in the shape of the
clusters, so we argue that the geometric disposition of the atoms does not
influence too much the MM values so that the dominating contribution is most
likely to be purely electronic. We separate the electronic part into two
contributions: the first one sets up a charge transfer from the cluster to the
surface, depopulating its states. The second, an $intra$–cluster rearrangement
of the spin–up and spin–down charges internally increases the up or down
population at the expense of the other. The gas phases of the adsorbed
clusters present higher values of their total MM than those upon adsorption.
Figure 5 presents, on the left, the reduction in the MM values (full black
squares) for the $trimers$ and $tetramers$ (upper and lower row respectively)
as a function of the A to E geometries. The total charge transfer per atom
from the clusters to the surface (grey filled circles) is also shown. On the
right we have plotted the up and down density of states (DOS) for the Fe2Pt–C
and Fe2Pt2(Fe–term)–C geometries as representative examples. As we distinguish
in the figure, not all the configurations after the adsorption present this
reduction, in particular Fe2Pt–(B,D) and FePt2–(A,B). The reduction will be a
complex balance due to the $intra$–cluster spin–up/down charge transfer and
also the surface to cluster charge transfer.

The reduction of the MM is not principally caused by the charge flowing
between the cluster and surface in all the cases but it is due to the
$intra$-cluster electron displacements as well. On the right, the DOS↑ for the
Fe2Pt–C and Fe2Pt2(Fe–term)–C configurations show a hump below the Fermi level
for the gas phases (grey thin solid line) around $-$0.5 eV for the first case
and at $-$0.2 eV for the second. Upon the adsorption these peaks move to the
conduction band implying a reduction in the up states. Part of this charge
moves to the O sites and passes internally to the down states. The down states
of the adsorbed clusters show a slightly different shape in the DOS compared
to those in gas phases. As we demonstrated the charge balance between the
cluster and the surface is quite complicated, nonetheless our data allow a
useful initial attempt to explain its behaviour.

In table 2 we summarize the MM/at values of all the configurations for the
magnetic and the nonmagnetic species of the clusters as well as the total
value in bold on the third column of each type of cluster configuration. For
the $trimers$, the Fe2Pt–$i$ configurations have higher MM values than those
of the FePt2–$i$ due to the presence of two magnetic atoms instead of only
one. The Fe2Pt shows the same MM values except the C configuration that has
0.56 $\mu_{B}$/at lower. More significant is the change for FePt2 wose MM
value, depending on the adsorption site, can vary by up to 0.57 $\mu_{B}$/at.
Coversely the trimers present the same MM values for all the adsorpion sites.
Upon inspection of table 2 and figure 3 we can conclude that there is no
strong relationship between the magnetic behaviour and the adsorption
energies.

Table 2:  Magnetic moment (MM) values in $\mu_{B}$/at of all the clusters deposited onto the MgO(001) surface as well as those obtained for the corresponding bulk alloys using the FR-PP formalism The first column displays the adsorption configurations, A–E, as well as the bulk. The MM values in the first and the second column of each kind of adsorbed geometry have been calculated by means of the equations MMM/NM and MMNM/NNM, respectively, whereas in the text, M refers to the magnetic atoms and NM to the non-magnetic ones. The third column shows MMtot/Ntot. | Fe2Pt |  |  | FePt2 |  |  | Fe2Pt2(Fe-term) |  |  | Fe2Pt2(Pt-term)
---|---|---|---|---|---|---|---|---|---|---
Configuration |  | M |  | NM |  | Total |  |  |  | M |  | NM |  | Total |  |  |  | M |  | NM |  | Total |  |  |  | M |  | NM |  | Total
A |  | 3.53 |  | 0.84 |  | 2.63 |  |  |  | 4.09 |  | 0.54 |  | 1.72 |  |  |  | 3.55 |  | 0.41 |  | 1.98 |  |  |  | 3.63 |  | 0.33 |  | 1.98
B |  | 3.64 |  | 0.65 |  | 2.64 |  |  |  | 4.12 |  | 0.82 |  | 1.92 |  |  |  | 3.39 |  | 0.60 |  | 2.00 |  |  |  | 3.72 |  | 0.30 |  | 2.01
C |  | 2.97 |  | 0.30 |  | 2.08 |  |  |  | 3.77 |  | 0.16 |  | 1.36 |  |  |  | 3.36 |  | 0.61 |  | 1.99 |  |  |  | 3.85 |  | 0.18 |  | 2.01
D |  | 3.61 |  | 0.67 |  | 2.63 |  |  |  | 3.85 |  | 0.53 |  | 1.63 |  |  |  | 3.44 |  | 0.52 |  | 1.98 |  |  |  | 3.73 |  | 0.31 |  | 2.02
E |  | 3.67 |  | 0.56 |  | 2.63 |  |  |  | 3.83 |  | 0.11 |  | 1.35 |  |  |  | 3.50 |  | 0.46 |  | 1.98 |  |  |  | 3.69 |  | 0.33 |  | 2.01
bulka |  | 3.12 |  | 0.18 |  | 1.65 |  |  |  | - |  | - |  | - |  |  |  | - |  | - |  | - |  |  |  | - |  | - |  | -
Bulk-Othersb |  | 2.96 |  | 0.34 |  | 1.65 |  |  |  | - |  | - |  | - |  |  |  | - |  | - |  | - |  |  |  | - |  | - |  | -
a LS-paper  , b galanakis . |  |  |  |  |  |

##  IV Conclusions

We have performed an extensive survey of an ampler set of adsorption positions
of the FexPty ($x,y\leq 1,2$) ultrasmall clusters on MgO(001). To evaluate the
preferential adsorption geometry of FePt on MgO we have calculated the
energies associated with the adsorption of $dimers$, $trimers$ or $tetramers$.
Furthermore, for each cluster size and shape we kept the Fe or Pt atom
@$top$–O and moved the outermost ones onto several MgO sites. The schematic
configurations are depicted in Fig. 2. The structural analysis shows that the
best adsorption geometries among all those studied are those in which they
covered the surface avoiding vertical growth, and thereby promoting the
wetting of MgO by FePt. After the adsorption, the $intracluster$ energy has
decreased by 1.5 eV and the the net MM reduces its values for all the
configurations at the expense of a depopulation of the Fe up–$d$ states,
transfering part of this charge to the Pt atoms and externally to the O sites.
We acknowledge that the charge balance as well as the Eads is a complex issue,
however our study shows that the overall conclusion is that the FePt wets the
MgO(001) surface. However, we also note that this is an initial study
investigating the fundamental interaction potential between FePt and MgO. At
non–zero temperatures the degree of wetting will be determined by a surface
free energy, which requires molecular dynamics calculations and is beyond the
scope of the current paper. However, the configurations studied here suggest a
promising starting point for the calculation of the relevant n–body
contributions to the FePt/MgO interaction potential which the MD calculations
will require.

Finally, the complex charge transfer processes at the FePt–cluster/MgO
interface predicted here might be expected to be reflected in changes in the
FePt MAE after the adsorption onto the MgO surface. However, this is an
interesting possible effect, which is beyond the scope of the present work but
certainly worthy of further investigation.

##  V Acknowledgments

The authors are grateful to Dr. Matthew I. J. Probert, Dr YK Takahashi and Dr.
T. J. Klemmer for helpful discussions. The financial support of the EU Seventh
Framework Programme under Grant No. 281043, FEMTOSPIN is gratefully
acknowledged.

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