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Epitaxial Fe films on ZnSe(001): effect of the substrate surface reconstruction on the magnetic
anisotropy
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2012 J. Phys.: Condens. Matter 24 236006
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IOP PUBLISHING
JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 24 (2012) 236006 (6pp)
doi:10.1088/0953-8984/24/23/236006
Epitaxial Fe films on ZnSe(001): effect of
the substrate surface reconstruction on
the magnetic anisotropy
S Tacchi1 , O Grånäs2 , A Stollo1,6 , M Madami1 , G Gubbiotti1,3 ,
G Carlotti1 , M Marangolo4 , M Eddrief4 , V H Etgens4,5 , M K Yadav2 ,
L Nordström2 and B Sanyal2
1
CNISM, Unità di Perugia—Dipartimento di Fisica and Università di Perugia, via A Pascoli,
I-06123 Perugia, Italy
2
Department of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
3
Instituto Officina dei Materiali del Consiglio Nazionale delle Ricerche (IOM-CNR), Sede di Perugia,
c/o Dipartimento di Fisica, Via A. Pascoli, I-06123 Perugia, Italy
4
Institut des NanoSciences de Paris, UPMC, CNRS UMR 7588, 4 place Jussieu, F-75252 Paris Cedex 5,
France
5
Fédération Lavoisier Franklin, Université de Versailles Saint-Quentin-en-Yvelines (UVSQ),
45 avenue des États Unis, F-78035 Versailles Cedex, France
E-mail: [email protected]
Received 12 November 2011, in final form 18 April 2012
Published 11 May 2012
Online at stacks.iop.org/JPhysCM/24/236006
Abstract
It is well known that Fe films deposited on a c(2 × 2)-reconstructed ZnSe(001) surface show a
strong in-plane uniaxial magnetic anisotropy. Here, the effect of the substrate reconstruction
on the magnetic anisotropy of Fe has been studied by in situ Brillouin light scattering. We
found that the in-plane uniaxial anisotropy is strongly reduced for Fe films grown on a
(1 × 1)-unreconstructed ZnSe substrate while the in-plane biaxial one is nearly unaffected by
the substrate reconstruction. Calculations of magnetic anisotropy energies within the
framework of ab initio density functional theory reveal that the strong suppression of
anisotropy at the (1 × 1) interface occurs due to complex atomic relaxations as well as the
competing effects originating from magnetocrystalline anisotropy and dipole–dipole
interactions. For both sharp and intermixed c(2 × 2) interfaces, the magnetic anisotropy is
enhanced compared to the (1 × 1) case due to the further lowering of symmetry. The
theoretical results are in agreement with the experimental findings.
(Some figures may appear in colour only in the online journal)
1. Introduction
Fe/ZnSe(001) has proved to be a very promising system. In
fact, thanks to the small lattice mismatch between Fe and
ZnSe and the low chemical reactivity between these two
materials, it is possible to grow epitaxial bcc (100) Fe films
of good crystallographic quality, without the formation of
magnetically dead layers at the interface [2, 3]. In previous
studies, it has been experimentally observed that, at the
initial stage of the epitaxial growth, Fe films deposited
on a ZnSe(001) surface exhibit a strong in-plane uniaxial
magnetic anisotropy (UMA) instead of the expected biaxial
In the past decade, hybrid ferromagnetic/semiconductor
(FM/SC) heterostructures have been extensively investigated
due to their potential applications in the field of spintronics,
where a ferromagnetic material is used to generate spinpolarized currents inside a semiconductor [1]. In this context,
6 Present address: Archimede Solar Energy s.r.l., Pisciarello 88, Villa San
Faustino, 06056 Massa Martana, Italy.
0953-8984/12/236006+06$33.00
1
c 2012 IOP Publishing Ltd Printed in the UK & the USA
J. Phys.: Condens. Matter 24 (2012) 236006
S Tacchi et al
Figure 1. LEED patterns of a Fe film 1 nm thick, taken at (a) 42 eV and (b) 90 eV.
for various cases by modeling interfaces between a thin
film of Fe and (1 × 1), sharp c(2 × 2) and mixed c(2 ×
2) ZnSe substrates, taking into account the effect of the
atomic relaxations properly. In agreement with experiments,
we found that the atomic relaxation has a weak effect on the
UMA for both sharp and mixed c(2 × 2) interfaces, whereas
it reveals a strong reduction of the uniaxial anisotropy for the
(1 × 1) ZnSe surface.
anisotropy arising from the lattice symmetry [4]. Theoretical
investigations of the Fe/ZnSe interface properties have been
performed to explain the origin of such an anisotropy, being a
critical issue for understanding the interfacial spin transport
process [5–7]. There are two major views regarding the
uniaxial anisotropy at the interface, namely (i) the chemical
bonding between Fe and ZnSe [8] and (ii) the anisotropic
strain [9] induced at the interface. Calculations for ideal
unreconstructed systems indicated that the uniaxial anisotropy
stems from the hybridization between the Fe layer with the
ZnSe layers below the interface [8]. In these calculations,
however, the optimized geometries of the interfaces between
the metals and semiconductors, e.g., Fe/ZnSe, were not
properly considered. In particular, the effect of the structural
modifications due to atomic relaxations at the interface has
been neglected.
In a previous work [10], the Brillouin light scattering
(BLS) technique has been exploited by some of us to
study the in-plane anisotropy of ultrathin Fe films deposited
on a c(2 × 2)-reconstructed ZnSe(001) surface. A strong
UMA, of interface origin, with the easy axis along the
[110] in-plane direction, has been found in films thinner
than about 2 nm. On increasing the film thickness, the
uniaxial anisotropy contribution decreases, while the expected
biaxial anisotropy of bulk Fe, with the easy axis along the
[100] in-plane direction, appears and becomes the dominant
one. In this study, we present a further step towards a
comprehensive understanding of the physical origin of the
magnetic anisotropy at the Fe/ZnSe(001) interface by a joint
experimental and theoretical study. The magnetic properties
of ultrathin Fe films deposited on a (1 × 1)-unreconstructed
ZnSe substrate have been studied by in situ BLS, paying
attention to the effect of the surface reconstruction of the
ZnSe(001) substrate on the magnetic anisotropies of the Fe
film. It is found that the in-plane uniaxial anisotropy is
dramatically affected by the substrate reconstruction, while
the biaxial one remains almost insensitive. In particular, the
UMA is nearly completely suppressed and retains a constant
value as a function of the film thickness. To explain the
above experimental data, we have performed ab initio density
functional theory to calculate magnetic anisotropy energies
2. Sample preparation and structural
characterization
Fe films were deposited on a substrate consisting of 10 nm
thick ZnSe layer, grown on a GaAs (001) buffer by molecular
beam epitaxy (MBE) at the Insitut des Nanosciences de Paris,
following the procedure described in previous works [11].
This substrate was protected with Se capping layer to permit
the transfer of the specimen to Perugia University. Here, the
sample was introduced into the ultrahigh vacuum chamber,
decapped by heating at T = 423 K for 30 min and then
heated up at T = 570 K to obtain a (1 × 1)-unreconstructed
ZnSe surface and finally cooled down to room temperature. Fe
films were deposited by means of electron beam evaporation
at a pressure of about 2 × 10−9 mbar, while the substrate
was kept at room temperature. The evaporation rate, typically
0.1 nm min−1 , was monitored by means of a quartz
microbalance. The structural surface characterization of the
deposited films has been performed by low energy electron
diffraction (LEED). In figure 1, LEED patterns relative
to the 1 nm thick Fe film are shown. Similar to the Fe
layers deposited on the c(2 × 2)-reconstructed ZnSe surface,
the Fe films grow with a well-ordered bcc(001) surface
(with the [100] Fe direction parallel to the [100] ZnSe
one), characterized by a c(2 × 2) reconstruction due to Se
segregation at the Fe surface. These findings indicate that
the crystallographic structure of Fe films is unaffected by the
reconstruction of the ZnSe substrate.
2
J. Phys.: Condens. Matter 24 (2012) 236006
S Tacchi et al
Figure 2. Brillouin spectra of the 2 nm thick Fe film, taken at
different values of the applied magnetic field applied along the
[110] direction. The incidence angle of light is 20◦ .
3. Brillouin scattering results
Magnetic characterization of the Fe films has been performed
by in situ BLS analysis. About 200 mW of monochromatic
light from a single-mode diode-pumped solid state laser
operating at λ = 532 nm was focused onto the sample
surface, using a camera objective of numerical aperture 2 and
focal length 50 mm. The back-scattered light was analyzed
by a Sandercock-type (3 + 3)-pass tandem Fabry–Perot
interferometer. The external magnetic field was applied
parallel to the film surface and perpendicular to the plane of
incidence of the light. A complete characterization of Fe films
has been achieved by systematic BLS measurements of the
spin-wave frequency as a function of: (i) the intensity of the
applied magnetic field (H), (ii) the in-plane direction of the
applied magnetic field with respect to the [100] direction of
the GaAs(001) substrate (φH ) and (iii) the angle of incidence
of light (θi ). This latter corresponds to change the magnitude
of the in-plane component of the wave vector q = 4π(sin θi )/λ
entering into the scattering process.
In figure 2, a sequence of BLS spectra relative to the
2 nm thick Fe film, taken at different values of the magnetic
field applied along the [110] direction, is shown. In addition
to the dominant peak, due to the elastically scattered light,
the so-called Damon–Eshbach (DE) spin-wave mode [12]
is clearly seen on both sides of the spectrum. Due to the
relatively low values of the film thickness, only this mode
is present in the spectra, characterized by a remarkable
Stokes–anti-Stokes intensity asymmetry, typical of magnons
in thin ferromagnetic films of absorptive materials [13]. The
Figure 3. Spin-wave frequency of Fe films having thicknesses of
1 nm (upper panel) and 2 nm (lower panel), as a function of the
in-plane direction of the applied magnetic field relative to the [100]
reference axis. The field intensity is 1.0 kOe while the incidence
angle of light is 20◦ . Filled points refer to Fe films deposited on an
unreconstructed ZnSe(001) surface, while open points refer to the
previously studied c(2 × 2)-reconstructed surface [10]. The
continuous curves are the results of the best-fit procedure to the data.
dependence of spin-wave frequency on the in-plane direction
of the applied magnetic field is shown in figure 3 for the two
samples studied. The measurements performed in the previous
study for two Fe films of identical nominal thickness grown on
the c(2 × 2)-reconstructed ZnSe surface are also reported for
comparison. As can be seen, the in-plane uniaxial anisotropy
is reduced when Fe is deposited on the unreconstructed
ZnSe(001) surface, instead of the c(2 × 2)-reconstructed
ZnSe one. To better quantify the effect of the substrate
reconstruction, a best-fit procedure of the experimental data to
the calculated frequencies was performed, using the analytical
expression of the DE mode frequency in the ultrathin
film approximation [10, 14]. This procedure enabled us to
determine both the phenomenological in-plane uniaxial (K2 )
and in-plane biaxial (K4 ) anisotropy constants, describing
the uniaxial (2K2 /MS ) and the biaxial (2K4 /MS )anisotropy
field, respectively. Concerning the out-of-plane anisotropy, it
was not possible to obtain an independent evaluation of the
phenomenological out-of-plane anisotropy constant Kout and
3
J. Phys.: Condens. Matter 24 (2012) 236006
S Tacchi et al
Table 1. Effective magnetization and magnetic anisotropy
constants of the Fe films, determined by the best-fit procedure of the
BLS data. The values obtained in the previous study [10] for Fe
films deposited on a c(2 × 2)-reconstructed ZnSe(001) surface are
reported for comparison in the parentheses.
d
4π Meff
(nm) (kOe)
2
1
Kout
K2
K4
105 (erg cm−3 ) 105 (erg cm−3 ) 105 (erg cm−3 )
13.4 ± 0.4 68 ± 3
(12.8 ± 0.3) (73 ± 1)
9.9 ± 0.6 85 ± 5
(7.4 ± 0.9) (100 ± 10)
0.5 ± 0.3
(1.2 ± 0.1)
0.5 ± 0.2
(2.3 ± 0.2)
2.3 ± 0.2
(2.4 ± 0.1)
0.8 ± 0.4
(0.5 ± 0.2)
of 4πDMS (where D is the demagnetizing factor), because
these two parameters are strongly correlated. Therefore,
the effective magnetization 4π Meff = 4π DMS − 2Kout /MS ,
which results from a competition between the saturation
magnetization and the out-of-plane anisotropy field, has been
estimated, providing information about the strength of the
out-of-plane anisotropy. We assumed a value of 4π DMS =
21.4 kG (the bulk Fe value) and 20.4 kG for the 2 nm
and the 1 nm thick film, respectively, following quantitative
results on the profile of the magnetization of Fe films at the
ZnSe(001) interface [3]. The exchange stiffness constant and
the effective gyromagnetic ratio have been fixed to the values
A = 2.0 × 10−6 erg cm−1 and g = 1.85 × 107 Hz Oe−1 ,
respectively.
The obtained values of the anisotropy constants are
shown in table 1. In the parentheses, the values obtained
in the previous study for the Fe films grown on c(2 ×
2)-reconstructed ZnSe surface are reported. As can be seen
in the case of Fe films deposited on the unreconstructed
ZnSe substrate, the in-plane uniaxial anisotropy is strongly
reduced and assumes a very small value as a function of the
Fe thickness. In contrast, the biaxial anisotropy increases with
the Fe thickness and it is almost unaffected by the different
surface reconstructions of the substrate. Finally, we found that
the out-of-plane anisotropy is slightly reduced in the Fe films
grown on the unreconstructed ZnSe substrate.
Figure 4. Lowest Fe layer and three substrate layers of the three
cases used to model the structure. Structure 1 refers to the full
coverage 1 × 1, while structures 2 and 3 depict the c(2 × 2) with
sharp interface and intermixed Fe, respectively. Only half of the unit
cell for a c(2 × 2) lateral cell is shown to compare with the 1 × 1
interface. The labels FeB , FeN and FeI refer to the bonding,
non-bonding and intermixed positions of Fe. Labels Bi refer to bond
nr. i, as refereed in table 2. Light blue arrows indicate the buckling
trend of the interface atoms. The figure has been made by VMD
software [17].
4. Theoretical calculations and discussions
In order to understand the effect of the interface structures on
the magnetic anisotropies, we have performed calculations for
three model cases. As calculations of the magnetocrystalline
anisotropies from first-principles demands very high accuracy,
the computational cost limits the size of these model systems.
The structures depicted in figure 4 represents possible
interface configurations likely to occur in this system, 1 ×
1 sharp, half-coverage sharp c(2 × 2) and half-coverage
c(2 × 2) with Fe intermixed. The unreconstructed samples
have full coverage and are likely to consist mainly of the
1 × 1 sharp structure (structure 1 in figure 4), the c(2 × 2)
reconstruction results in half-coverage, hence the interface
structure will, to a large extent, consist of the c(2 × 2)
sharp and intermixed model systems. The computational unit
cell consists of eight layers of Zn and Se with the lowest
layer passivated by pseudo-hydrogen atoms to terminate the
dangling bonds. Three monolayers (MLs) of Fe are used in all
three models. The geometries were optimized by minimizing
the Hellmann–Feynman forces in the projector augmented
wave method in the Perdew–Burke–Ernzerhof generalized
gradient approximation as implemented in the Vienna ab
initio simulation package (VASP) [15]. The lowest Se and
Zn layers are fixed in their bulk positions, allowing the
rest of the unit cell to relax towards a bulk-like structure.
Magnetic anisotropy energies (MAEs) were calculated by
the full potential linearized muffin tin orbital (FPLMTO)
method [16] using the optimized geometries obtained
from VASP calculations. The force theorem approach was
4
J. Phys.: Condens. Matter 24 (2012) 236006
S Tacchi et al
Table 2. Calculated bond distances showing the relaxation of the
interface. The calculated bulk ZnSe bond is 2.49 Å. Note that the
non-bonding Fe site in structure 2 and 3 is equivalent, but due to the
difference in the underlying layer the bonds B2 and B4 are
inequivalent. This inequivalence gives rise to a stripe-like relaxation
pattern in the [100] direction.
Bond
Sharp
1 × 1 (Å)
Sharp
c(2 × 2) (Å)
Intermixed
c(2 × 2) (Å)
B1 :Zn–FeN
B2 :FeN –FeB
B3 :Zn–FeB
B4 :FeN –FeB
B5 :FeI –FeB
B6 :FeI –FeN
2.57
2.45
2.62
n/a
n/a
n/a
2.62
3.19
2.69
2.57
n/a
n/a
2.53
3.02
2.62
2.74
2.38
2.38
considered to calculate MAEs by taking the difference in
the sum of the eigenvalues along different crystallographic
directions. We have checked the convergence of MAE with
respect to k-points in the Brillouin zone. Our calculations
suggest that one needs a k-mesh of 80 × 80 × 1 to achieve the
convergence for the (1 × 1) interface while a 16 × 16 × 1 set
is sufficient for a c(2 × 2) interface. The contribution from the
classical interaction between the magnetic dipoles is summed
using Ewald’s technique.
We briefly discuss here the optimized geometries of
the interfaces as these have been discussed in the literature
before [5]. At the interface between Fe and ZnSe, one
can classify two different types of Fe atoms, one (FeB )
bonded to Zn following the stacking order of zinc blende
structure and the other (FeN ) which is not bonded. The
bond lengths for different interfaces are listed in table 2.
The sharp 1 × 1 interface shows a minor relaxation with a
buckling of ∼0.05 Å in the interface Fe layer. A previous
work reported that the Fe–Se hybridization breaks the fourfold
symmetry, even without relaxation effects [8]. The models
based on the c(2 × 2) surface shows a dramatic increase in
the FeN –FeB bond distance, due to in-plane relaxations. FeN
are approaching the vacancy/FeI site resulting in a stripe-like
relaxation pattern, following the underlying c(2 × 2) surface.
As this is a more anisotropic environment, the large uniaxial
component arises for these models.
For the (1 × 1) interface, the system is almost isotropic,
hence a strong quenching of the uniaxial behavior is observed
in the calculations. The reduction of MAE is in agreement
with the experimental results, as seen in figure 5. The MAE
value of 2.5 µeV/interface Fe atom is on the verge of what is
possible to converge. It should be noted also that the classical
contribution from the dipole–dipole interaction opposes that
of the spin–orbit-induced contribution, reducing the uniaxial
behavior further. The value of the uniaxial anisotropy is much
reduced compared to that reported earlier [8]. This is due
to the consideration of complex atomic relaxations in the
present case involving a proper consideration of interplanar
separations and buckling effects in an atomic layer. However,
one should note that the qualitative understanding of the origin
of uniaxial anisotropy in terms of anisotropic interfacial bonds
remains unchanged though the quantitative estimates of the
anisotropy energies are influenced by geometry.
Figure 5. Calculated MAE versus in-plane angles for three
different model systems considered. NFe denotes the number of Fe
atoms at the interface.
For both sharp and intermixed c(2×2) interfaces, we have
found the easy axis to be in the [110] direction, as clearly
indicated by the position of the minimum at an in-plane
angle of 45◦ from the Cartesian axes in the plane. Once
again, this is in agreement with the experimental findings.
The corresponding MAEs are 29.2 and 75 µeV/interface Fe
atom. Note that the energies are much higher than the case of
a (1 × 1) interface. Also, the results indicate that intermixing
between Fe and Zn layers at the interface enhances the MAE.
The increase in MAE occurs due to the lowering of symmetry
at the interface. In the absence of atomic relaxations, the
intermixed Fe atoms are still in a quadratic environment in
a c(2 × 2) environment. This symmetry is, however, broken
by the relaxations of atoms due to different forces exerted
on them. Also, the proximity to the Se layer guarantees that
the hybridization is larger than in the two other model cases,
hence a large uniaxial contribution is expected. In the sharp
c(2×2) system, the voids give rise to relatively large buckling
effects, where the Fe atoms positioned above the voids buckle
upwards, giving rise to relaxations breaking the quadratic
positioning of the Fe atoms, resulting in a large uniaxial
component.
5. Conclusion
The magnetic properties of Fe films deposited on a (1 ×
1-unreconstructed ZnSe substrate have been studied by in situ
BLS measurements and compared to the case of deposition on
the c(2 × 2) surface. In both cases we found that the Fe films
grow with a well-ordered bcc(001) crystallographic structure.
Nonetheless the magnetic properties are strongly affected by
the substrate reconstruction. In particular, when the Fe films
are grown on a (1 × 1)-unreconstructed ZnSe substrate the
in-plane uniaxial anisotropy is strongly reduced, while the
in-plane biaxial one is unaffected by the ZnSe reconstruction.
The experimental results have been qualitatively interpreted
by ab initio density functional calculations. These provide
evidence of a significant suppression of the UMA for the (1 ×
1)-unreconstructed surface, thanks to the atomic relaxation as
5
J. Phys.: Condens. Matter 24 (2012) 236006
S Tacchi et al
well as the competing effects arising from magnetocrystalline
anisotropy and dipole–dipole interactions. In contrast, both
sharp and mixed c(2 × 2) interfaces yield a relatively large
uniaxial anisotropy due to the increased asymmetries in
bonding at the interface.
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Acknowledgments
We acknowledge the Swedish Research Council and Swedish
Institute for financial support and the Swedish National
Infrastructure for Computing (SNIC) for the allocation of
supercomputing time.
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