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J. Appl. Cryst. (2014). 47 doi:10.1107/S1600576714021049 1 of 10
Journal of
AppliedCrystallography
ISSN 1600-5767
Received 28 July 2014
Accepted 22 September 2014
# 2014 International Union of Crystallography
Self-organization of Fe clusters on mesoporous TiO2
templates
Patrick Ziegler,a Neelima Paul,b Peter Muller-Buschbaum,c Birgit Wiedemann,a
Wolfgang Kreuzpaintner,a Jaru Jutimoosik,d Rattikorn Yimnirun,d Annette Setzer,e
Pablo Esquinazi,e Peter Bonia and Amitesh Paula*
aTechnische Universitat Munchen, Physik Department E21, Lehrstuhl fur Neutronenstreuung,
James-Franck-Strasse 1, D-85748 Garching bei Munchen, Germany, bForschungs-Neutronenquelle
Heinz Maier-Leibnitz, Lichtenbergstrasse 1, 85748 Garching bei Munchen, Germany, cTechnische
Universitat Munchen, Physik Department E13, Lehrstuhl fur Funktionelle Materialien, James-Franck-
Strasse 1, D-85748 Garching bei Munchen, Germany, dSchool of Physics, Institute of Science and
NANOTEC-SUT Center of Excellence on Advanced Functional Nanomaterials, Suranaree University
of Technology, Nakhon Ratchasima 30000, Thailand, and eDivision of Superconductivity and
Magnetism, University of Leipzig, D-04103 Leipzig, Germany. Correspondence e-mail:
Fe layers with thicknesses between 5 and 100 nm were sputtered on mesoporous
nanostructured anatase TiO2 templates. The morphology of these hybrid films
was probed with grazing-incidence small-angle X-ray scattering and X-ray
reflectivity, complemented with magnetic measurements. Three different stages
of growth were found, which are characterized by different correlation lengths
for each stage. The magnetic behavior correlates with the different growth
regimes. At very small thicknesses the TiO2 template is coated and a porous Fe
film results, with in-plane and out-of-plane magnetization components. With
increasing thickness, agglomeration of Fe occurs and the magnetization
gradually turns mostly in plane. At large thicknesses, the iron grows
independently of the template and the magnetization is predominantly in plane
with a bulk-like characteristic.
1. IntroductionIn the pursuit of spintronic materials, suitable for devices that
are compatible with silicon technology, self-organized struc-
tures are often preferred. Self-organization (regular distribu-
tion) is a low-cost alternative way to fabricate materials
structured down to a few nanometres. It can result in inter-
acting magnetic memory dots which are suitable for spin
injection in semiconductors. Recently, Matthieu et al. (2006)
found a high-ordering-temperature (TC) ferromagnetic phase
in self-organized Mn-rich nanocolumns that are surrounded
by an Mn-poor matrix.
It is obvious that understanding the properties of metal–
oxide interfaces and their formation processes is of great
importance to optimize the characteristics of spintronic
devices. Depending on the preparation conditions and the
reactivity of the involved species, single metal atoms can
diffuse into the magnetic oxide and act as a dopant. However,
so far little work has been done on the growth and structure
development of metal layers on self-structured semi-
conducting oxides. The metal–semiconductor morphology
depends on the chemical interaction, the growth behavior and
the interface properties, which determine the diffusivity.
A promising way to achieve room-temperature ferro-
magnetism in ferromagnetic semiconductors was proposed by
Dietl et al. (2000) in the form of the so-called diluted magnetic
semiconductors (DMSs). Since then, there have been
numerous reports of ferromagnetic semiconductors, involving
a variety of semiconducting materials such as ZnO, SnO2, Ge,
GaN or GaAs doped with transition metals like Fe, Co, Mn, Ni
etc. (Kobayashi et al., 2005; Fitzgerald et al., 2006; Dumm et al.,
2000; Filipe & Schuhl, 1997). However, there are several
problems for these DMS systems as they suffer from
secondary phases (inhomogeneities), leading to magnetic
nanoclustering inside the semiconductor. Recent research
revealed that certain defects, like vacancies and/or atoms, help
to stabilize a magnetically ordered phase in several oxides
(Esquinazi et al., 2013). In particular, TiO2 has often been used
as wide-gap dilute magnetic oxide. Even though the rutile
phase of TiO2 is thermodynamically stable, it has a high
mobility of n-type charge carriers and a large thermopower.
In the present investigation we use nanostructured porous
(pore size about 20–50 nm) TiO2 network films as templates
for the self-assembly (random distribution) of Fe. The film
morphology is probed with grazing-incidence small-angle
X-ray scattering (GISAXS) (Naudon et al., 1998; Muller-
Buschbaum, 2003; Perlich et al., 2009). In principle, the TiO2
network is expected to restrict the mobility, forming a dot-like
mesh of Fe atoms. However, one should note that we are not
concentrating on achieving a high-TC dilute magnetic oxide in
this article; rather, we focus on the aspect of self-organization
of a magnetic metal on a structured semiconducting oxide film.
As a consequence, in the present case, the Fe thicknesses are
chosen to be so large that they cannot be considered as a
dilute species in the semiconductor. We focus on three
different stages of growth of the nanoclusters. Interestingly, we
find a direct correlation of the growth morphology and
structure with the magnetic response for these stages.
2. Sample preparation
The nanostructured templates used for depositing Fe films
were anatase TiO2 mesh-like structures. These TiO2 templates
were prepared on Si substrates using the block copolymer
assisted sol–gel method, which resulted in foam-like porous
titania network films. Details of this preparation method are
described by Cheng & Gutmann (2006) and Niedermeier et al.
(2012). Fe layers with five different thicknesses were grown on
top of the nanostructured TiO2 surface by magnetron sput-
tering. The corresponding samples are labeled as Fed, with d =
0, 5, 10, 20, 50 and 100 nm. We note that Fe layers with
thicknesses of �1–3 nm were also deposited on similar titania
templates (but grown with a different block copolymer base).
We exclude them in the present work since they do not exhibit
any magnetic response for the as-deposited specimens, as this
usually becomes apparent after annealing. During deposition,
the Ar pressure in the magnetron sputtering chamber was 3 �
10�3 mbar (1 mbar = 100 Pa). The process was started at a
base pressure of 5� 10�7 mbar. The Fe was deposited at room
temperature and at a rate of 0.07 nm s�1.
3. Experimental methods
The nanostructure at the sample surface has been probed with
scanning electron microscopy (SEM). Atomic force micro-
scopy (AFM) to identify the size and the structure and
magnetic force microscopy (not shown) to identify the
potential magnetic domains were also performed. The struc-
tures of the TiO2 template and of the Fe films on top of these
templates have been investigated with conventional X-ray
diffraction (XRD) methods. Thin-film characterization was
based on measurements using GISAXS, diffuse X-ray scat-
tering (XDS) and X-ray reflectivity (XRR).
We performed GISAXS measurements in noncoplanar
scattering geometry to map the lateral correlations using a
Ganesha 300 XL SAXS–WAXS system (SAXSLABApS,
Copenhagen, Denmark). The X-ray radiation was produced at
50 kV/0.6 mA from a Cu anode with a wavelength of � =
0.154 nm. The horizontal and vertical beam size was 0.4 and
0.3 mm with a divergence of 1 and 0.1 mrad, respectively. The
in-plane � were in the range of �1.15�. The chosen incident
angle of the X-rays of �i ¼ 0:5� was near the critical angle �c
for total reflection of our samples. A Pilatus 300K solid-state
two-dimensional photon-counting detector with a resolution
of 172 mm at a detector-to-sample distance of around 1.058 m
was used to record the intensity at room temperature. The
XDS and XRR measurements were performed with a D5000
instrument operating at 40 kV/40 mA from a Cu anode with a
wavelength of � = 0.154 nm.
X-ray absorption near-edge structure (XANES) spectra
were acquired at Beamline 5 (SUT-NANOTEC-SLRI) (with
electron energy of 1.2 GeV, bending magnet, beam current 80–
150 mA, 1.1–1.7 � 1011 photons s�1) at the Synchrotron Light
Research Institute (SLRI), Nakhon Ratchasima, Thailand.
The Fe K-edge spectra were measured in the fluorescent mode
with a four-element Si drift detector. A double-crystal
Ge(220) monochromator was used to scan the energy of the
synchrotron X-rays with the range of 7100–7200 eV and an
energy step of 0.2 eV for Fe K-edge XANES spectra. The
XANES region corresponds to the excitation of core electrons
to unoccupied bound states or to low-lying continuum states.
Thus, XANES provides information about the chemical
composition of the deposited Fe with various thicknesses.
Different scattering geometries at grazing incidence,
measuring specular reflection, scattering in the plane of inci-
dence and scattering perpendicular to the plane of incidence,
were employed. This way one can estimate the range of
accessible correlation lengths from the momentum transfers
along the three different axes owing to the scattering
geometry for small angles.
The total scattering vector is the difference of the wave-
vector of the incident beam and the scattered beam:
Q ¼ ki � kf; ð1Þ
Qx
Qy
Qz
0@
1A ¼ k
cos �f cos�� cos�i
cos �i sin�sin �i þ sin �f
0@
1A; ð2Þ
where �i is the incidence angle of the X-rays and �f is the angle
of the scattered wavevector k (k = |k| = 2�/�) in the xz plane.
Here � is the wavelength and � is the angle in the xy plane,
which is relevant to determine lateral correlation lengths. A
schematic of the GISAXS geometry is shown in Fig. 1.
XRR measurements only provide information on the
thickness and roughness of the layers, since the signal is
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2 of 10 Patrick Ziegler et al. � Self-organization of Fe clusters J. Appl. Cryst. (2014). 47
Figure 1Sketch of the typical scattering geometry for GISAXS measurementsfrom a sample. The sample is represented here by an atomic forcemicroscopy image of Fe100 in the QxQy plane and the correspondingdetector image in the QzQy plane.
independent of Qy and Qx because �i ¼ �f and � ¼ 0 in this
geometry. The corrections in these measurements are
obtained by longitudinal off-specular measurements (XDS) at
an offset angle (� ¼ 0:15�) of the specular direction. The
lateral components of the scattering vector Q are measured
using off-specular scans and GISAXS. The transverse scans
along Qx are measured as a function of Qz. Information about
horizontal structures was extracted from horizontal line cuts
from the two-dimensional GISAXS data, which were taken at
the position of the Yoneda peak (Yoneda, 1963), the maxima
of the Fresnel transmission coefficients.
Conventional in-plane and out-of-plane magnetization
loops were measured at various temperatures and fields using
a superconducting quantum interference device (SQUID)
from Quantum Design. The temperature dependence of the
magnetization was measured in a field of 10 mTafter zero-field
cooling (ZFC) and after field cooling (FC) in a field of 1 T.
4. Results and discussion
4.1. Scanning probe microscopy by SEM and AFM
The nanostructure of the substrate (Fe0) is shown in the
SEM image in Fig. 2(a). The surface indicates a very rough
texture, which is expected because the preparation process
leads to a random network structure (Kaune et al., 2009, 2010).
Fig. 2(b) shows a SEM image of Fe100 with identical magnifi-
cation. The surface looks smoother, indicating that the
template is poorly replicated in the case of the thick Fe layer.
Although the topography gets blurred, the distance between
the two brighter or sharper regions (�25 nm) remains of the
same order of magnitude.
The AFM image of Fe0, the pure titania surface, is shown in
Fig. 3(a), and as an example that of Fe100, the thickest Fe film
on the template, is shown in Fig. 3(b). The height of the
structure is roughly estimated to be h0 ¼ 33 (2) nm. Note that
h0 is fairly constant for all six samples, which means that there
are no filling effects caused by sputtering and the change in the
SEM images is due to a variation in their jaggedness only. A
Fourier transformation of the images, which is shown in
Figs. 3(c) and 3(d), indicates that the mesh-like titania struc-
ture does not have any well pronounced distances, as they
would be visible in the reciprocal space representation.
Instead, the titania templates are fairly isotropic. This isotropy
is maintained if Fe is deposited on top of the titania templates,
in particular for Fe100.
4.2. XRD, XRR and XDS measurements and analysis
Fig. 4 shows an example of the XRD data of Fe20, as a
representative deposited Fe film on the titania nanostructure
template. Note that all six samples are grown on identical
substrates using identical methods and values for deposition
and can be assumed as identical except for the layer thickness.
The data confirm the presence of Fe on a template which has
an anatase structure – a polymorph of TiO2 (Cheng &
Gutmann, 2006). The average grain size of the polycrystalline
Fe20 sample is calculated from the FWHM of the peaks in the
diffraction pattern as �1.98 nm for anatase TiO2 and 3.33 nm
([110]) and 25 nm ([100]) for Fe crystallites using the Scherrer
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J. Appl. Cryst. (2014). 47 Patrick Ziegler et al. � Self-organization of Fe clusters 3 of 10
Figure 2SEM images of (a) the pure anatase surface of TiO2 in Fe0 and (b) thesurface of Fe in Fe100 with the thickest Fe layer (100 nm). The thick Felayer leads to a blurring of the surface image. The insets show a zoomedportion of the images.
Figure 3AFM images of (a) the pure anatase surface of TiO2 in Fe0 and (b) thesurface of Fe in Fe100 with the thickest Fe layer (100 nm). CorrespondingFourier transformations of the AFM data, showing ring-shaped intensity,for (c) Fe0 and (d) Fe100, which have been analyzed to identify somesignature of a regular structure from that of a random structure.
Figure 4Representative XRD measurement of sample Fe20 with marked Braggpeaks of the Si substrate, of Fe 110 and of anatase TiO2 101. The jumps inthe intensity around the Si 400 peaks are due to misalignment of the beamwith respect to the substrate plane.
formula. Grains can often be agglomerates of many small
crystallites that are seen by XRD.
The XRR and the XDS data (scans along Qz) are shown in
Fig. 5(a) and the true specular data (off-specular corrected)
along with their fits in Fig. 5(b). Subtracting the longitudinal
offset data from the specular data gives cleaner specular data
(true specular) devoid of the off-specular contribution that
may have been included owing to possible relaxed resolution
along Qx. For most practical purposes it does not make any
significant difference in the fit parameters, particularly for
bilayer-type systems (unlike the case of a periodic multilayer
system) with small roughness, since the off-specular intensities
remain much lower than the specular part. The reflectivity
data were analyzed by means of a Parratt fitting routine used
to calculate the optical reflectivity following an iterative model
within the dynamic scattering theory (Parratt, 1954; Daillant &
Gibaud, 2009). The film was modeled as consisting of layers of
specific thickness, roughness and scattering length density
(SLD). An intermediate layer is not required, indicating that
there is little interdiffusion. The roughness is very high owing
to the nanostructure of the sample and physical information
about the roughness is irrelevant. The thickness of the anatase
titania layer [assumed from the sputtering rate to be da =
100 (10) nm] and SLD (estimated to be around 3.68 �
10�3 nm�2) were found to be very similar for all samples, as
shown in Fig. 6(a). A variation of thickness (which matches
quite well with the nominal ones) and SLD for the Fe layer
and the top oxide layer was obtained. The Kiessig oscillations
are very poor owing to the high roughness (�3.0 nm), which
can give some error in the estimation.
The information about the SLD (re�) or the electron
density (�) that can be extracted from the position of the
critical angle at the edge of total reflection (�2c = �2re�/�) can
also be used to determine the porosity � using the following
formula: � ¼ 1� �simul=�theory. Here re is the electron radius
and � is given by the atomic density (N) � the atomic number
(Z). The term SLD is generally used in the case of neutron
reflectivity but can be used for X-rays as well owing to its
expressional similarity. The porosity of Fe0 could be deter-
mined as � ¼ 0:56 for the TiO2 template. Compared with the
highest reported porosities of titania network-type nano-
structured films, which were prepared via a block copolymer
assisted sol–gel synthesis, this value is very moderate (Kaune
et al., 2009, 2010). For samples with Fe, the scattering length
density (�simul) is a mixture of the SLDs of Fe and its oxides
(FeO, Fe2O3, Fe3O4) along with Ti and its oxide (TiO2). It is
therefore difficult to differentiate the porosity of Ti from that
of Fe, as the corresponding critical angles are juxtaposed. The
variation of SLDFe has been plotted in Fig. 6(b), showing its
evolution as it approaches the bulk value of Fe (�5.8 �
10�3 nm�2).
The Qz versus Qx map for the example of sample Fe20 is
shown in Fig. 7. No Bragg sheet intensities along the hori-
zontal axis are seen, indicating no vertical correlation from
correlated interface roughness of the structure (Holy &
Baumbach, 1994; Daillant & Belorgey, 1992). A simulation of
the data was calculated within the distorted-wave Born
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4 of 10 Patrick Ziegler et al. � Self-organization of Fe clusters J. Appl. Cryst. (2014). 47
Figure 6(a) SLD profiles of the samples. (b) SLD profile of Fe layer versus dFe.
Figure 5(a) XRR and XDS data along with (b) the off-specular corrected (truespecular) data (symbols) and fits (solid cyan lines) calculated with theParratt algorithm to determine the SLD and the roughness of eachsample. The different samples are indicated as explained in the text. Thecurves are shifted along the intensity axis for clarity of the presentation.The XRR signals from Fe50 and Fe100 are particularly overshadowed bythe comparable off-specular signal from the underlying nanostructureeven at low angles, signifying their low reflectivity.
approximation (DWBA) according to the model of Ming et al.
(1993), yielding a lateral correlation length �k ’ 30 nm, as
shown in Fig. 8. This model describes an intermediate case
between vertically uncorrelated and vertically correlated
layers. It assumes that the vertical correlations do not depend
on the lateral size of the roughness.
4.3. XANES
Fig. 9 shows a comparison of the measured Fe K-edge
XANES spectra from the samples (solid symbols) and the
reference spectra from each of the possible constituents that
can produce the absorption edge, for example, Fe, FeO, Fe3O4
and Fe2O3. By considering Fe, FeO, Fe3O4 and Fe2O3 as the
parent components, the XANES spectra of the samples were
fitted (lines) with a superposition of XANES profiles of the
parent components using the linear combination analysis
(LCA) method. The fitting was performed using the package
ATHENA (Ravel & Newville, 2005) with the LCA tool. The
fits are shown in the figure together with the measured
XANES spectra. In this way we estimate the weighted
proportions of the constituents in the samples. They are
composed of phase-separated regions that differ negligibly in
the proportion of their respective constituents (Fe, FeO, Fe3O4
and Fe2O3) from sample to sample. The results indicate that
there are negligible traces of FeO in the samples. The main
constituents are Fe with proportions of Fe2O3 and Fe3O4. The
results can be seen in Table 1. The results show an obvious
trend of decreasing percentage of oxidation within the Fe
layer with increasing thickness of the layer.
4.4. GISAXS measurements and analysis
4.4.1. GISAXS measurements. Fig. 10 shows the two-
dimensional GISAXS data as reciprocal space maps Qz versus
Qy for all samples. The GISAXS measurements were taken at
�i = 0.5�. The reason for choosing an angle above the total
reflection edge was to allow the beam to penetrate the entire
film. One can expect to see the specular peak (S) and the
material-specific Yoneda peak (Y) well separated. Moreover,
other scattering features arising from possible correlations of
interfaces can be detected (Salditt et al., 1995; Muller-Busch-
baum & Stamm, 1998).
For an Fe layer thickness of 5–50 nm, the GISAXS patterns
show intensity modulations caused by resonant diffuse scat-
tering (due to scattering from the total thickness) (Lee et al.,
2008). For a further increase in thickness (�50 nm), no
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J. Appl. Cryst. (2014). 47 Patrick Ziegler et al. � Self-organization of Fe clusters 5 of 10
Table 1Overview over the percentage of iron oxide that has been determined byfitting the XANES measurements.
Sample Fe3O4 ratio (%) Fe2O3 ratio (%)
Fe5 43.4 35.3Fe10 39.9 13.1Fe20 21.1 2.5Fe50 14.1 0Fe100 8.1 0
Figure 8XDS measurement (solid symbols) on sample Fe20 for Qz = 0.8 nm�1,shown together with a simulation in the framework of the DWBA todetermine the lateral correlation length along Qx. The positions of theYoneda wings (Y) are indicated with arrows. The mismatch in the widthof the specular peak is due to multiple surfaces of the nanostructures andthe resolution limit of the detector.
Figure 9XANES measurements (symbols) of all samples and corresponding fitsbased on different proportions of Fe oxides. The curves are shifted alongthe y axis for clarity of the presentation.
Figure 7Example of a two-dimensional Qz–Qx map of sample Fe20 measured inX-ray diffuse scattering geometry. The light-blue lines indicate thepositions of the Yoneda wings and the yellow line is the Qz position at0.8 nm�1, where a line cut has been extracted.
intensity modulations are visible as they are no longer resol-
vable with the used setup.
The Yoneda peaks are well resolved in all cases as �i = 0.5�
has been chosen. The vertical position of the Yoneda peak
(Y = �f + �c) moves towards higher angles with increasing Fe
thickness, indicating the increased loading with Fe. If the
samples had had well defined lateral structures, well defined
side maxima of the Yoneda peak would be visible in the
horizontal direction of the two-dimensional GISAXS data.
Since there are no such side peaks visible, we can exclude a
high degree of ordering of the nanostructures (e.g. no well
defined nearest neighbor order). Instead of such peaks, the
intensity that we see is broadly spread out in the horizontal
direction in all cases. This is due to the presence of well
resolved lengths scales for structures with a lower degree of
ordering.
4.4.2. GISAXS analysis alongQz. Vertical line cuts from the
two-dimensional GISAXS data (intensity profiles along Qz at
Qy = 0) are shown in Fig. 11 for all six samples. The main
features are the sharp specular peaks and broad Yoneda peaks
for the respective material constituents. With an increase in
the Fe film thickness, the critical angle is gradually shifted till it
reaches �c ’ 0:4�. Fig. 11 shows the evolution of �c with the Fe
layer thickness. Note that the critical angle obtained from the
GISAXS data, for example in the case of Fe20, is very similar
to that obtained from the XRR data (Qz ’ 0.64 nm�1). The
position of �c saturates at an Fe thickness of around 30 nm,
which approximately matches the height (h0) of the template.
By analyzing the difference in the Yoneda position between
Fe0 and Fe100 one can see that there is a superposition of two
distinct Yoneda peaks. One Yoneda peak arises from the
anatase titania network film (marked with an arrow pointing
downwards) and another one from the Fe deposited onto this
film (marked with arrows pointing upwards). From the
Yoneda peak positions one can determine the porosity of the
Fe films on titania. Since the variation of the position of the
Yoneda peak shifts with Fe thickness, we restrict the calcula-
tion to Fe0 only.
The porosity of Fe0 from the position of the Yoneda peak in
the GISAXS pattern gives � ¼ 0:61, which is similar to that
determined by XRR.
4.4.3. GISAXS analysis along Qy. Horizontal line cuts from
the two-dimensional GISAXS data (intensity profiles along
Qy) were taken at the Yoneda peak position of Fe for each
sample. These line cuts are shown in Fig. 12 on a log–log scale,
together with a fit to determine the lateral structure lengths.
The Yoneda wings arise because of the increase in scattering
caused by the maxima in the Frensnel transmission function
and are thus a signature of the overall roughness. The diffuse
scattering along the peak position is due to the regularity of
the nanostructures. The horizontal line cuts do not show well
pronounced maxima but have a broad distribution. Thus the
samples exhibit a distribution of small-scale lateral structures.
Because the polycrystalline material probed here is on top
of a mesoporous material, one can choose the model of
supported islands. In the first approximation, the form factor
of the host material is well represented by a cylindrical model
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6 of 10 Patrick Ziegler et al. � Self-organization of Fe clusters J. Appl. Cryst. (2014). 47
Figure 11Vertical line cuts from the two-dimensional GISAXS data, which havebeen extracted at the position Qy = 0. The arrows mark the Yoneda peaksof the anatase (down arrow) and the Fe structure (up arrows). Theintensity is normalized with respect to the Fe0 data. The line cuts areplotted with an offset for clarity. In the inset we plot the variation of �c,depicting its dependence on the Fe layer thickness. The dash–dot linerepresents the �c value of the anatase phase of TiO2.
Figure 10Two-dimensional GISAXS data measured at an incident angle of �i =0.5� for all samples. All images show the same color scale and an equalarea of the detector. The specular peak (S) and the Yoneda (Y) peak areindicated by arrows in each case.
and the structure factor by a Percus–Yevick three-dimensional
type with a local monodisperse approximation of size distri-
bution consisting of two coexistent dominant length scales. For
the Fe deposits on top, although the island sizes are rather
irregular, the assumption of cylindrical particles fits to the data
very well. The peak shape of the Qy profile is a convolution of
the form factor and structure factor involved. The form factor
was considered to be cylindrical, and the cluster size (2R) and
the intercluster distance (�) were taken as the fitting para-
meters. A Gaussian distribution of R was allowed in the fits. A
schematic of the model geometry is shown in Fig. 13.
The fits to the data were done using the effective surface
approximation (ESA) of the DWBA (Muller-Buschbaum,
2009) and are shown in Fig. 12. We have considered an
assembly of two isolated cylinders with radii R1 and R2. The
details of the model used here can be found elsewhere (Sarkar
et al., 2014). The parameters that have been extracted from the
fit are shown in Table 2. For the anatase phase we assume a
cylinder of radius R1 with a correlation length �a (or �R1) in
our model. For Fe, we consider another cylinder of radius R2
with a correlation length �Fe (or �R2). Initially we found �a =
160 (12) nm, while �Fe shows some variation with the thickness
of the Fe film.
The correlation of Fe can be divided into three regimes.
Regime I is for thickness up to 5 nm, regime II is between 10
and 20 nm, and region III is beyond 20 nm. In regime I, Fe
takes a form similar to the underlying anatase template. Note
that the Fe with a cylinder of radius R2 is different from the
underlying cylinder with radius R1. It has a smaller correlation
length (�R2 <�R1) than the template. This is a stage of surface
bonding of Fe to the template. The atoms do not agglomerate
with other atoms because of their low mobility, as the template
radius R1 increases marginally after Fe is deposited, probably
owing to some imbalance in the deposits.
For the next stage, in regime II, we find increasing surface
coverage with the onset of agglomeration. Thus, a drastic
decrease in �R2 (from 80 to 30 nm) occurs as the atoms
agglomerate. However, this does not affect the correlation
length of the underlying template. This trend continues until
Fe20.
In regime III, a slight increase in R2 along with the lateral
correlation length (�R2) is observed for samples beyond Fe50.
In this regime the structures become independent of the
template, as the Fe layer matches the average height of the
underlying TiO2 template, h0, which is �30 nm. With
increasing Fe adatoms the layer grows in height with packed
grains. A schematic of the growth process at different stages is
shown in Fig. 14.
4.5. Magnetization measurements
4.5.1. Magnetization versus field. Fig. 15 shows the SQUID
hysteresis loops at T = 5 K and T = 300 K for Fe5–Fe100. The
diamagnetic signal from Fe0 is subtracted from the hysteresis
loops. The applied field is parallel to the film plane. The
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J. Appl. Cryst. (2014). 47 Patrick Ziegler et al. � Self-organization of Fe clusters 7 of 10
Figure 14Schematic of the Fe layer growth process. Three different stages ofgrowth are identified and indicated in the figure. The thickness dFe wasdetermined from XRR, while the average height h0 is estimated from theatomic force microscopy images.
Figure 12Horizontal line cuts from the two-dimensional GISAXS data for allsamples are plotted in a log–log presentation. The fits to the data (cyanlines) are also shown.
Table 2Overview over the lateral correlation lengths that has been determinedby fitting the vertical line cuts of the two-dimensional GISAXS data.
Sample�R1 (�a) (nm)� 12
R1 (nm)� 2.5
�R2 (�Fe) (nm)� 3.0
R2 (nm)� 0.7
Fe0 160 19 NA NAFe5 150 21 80 6.4Fe10 150 14 30 5.7Fe20 150 14 29 5.7Fe50 200 20 40 7.5Fe100 200 20 42 8.3
Figure 13Sketch of the cylindrical model used for analyzing the GISAXSmeasurements with cluster sizes (2R1, 2R2) and intercluster distances(�R1, �R2).
hysteresis loops of Fe50 (green curve) and Fe100 (orange curve)
show a classical ferromagnetic behavior of bulk iron. Note that
the magnetic moment for bulk Fe is 2.2 B per atom (Billas et
al., 1993). The slight increase in moment of Fe20 (2.4 B per
atom) seen in the figure for Fe20 (magenta curve) could
originate from the comparable sizes of the grain and dFe
(Tiago et al., 2006). This can be compared with the reduced
moment and higher saturation fields for Fe5 (red curve) and
Fe10 (blue curve).
The lowering of magnetic moment with thickness could be
caused by a demagnetization factor due to lowering of the
thickness and/or loss of neighbors. One may note that the
saturation field increases with lowering of thickness. It varies
from around 60 mT (Fe100) to 300 mT (Fe5) when measured at
5 K in the film plane. This gives an indication that the easy
direction of magnetization is gradually turning out of plane.
We plot in Fig. 16 the out-of-plane magnetization for the Fe5
sample at 5 and 300 K. A saturation moment, comparable to
the in-plane moment, is clearly evident in the out-of-plane
measurement as well. This indicates the demagnetization
effect in the film plane with the lowering of thickness.
4.5.2. Magnetization versus temperature. The coercivity of
the samples exhibits a typical ferromagnetic behavior and is
shown in Fig. 17 for Fe5 and Fe100 as representatives of two
stages of growth. The decrease in coercivity with decreasing T
for Fe5 is possibly due to the out-of-plane orientation of
magnetization which freezes at low temperatures. A similar
kind of enhancement and drop of coercivity with temperature
has been reported previously (Xu, 2007). The origin for the
anomalous temperature dependence of the coercivity is not
well understood, but some of the hints provided in that work
may also apply in our case, namely the surface anisotropy and
stress distribution, especially at the near-surface region. The
coercivity for Fe100, on the other hand, remains monotonic.
The temperature dependence of the magnetization (FC and
ZFC) is shown in Fig. 18 for Fe5, Fe20 and Fe50. The curves
beyond Fe50 are very similar. They also show a ferromagnetic
behavior. The change in the profiles could possibly be due to
the magnetization component turning out of plane for lower
Fe thickness. This is evident as we follow the ZFC curves,
where the magnetic moment at low temperature (below
150 K) is seen to increase gradually with Fe thickness. The
grains (kinetically arrested) are not rotating similarly with
temperature for different thicknesses. Furcation of ZFC and
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8 of 10 Patrick Ziegler et al. � Self-organization of Fe clusters J. Appl. Cryst. (2014). 47
Figure 18Plots of FC and ZFC out-of-plane magnetic moment with temperature forsamples (a) Fe5, (b) Fe20 and (c) Fe100 as representatives of the threeregimes of growth. The applied in-plane field was 10 mT.
Figure 16Out-of-plane magnetization measurements of the Fe5 sample at 5 and300 K.
Figure 15Magnetization measurements of all samples with a magnetic layer for (a)5 K and (b) 300 K. The field sweeps have been done up to 1 T, but thefield range has been zoomed for clarity around the coercive fields. Adashed line indicating the bulk Fe magnetic moment is shown forcomparison.
Figure 17Temperature dependence of the coercivity of the in-plane magneticmoment for samples Fe5 and Fe100 as representatives of the extremestages of growth.
FC shows some irreversibility but no signature of super-
paramagnetism (Hansen & Mørup, 1998). The ZFC curves
indicate a broad distribution of grain sizes which can be
inferred from the absence of a peak. These grains respond at
different temperatures, and there is no definite blocking
permitted. The in-plane moments at various temperatures
show an increase with the increase in thickness for the FC
curves.
In regime I, we find a significant out-of-plane component of
magnetization, even though the thickness of the Fe layer in Fe5
and Fe10 is large enough to turn the moments in plane. This
may be due to the high percentage of oxidation, which may
reduce the effective magnetic thickness drastically. We can see
a clustering type of effect as we follow the ZFC curve for Fe5.
However, this does not lead to superparamagnetism. It shows
thermal stability beyond 200 K. Most likely, the deposition
process of Fe on the mesoporous template leads to statistically
distributed magnetic anisotropy axes. The competition
between the anisotropy energy and the exchange interaction
can often lead to noncollinear spin structures (Fraile Rodrı-
guez et al., 2010). As a result, the magnetic moments of the Fe
islands have become canted by a certain angle.
In regime II, for Fe20, we find a transition of the out-of-
plane moments to in plane. This is expected as the agglom-
erated species start to form a complete layer. Note that the
oxidation of the Fe layer is limited to a few monolayers only.
The superparamagnetic behavior of the clusters is also absent
in this regime. In this regime, we can expect the competition
between the anisotropy energy and exchange interaction to
reduce a little as the exchange energy gains its strength from
the number of Fe agglomerates. This obviously increases the
magnetic moment to its maximum value. The net magnetiza-
tion of a cluster ensemble can be stabilized by interparticle
and particle–template interactions.
Beyond this regime (regime III), for Fe50, the magnetization
remains stable at low temperatures but shows thermal
instability beyond 150 K, typical of bulk-like characteristics.
The fact that we observe bulk-like moments in Fe nano-
particles reflects the fact that the exchange interaction clearly
dominates over the magnetic anisotropy energies in this
regime.
5. Conclusions
In conclusion, we report on the growth of Fe on a mesoporous
structure of titania anatase. We investigated the lateral and
longitudinal correlation of the Fe layers as a function of
thickness using XRR and GISAXS. We find three different
regimes of lateral correlation, which can be correlated with the
magnetic properties of the layer. According to our results,
regime I has a range of layer thickness up to 5 nm. The Fe
diffuses into the TiO2 anatase structure (leading to porous Fe).
However, the correlation length (80 nm) remains smaller than
the correlation length of the template (150 nm), indicating a
different mode of growth. The magnetization has in-plane and
out-of-plane components responding differently with a
variation of the temperature. Regime II includes layer thick-
nesses around 10–20 nm. In this regime we have a change over
from wetting to agglomeration on the semiconductor
template. This reduces the correlation length drastically to
around 30 nm. The magnetization gradually turns mostly in
plane. The third regime is above 20 nm. In this regime Fe
grows with a correlation length of approximately 40 nm. The
magnetization is predominantly in plane and the behavior and
moment value have a bulk-like characteristic.
The experimental results demonstrate the impact of the
deposition kinetics on the physical properties of supported
islands in the nanometric regime. The complex relation of
lateral structure, particle orientation and morphology raises
the question of exploring the same with single-particle sensi-
tivity. On the basis of these findings, we are confident that our
results will contribute to a further understanding of self-
assembly of Fe within nanostructured dilute magnetic oxides.
We would like to thank A. Bauer for his initial trial
magnetization measurements using the physical property
measurement system. This work was supported by the
Deutsche Forschungsgemeinschaft via the Transregional
Collaborative Research Center TRR 80 and partially
supported by the collaborative project SFB 762 ‘Functionality
Oxide Interfaces’. We thank Ezzeldin Metwalli for help with
setting up the GISAXS instrument. Martin Niedermeier is
acknowledged for his help in preparation of the TiO2
template. PMB acknowledges Nanosystems Initiative Munich
for funding.
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