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X-ray absorption spectroscopy on magnetic nanoscale systems for modern applications

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X-ray absorption spectroscopy facilitated by state-of-the-art synchrotron radiation technology is presented as a powerful tool to study nanoscale systems, in particular revealing their static element-specific magnetic and electronic properties on a microscopic level. A survey is given on the properties of nanoparticles, nanocomposites and thin films covering a broad range of possible applications. It ranges from the ageing effects of iron oxide nanoparticles in dispersion for biomedical applications to the characterisation on a microscopic level of nanoscale systems for data storage devices. In this respect, new concepts for electrically addressable magnetic data storage devices are highlighted by characterising the coupling in a BaTiO3/CoFe2O4 nanocomposite as prototypical model system. But classical magnetically addressable devices are also discussed on the basis of tailoring the magnetic properties of self-assembled ensembles of FePt nanoparticles for data storage and the high-moment material Fe/Cr/Gd for write heads. For the latter cases, the importance is emphasised of combining experimental approaches in x-ray absorption spectroscopy with density functional theory to gain a more fundamental understanding.
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1 © 2015 IOP Publishing Ltd Printed in the UK
Reports on Progress in Physics
C Schmitz-Antoniak
X-ray absorption spectroscopy on magnetic nanoscale systems for modern applications
Printed in the UK
062501
ROP
© 2015 IOP Publishing Ltd
2015
78
Rep. Prog. Phys.
ROP
0034-4885
10.1088/0034-4885/78/6/062501
6
Reports on Progress in Physics
X-ray absorption spectroscopy on magnetic
nanoscale systems for modern applications
CarolinSchmitz-Antoniak
Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), University of
Duisburg-Essen, Lotharstr. 1, D47048 Duisburg, Germany
Present address: Peter Grünberg Institute (PGI-6), Forschungszentrum Jülich, D-52425 Jülich, Germany
E-mail: carolin.antoniak@uni-due.de
Received, revised 5 December 2014
Accepted for publication 24 March 2015
Published 1 June 2015
Invited by Sean Washburn
Abstract
X-ray absorption spectroscopy facilitated by state-of-the-art synchrotron radiation technology
is presented as a powerful tool to study nanoscale systems, in particular revealing their static
element-specic magnetic and electronic properties on a microscopic level. A survey is given
on the properties of nanoparticles, nanocomposites and thin lms covering a broad range of
possible applications. It ranges from the ageing effects of iron oxide nanoparticles in dispersion
for biomedical applications to the characterisation on a microscopic level of nanoscale systems
for data storage devices. In this respect, new concepts for electrically addressable magnetic
data storage devices are highlighted by characterising the coupling in a BaTiO
3
/CoFe
2
O
4
nanocomposite as prototypical model system. But classical magnetically addressable devices are
also discussed on the basis of tailoring the magnetic properties of self-assembled ensembles of
FePt nanoparticles for data storage and the high-moment material Fe/Cr/Gd for write heads. For
the latter cases, the importance is emphasised of combining experimental approaches in x-ray
absorption spectroscopy with density functional theory to gain a more fundamental understanding.
Keywords: x-ray absorption spectroscopy, magnetic circular dichroism, magnetism,
nanoparticles, multiferroics
(Some guresmay appear in colour only in the online journal)
1. Introduction
Nanoscale systems comprise of components or structures in the
size range 1100 nm playing a fundamental role for advances
in medicine, biology, chemistry, physics, material science and
related elds. The beginning of the nanotechnology era was
marked by Faradays report on size-dependent optical proper-
ties of colloidal gold nanoparticles in 1847. Although the ruby
colour of Au nanoparticles had already been exploited in glass-
making in the ancient world, e.g. for the dichroic glass of the
famous Lycurgus cup, Faraday was the rst who published the
synthesis of Au nanoparticles and stated that, 'a mere variation
in the size of [gold] particles gave rise to a variety of resultant
colours [1]. Nowadays, this effect is explained by surface plas-
mon resonances [2] and is one example of the tunable physi-
cal properties of nanoscaled systems. In general, characteristic
properties may evolve due to the large surface-to-volume ratio,
different crystal structures and nite-size effects. It is a major
challenge in nanoscience to predict the physical and chemical
properties of new systems, and to tailor the material to serve
the desired purpose or function.
For the preparation of nanoscale systems, different approaches
are pursued that can be classied as top down and bottom
up methods, respectively, as depicted in gure 1. The former
describes the division of a massive solid into smaller portions e.g.
by the use of lithographic patterning or milling. Starting from
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0034-4885/15/062501+30$33.00
doi:10.1088/0034-4885/78/6/062501
Rep. Prog. Phys. 78 (2015) 062501 (30pp)
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2
bulk materials, which were coarsely grinded to micropowders,
high-energy ball mills, commonly equipped with grinding media
of steel or tungsten carbide, can be used to produce nanoparti-
cles. These particles are characterised by a broad size distribution
often accompanied by a broad shape distribution. A size selec-
tion may be performed e.g. by centrifuging the particles after
dispersing them in ethanol. Narrow size distributions, shape con-
trol and highly ordered arrangements of nanoscale objects can
be achieved by using lithography methods. The most common
technique in this eld is electron beam direct-write lithography.
Using this method, the nanopattern is written directly with the
electron beam on a polymeric resist that has been brought onto
the primary material, e.g. a thin lm grown onto a substrate.
Either exposed or non-exposed regions of the resist are subse-
quently removed. The resulting nanostructures of the resist lm
can be transferred to the material below by etching or ion sputter-
ing. Several other lithography methods are used, e.g. the classical
optical lithography, extreme ultraviolet or even x-ray lithography,
as well as ion beam lithography. A promising replication tech-
nique for nanopatterns is the nanoimprint lithography [3]. Several
other methods exist in the eld of lithography, the interested
reader may be referred to [4, 5] and references therein.
On the other hand, a special lithography, i.e. nanosphere
lithography [68], is a bottom up method. It uses micrometer-
sized spherical particles that self-assemble in a closed-packed
monolayer as an evaporation mask for the patterned growth
of nanoparticles. In general, bottom up methods are based
on molecular or atomic self-organisation producing size- and
shape-controlled nanomaterials and include gas-phase prep-
aration, chemistry and crystal growth techniques. All of the
nanoscale systems chosen in this work as examples are pre-
pared by bottom up methods, i.e. wet-chemical synthesis (sec-
tions 5.2 and 5.3), pulsed laser deposition (section 5.5) and
molecular beam epitaxy (section 5.4).
The organisation of this review is as follows: after a short
survey on nanomagnetism in section2, possible applications
of nanoscale systems in section 3 and on x-ray absorption
spectroscopy in section4, synchrotron radiation and experi-
mental methods, recent results relating electronic structure,
magnetism and ageing effects of iron oxide nanoparticles
for biomedical applications are presented in section5.2. For
future technological applications in data storage and record-
ing, a different Fe-based nanoscale system, i.e. self-assembled
ensembles of FePt nanoparticles, are discussed in section5.3 in
addition to the high-moment material Fe/Cr/Gd in section5.4,
nally presenting a prototypical model system for electric
addressable magnetic data storage media in section5.5. At the
end, a concluding summary and an outlook are given.
2. Basic concepts in nanomagnetism
This review focusses on magnetic nanoscale systems. To this
end, some special magnetic properties that are connected to
the small size of magnetic objects are discussed in this subsec-
tion. Mainly solid samples such as nanoparticles deposited on
a substrate and also some properties of ferrouids are briey
presented here. Details on magnetic phenomena beyond the
scope of this work can be found in e.g. the publication of
Bader [15] for opportunities in nanomagnetism, Vaz et al [16]
for a focus on the magnetism of ultrathin lms, Sander [17]
on magnetic anisotropy and spin reorientation in nanostruc-
tures, and Ramesh and Spaldin [18] on nanoscale multiferro-
ics. Here, we focus on the treatment of superparamagnetism
of ensembles of nanoparticles with a size distribution as it is
important for possible applications as magnetic data storage
media (see sections3.2 and 5.3) and the response to ac elds
important for biomedical applications (see sections 3.1 and
5.2). The key value for the applicability of nanoparticle sys-
tems is the relaxation time of the magnetisation which will be
introduced in the following.
In general, the magnetic anisotropy energy E
A
is the
energy needed to turn the magnetisation from its easy
direction into a hard direction of magnetisation, where
easy direction denotes a direction of magnetisation yield-
ing minimum ground state energy of the system and hard
direction for maximum ground state energy. In the absence
of external magnetic elds, the magnetic anisotropy energy
determines the direction of magnetisation forcing it to the
easy direction(s) of the magnetic system. Beside the mag-
netocrystalline anisotropy that couples the easy direction(s)
to the crystal lattice, shape anisotropy minimising magnetic
stray elds, and surface anisotropy caused by the break of
local symmetry at the surface, have to be taken into account,
especially in nanoscale systems. Deviations from a perfect
spherical shape of nanoparticles and different surface aniso-
tropies for different facets and edges are usually described
Figure 1. Schematic illustration of top down and bottom up methods for the preparation of nanoparticles.
Rep. Prog. Phys. 78 (2015) 062501
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3
by a uniaxial net anisotropy. This anisotropy combined with
interaction effects e.g. between nanoparticles in an ensem-
ble is subsumed under the concept of an effective anisotropy
energy density constant K
eff
with
=EKV
Ae
ff
(1)
where V is the particles volume. The volume dependence
of the magnetic anisotropy energy (MAE) E
A
gives rise to
the effect of superparamagnetism when the thermal energy
overcomes the energy barrier E
A
and the magnetisation is no
longer xed in one direction, but uctuates and the sample
appears to be a paramagnet [19]. The prex super originates
from the description of single domain nanoparticles carrying a
so-called macrospin as sum of all atomic spins. The macrospin
and its magnetic moment amounts to several 10
3
μ
B
which
is orders of magnitude larger than the magnetic moment in a
classical paramagnet.
From equation(1) it is obvious that the smaller the nano-
particle is, the lower the energy barrier and the lower the
temperature at which the magnetisation starts to uctuate.
This temperature is referred to as the blocking temperature
T
B
. Note that the blocking temperature is not just a material-
specic parameter, but depends as well on the time window
of the measurement method: if the time window for the
measurement of the magnetisation is smaller than the time
needed to ip the magnetisation, the uctuations cannot be
monitored and one would conclude that the blocking tem-
perature is at higher values than the actual sample tempera-
ture. If the measurement of the magnetisation is slower than
the time constant of the uctuations, the magnetisation is
reduced to zero without any magnetic eld applied and one
would conclude that the blocking temperature is below the
actual sample temperature.
The time constant for these uctuations is called Néel relax-
ation time τ
N
and was introduced in 1949 by Néel to explain
time dependent magnetisation effects in single-domain mag-
netic minerals [20]. Later, a more rigorous derivation of the
time dependence of the magnetisation uctuations was pub-
lished by Brown [21]. The Néel relaxation time of a single
domain particle is given by an Arrhenius law:
ττ τ==
Ek
TK
VkTexp[ /( )] exp[ /( )]
N0 AB 0eff B
(2)
where τ
0
is an intrinsic relaxation time in the range of 10
12
10
9
s for nanoparticles [21] and k
B
T is the thermal energy.
As described above, the blocking temperature is reached if
the time window of the measurement equals the Néel relax-
ation time τ
m
= τ
N
. In conventional magnetometry, e.g. using
a superconducting quantum interference device (SQUID), the
time window is in the order of τ
m
= 10
2
s yielding T
B
VK
eff
/
(30k
B
) with ln[τ
m
/τ
0
] = α
m
30. In conventional x-ray absorp-
tion spectroscopy the value of τ
m
is similar (1–10s) if the sig-
nal is averaged by the detection electronics.
For a monodisperse system of identical nanoparticles,
the magnetisation above T
B
in a magnetic eld H follows a
Langevin function L[x] = coth[x] 1/x with x = M
s
Vμ
0
H/
(k
B
T) that can be written for small magnetic elds and high
temperatures, i.e. x 1, as
μ
≈= MM
x
VM H
kT
TT
33
,
sp
s
s
2
0
B
B
(3)
Below the blocking temperature, the magnetisation depends
on the magnetic history of the sample: if it is cooled down
below T
B
in an applied magnetic eld (eld cooled, FC), the
magnetisation remains trapped at its value according to equa-
tion(3) with T = T
B
:
μτ
τμ
≈=M
VM H
kT
MH
K3
ln[/]
3
bl
sm
s
FC
2
0
BB
0
2
0
eff
(4a)
If the sample is cooled down in the absence of a magnetic eld
applied (zero eld cooled, ZFC), the magnetisation amounts to:
μ
M
MH
K3
bl
s
ZFC
2
0
eff
(4b)
It can clearly be seen by comparison between equation(4a)
or equation (3) on the one hand and equation (4b) on the
other hand that in the ZFC case the ferromagnetically blocked
nanoparticles are characterised by a magnetisation that is
smaller than the superparamagnetic particles close to T
B
. The
latter nanoparticles exhibit a magnetisation which is larger by
a factor α
m
= ln[τ
m
/τ
0
] 30. This was discussed as a thermally
enhanced susceptibility by Wohlfarth [22] and gives the possi-
bility to estimate the effective anisotropy for a known particle
size from conventional magnetometry quite reasonably.
However, equations(3)(4b) only hold for an ensemble of
identical nanoparticles with exactly the same size and shape. In
experiments, ensembles of nanoparticles exhibit a distribution
of volumes and, consequently, a distribution of blocking tem-
peratures. This was taken into account e.g. by Respaud et al
[23] for the simulation of ZFC and FC SQUID magnetometry
data. In this approach, the temperature-dependent magnetic
moment is described as a sum of magnetic moments of super-
paramagnetic and blocked particles including a log-normal
volume distribution D(V). The limit volume, i.e. the maximum
volume for a superparamagnetic particle at a given tempera-
ture, is dened according to equation(2) as V
lim
= α
m
k
B
T/K
eff
.
The different values of magnetisation and their temperature
dependences for the ZFC and the FC case can be written as:
μ
μ
+
m
MH
kT N
VD
VV
MH
KN
VD
VV
3
1
()d
3
1
()d
s
V
s
V
ZFC
2
0
B
0
2
2
0
eff
lim
lim
(5a)
μ
αμ
+
m
MH
kT N
VDVV
MH
KN
VD
VV
3
1
()d
3
1
()d
s
V
ms
V
FC
2
0
B
0
2
2
0
eff
lim
lim
(5b)
with a normalisation factor
=
N VD
VV
()d
0
. The rst term
represents the superparamagnetic fraction with small volumes
and is equal for both the ZFC and FC cases. The second term
represents the ferromagnetically blocked fraction with larger
volumes and is different by a factor of α
m
= ln[τ
m
/τ
0
] 30 as
Rep. Prog. Phys. 78 (2015) 062501
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4
described above. Note that in the literature, erroneous equa-
tions are used frequently, where the integrand for the super-
paramagnetic fraction is V D(V) instead of V
2
D(V) and for the
blocked fraction D(V) instead of V D(V), respectively. The miss-
ing factor of V originates from summing up the two contribu-
tions of the magnetic susceptibilities for superparamagnetic and
blocked particles without taking into account that the magnetic
moment is the additive quantity and not the magnetisation [23].
Simulations of ZFC and FC curves are presented in g-
ure2 for different volume distributions around the same mean
volume of V = 33.5 nm
3
that corresponds to a spherical shape
of the particle with a diameter of d = 7 nm. The standard devi-
ation of the volume distribution was chosen to be σ
V
= 0, 0.15,
0.30 or 0.45. The corresponding distributions of diameters
assuming spherical nanoparticles are characterised by σ
d
= 0,
0.05, 0.10 or 0.15 which is usually termed as monodisperse in
the literature. The effective anisotropy density constant was
chosen to be K
eff
= 2 × 10
5
J
3
and a small magnetic eld of
10 mT was used. The FC and ZFC curves were normalised to
the same magnetisation at high temperatures.
It can be clearly seen that even a very narrow but nite size
distribution yields a signicant softening of the formally sharp
transition at T
B
. Since the median volume and K
eff
is the same
as well as H and τ
0
, the median blocking temperature T
B
88
K is identical in all four cases. Note that the median block-
ing temperature is neither the temperature at which the ZFC
magnetisation is maximum (T
max
), nor the inection point of
the ZFC curve. At rst glance this nding seems trivial, but
in the literature no standard procedure to obtain T
B
can be
found as discussed e.g. in the work of Tournus and Tamion
[25]. However from our experience, the inection point is a
much butter approximation of the blocking temperature than
the temperature of the maximum ZFC magnetisation.
In an improved two states model, a transition temperature
between superparamagnetic and ferromagnetic behaviour is
introduced which can be formally written as
α
α
τ
T
KV
k
KV
kf
withln
B
eff
B
eff
0B
T
(6)
with an α that is now not dependent on the time window of
the measurement and intrinsic relaxation time as in the com-
mon two states model presented above, but is dependent on the
effective anisotropy constant, the volume and the experimental
temperature sweeping rate f
T
. In [25] the authors also point out
that the sharp transition for purely monodisperse nanoparticles
is just an artefact due to the simple model used. There exists
a natural width of the ZFC peak of about 10% [24, 25] which
is usually hidden behind the broadening caused by the volume
dispersion. Assuming that the natural broadening is negligible,
FC-ZFC magnetometry measurements can be used to extract
the volume distribution and, consequently, MAE and blocking
temperature distributions. Following equations(5a) and (5b),
the difference between FC and ZFC magnetisation is given by
αμ
Δ
=− =
mm m
MH
KN
VD
VV
(1)
3
1
()d
ms
V
FC ZFC
2
0
eff
lim
(7)
Further assuming that the distribution of anisotropy energies
arises directly from the volume distribution, we have D(E
A
)
dE
A
= D(V) dV. Using (1) one gets
αμ
Δ=
m
MH
KN
E
K
DE E
(1)
3
1
()d
ms
E
2
0
eff
A
eff
AA
lim
(8)
with E
lim
= K
eff
V
lim
= α
m
k
B
T. The rst derivative of ΔM with
respect to T reveals the MAE distribution. Using the chain rule
to calculate the derivative and omitting the constant prefactors
yields
α
α
Δ
∝− −⇒∝−
Δ
m
T
kT
K
DE DE
T
m
T
d
d
(1)()()
1d
d
m
m
2
B
2
eff
AA
(9)
The distribution of blocking temperatures can be deduced in
the same way, which leads to
Figure 2. Simulated normalised magnetisation of eld cooled (FC) and zero eld cooled (ZFC) magnetic moments of nanoparticle
ensembles with different standard deviations of log-normal volume distribution.
Rep. Prog. Phys. 78 (2015) 062501
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5
⇒∝
Δ
DT
T
m
T
()
1d
d
B
(10)
These relations, although not exact, can be helpful to get
an idea about MAE distribution and blocking temperature
distributions from experimental FCZFC curves. In the lit-
erature, again, one can nd erroneous or over-simplied
equationsomitting the factor 1/T or even neglecting the con-
tribution of the blocked particles. In [25] the deviations from
the real distributions behind a ZFCFC curve are analysed by
simulations and discussed in detail.
The uctuations of magnetic moments not only inuence the
quasi-static magnetic properties in conventional dc magnetom-
etry, but also the response to an alternating magnetic eld. When
the relaxation time of particles is longer than the period of an
applied ac magnetic eld, the rotation of the magnetisation lags
behind the changing external magnetic eld. As explained in the
work of Rosensweig [26], this means conversion of magnetic
work into internal energy and self-heating of the nanoparticles
occurs. The power dissipation can be written as [26]:
μχ ωμχω
ωτ
ωτ
==
+
PH H
1
2
1
21
()
0
2
0
2
2
(11)
where χ is the imaginary part of the magnetic susceptibility
χ, H is the amplitude of the ac magnetic eld, ω its angular
frequency and τ the relaxation time of the nanoparticle. If the
particle is still deposited on a solid substrate as claimed in
the beginning of this subsection, τ equals the Néel relaxation
time τ = τ
N
. If the particle is dispersed in a liquid, indispens-
able for any in vivo application, a second relaxation mecha-
nism occurs, i.e. the Brown relaxation that is responsible for
frictional losses. It describes the case when the magnetisation
direction is locked to a crystallographic axis and the whole
particle rotates to align the magnetisation with the external
magnetic eld. This relaxation time τ
B
depends on the viscos-
ity of the surrounding liquid η and the particle volume, more
precisely on the hydrodynamic volume V
h
that may be larger
than the geometric volume of the particle, according to:
τ
η
=
V
kT
3
h
B
B
(12)
The total relaxation time is given by
τ ττ=+
−−
1
N
1
B
1
. Heat may
be also generated in the particles by different power loss pro-
cesses such as hysteresis losses for blocked particles, induced
eddy currents or magnetic resonance phenomena. For ferro-
magnetically blocked particles, the hysteresis losses are given
by the area of the static hysteresis of eld-dependent mag-
netisation, which is proportional to the anisotropy. To obtain
substantial heating of the particles, highly anisotropic materi-
als should be used. However, in applications, the ac magnetic
eld amplitude is usually too small to magnetically saturate
hard magnets and, for minor hysteresis loops, the generated
heat is reduced. In addition, the hysteresis loop becomes sig-
nicantly narrower for an ensemble of nanoparticles with ran-
domly oriented crystallographic axes as is also the case for in
vivo applications, again, reducing the possible heating.
It has been shown in the experimental work of Hergt
et al [27], that the generated heat of superparamagnetic
nanoparticlesas described by equation (11)greatly
exceeds the value even for the best ferromagnetic sample
(extrapolated to 209 W
1
compared to 75 W
1
at H = 14 kA
m
1
and a frequency of 300 kHz). Inductive heating by eddy
currents can usually be neglected due to the small particle size
and magnetic resonance effects occur at very high frequencies
in the Hz range. However, for most of the applications for the
self-heating of nanoparticles, ac magnetic elds in the kHz and
MHz range are used as will be presented in the next subsection.
3. Modern applications of nanoscale systems
Nanoscale systems have generated much interest in various
elds of application. Their large surface-to-volume ratio makes
them suitable for efcient catalysis processes [9, 10] and sur-
face facetting offers the possibility for additional selectivity
in catalysis. The small size of nanoparticles is also useful for
in vivo applications in biology and medicine, as well as for
advanced device miniaturisation in technology. In this section,
we discuss recent progress in biomedical applications, before
we turn to the discussion of using magnetic nanosystems for
high density data storage devices and the fabrication of new
nanoscale materials for magnetic write heads.
3.1. Biomedical theranostics with iron oxides
Biocompatible iron oxide nanoparticles can be used e.g. as
contrast enhancers in magnetic resonance imaging (MRI) [11,
12], drug delivery, for cell labelling [13, 14] or in hyperthermia
cancer treatment. The latter was already successfully tested
for functionalised iron oxide nanoparticles and is approved in
the European Union for the treatment of brain tumours. The
iron oxide nanoparticlesγ-Fe
2
O
3
(maghaemite) or Fe
3
O
4
(magnetite)can be injected directly into a tumour; simi-
lar to a biopsy procedure, injected into the arterial supply of
tumour tissue, and/or it will be enriched at tumour sites by an
appropriate antibody-conjugation [29]. The latter is advanta-
geous, if the hyperthermia treatment must be repeated, while
the direct injection is usually connected to a higher local con-
centration of nanoparticles. A review on the use of iron oxide
nanoparticles in hyperthermia can be found e.g. in [30].
By application of an alternating magnetic eld, the parti-
cles generate heat according to equation(11) that may destroy
the surrounding cancer cells or support chemotherapies where
already a moderate tissue heating leads to a more effective
cell destruction [13]. This is schematically shown in gure3
for a brain tumour (brownish area). The key value to charac-
terise the efciency of hyperthermia treatment is the specic
absorption rate (SAR). It is a measure of the rate at which
energy is absorbed by the tissue when exposed to an alternat-
ing electromagnetic eld and is given by
==
P
m
c
T
t
SAR
d
d
i
(13)
where c
i
is the specic heat capacity of the tissue of mass m.
However, heating is reduced by blood ow and tissue perfu-
sion that is quite difcult to model. In order to enhance the
Rep. Prog. Phys. 78 (2015) 062501
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6
SAR value, high frequencies ω and large amplitudes H of the
alternating magnetic eld seem to be desirable according to
equation (11). But both values are limited to avoid unwanted
physiological responses such as arrhythmia, stimulation of
peripheral and skeletal muscles and a non-specic heating by
eddy currents induced in the tissue. As usable ranges of frequen-
cies and magnetic eld amplitudes ω = 0.3 1.2 × 10
6
s
1
and
H = 0 15 × 10
3
Am
1
were identied, respectively [13]. Since
heating by eddy currents is proportional to the square of the prod-
uct Hω, high values of both H and ω give rise to a non-localised
additional heating of healthy tissue. After doing experiments on
numerous persons, Atkinson et al recommend an upper limit for
the thorax, i.e. Hω 3 × 10
9
Am
1
s
1
or related to the ordinary
frequency H f 4.85 × 10
8
Am
1
s
1
[31]. For the extremities,
higher values of the product may be used.
Iron oxide nanoparticles can also be used as contrast agents
in MRI. This method is based on nuclear magnetic resonance
(NMR) which describes the resonant absorption of an alter-
nating magnetic eld applied perpendicularly to a static mag-
netic eld. Resonant absorption occurs if the frequency of
the alternating magnetic eld equals the Larmor precession
frequency of the nuclear magnetic moments. For MRI, usu-
ally NMR of hydrogen nuclei, i.e. protons, is used because
hydrogen is present in all biological tissues. For a static mag-
netic eld of μ
0
H = 1 T, the Larmor frequency of protons is
ω
L
267.54 × 10
6
s
1
or f
L
42.58 MHz, respectively.
The macrospin of the nanoparticles is connected to a large
magnetic stray eld that alters the relaxation time of the pro-
tons in the nearest environment. In general, there three dif-
ferent relaxation times exist: T
1
, T
2
and
T
*
2
. The longitudinal
relaxation time T
1
, is the decay constant for the recovery of
the nuclear spin magnetisation component along the direction
of the external magnetic eld towards its thermal equilibrium
value. It is commonly called spinlattice relaxation since it
involves the exchange of energy with its surroundings. It can
be signicantly shortened by paramagnetic Gd(III) complexes,
which are mostly used as MRI contrast agents. Thermal vibra-
tions of the magnetic metal ions yield an electromagnetic eld
that oscillates with a frequency corresponding to the energy
between the high-energy states (aligned with the external
magnetic eld) and thermal equilibrium increasing the rate of
stimulated emission and shortening T
1
as a consequence.
The transverse relaxation time T
2
is the decay constant for
the magnetisation component perpendicular to the external
eld and corresponds to a phase decoherence of the transverse
nuclear spin magnetisation. Since T
2
is affected only by the
dynamics of the nuclear spins, it is called spinspin relaxation
time. Magnetic eld inhomogeneities yield a distribution of
resonance frequencies resulting in a dephasing of nuclear spins
as well. The latter decay constant is denoted
T
*
2
. The use of
magnetic nanoparticles as contrast agents indirectly inuences
the T
2
and
T
*
2
relaxation. This gives rise to a higher contrast in
the spin echo MRI which is used as a method to visualise the
transverse relaxation behaviour. Besides biocompatibility, a
high net magnetic moment of the nanoparticles is an important
requisite for a high MRI contrast. Therefore, magnetite (Fe
3
O
4
)
nanoparticles are favoured over maghaemite (γ-Fe
2
O
3
) as con-
trast agents. However, when stored under ambient conditions,
Fe
3
O
4
oxidises towards γ-Fe
2
O
3
and the magnetic moment per
formula unit (f.u.) decreases according to [32]:
δμ
=−
m
f.u.
3.83
4
(42
),
s
B
(14)
where 0 δ 1/3 represents the degree of oxidation: Fe
3
O
4
is
characterised by δ = 0 and γ-Fe
2
O
3
by δ = 1/3. In section5.2,
an x-ray absorption study is presented on ageing effects of
Fe
3
O
4
nanoparticles dispersed in a solvent. As reported in [33]
as well, freshly prepared Fe
3
O
4
nanoparticles are further oxi-
dised to a more γ-Fe
2
O
3
-like state after three days.
3.2. High-anisotropic nanoparticles for magnetic
data storage
For technological applications at room temperature and
above, one crucial point is the thermal stability of magnetic
and electronic properties. To achieve a magnetisation that is
stable over ten years, i.e. τ 3 × 10
8
s, the ratio of anisotropy
energy to thermal energy should be around 4050 depending
on τ
0
. According to equation(2), the larger K
eff
, the smaller the
critical particle size for stable magnetisation at room tempera-
ture. Since FePt and CoPt are known for their large magneto-
crystalline anisotropy in the bulk material of their chemically
ordered phase (L1
0
crystal symmetry), these systems are
prime candidates for magnetic data storage using nanoparticle
ensembles. In a simple picture, the high magnetocrystalline
anisotropy is caused by the tetragonal distortion of FePt and
CoPt in the chemically ordered state along the stacking direc-
tion of atomic layers of Fe and Pt in combination with the
large spinorbit coupling in Pt.
The use of FePt nanoparticles as magnetic storage media
with the magnetisation direction of one single particle rep-
resenting one bit has been discussed for more than a decade.
However, there are still several obstacles that have to be over-
come. In particular, there seems to be a reduced MAE in the
nanoparticles with respect to the corresponding bulk material,
the arrangement of nanoparticles in dense regular superlat-
tices over large areas is not satisfactorily solved and the align-
ment of the easy axes of magnetisation is another delicate task.
Figure 3. In hyperthermia, magnetic nanoparticles are brought
into a tumour (brownish area) and heated by an external alternating
magnetic eld as schematically shown for a human brain. Used with
permission from MagForce AG [28].
Rep. Prog. Phys. 78 (2015) 062501
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7
Regarding the MAE, it has been reported that the L1
0
crystal
symmetry which is connected to the large MAE in the bulk
material is not energetically favourable for small FePt nano-
particles [34, 35]. In addition, the surface may disturb the
formation of a perfectly L1
0
ordered crystal structure and the
tendency of Pt to segregate at the surface has been investigated
for thin lms [36, 37] and nanoparticles [38, 39]. Regarding
the alignment of easy axes of magnetisation, an interest-
ing approach has been published by the group of Sellmyer
[40, 41]. They prepared nanostructured FePt/B
2
O
3
by magne-
tron sputtering on glass substrates. Annealing at 500 °C, which
is above the melting temperature of B
2
O
3
, yields an orienta-
tion of easy axes of the embedded FePt clusters. The mecha-
nism behind the orientation process is not fully understood yet
and discussed e.g. by Ichitsubo et al [42]. However, the strong
stress on the FePt nanoparticles produced by the surrounding
B
2
O
3
matrix reduces also the volume of the FePt unit cell that
is accompanied with a strongly reduced Curie temperature
[43]. Even if a successful orientation of nanoparticles with the
desired high magnetic anisotropy and a regular 2D arrangement
could be realised, high stray elds will be needed to reverse the
magnetisation of the nanoparticle in order to write a bit. A pos-
sibility may be heat-assisted writing by heating the nanoparticle
before writing to make the magnetisation reversal easier [44].
This is a delicate task since the heating has to be focussed on a
single nanoparticles area and may be quite energy consuming.
Another aspect for application of FePt nanoparticles is
the problem of oxidation: iron oxides may alter the magnetic
properties of the nanoparticles. A possibility to avoid oxida-
tion is capping with a thin protective layer. In section5.3 we
present a study on the inuence of different capping materi-
als on the magnetic moments and the effective magnetic ani-
sotropy, which has been studied in detail by means of x-ray
absorption spectroscopy and density functional theory [140].
To date, there is no commercial solution using nanoparti-
cles in hard disk drives as carrier of the information stored.
They can only be found in the ferrouid sealing the spindle
motor which rotates the platters (gure4).
3.3. Electrically addressable magnetic data storage
Multiferroic materials showing both magnetic and electric
ordering allow an additional degree of freedom in the design
of actuators, transducers and storage devices and thus have
attracted scientic interest from the technological perspec-
tive as well as from basic research [47]. A possibility to store
information with a low energy consumption may be the use
of articial multiferroic nanocomposites in which the bit can
be written by application of a voltage without an electric cur-
rent. In 1972, van Suchtelen et al [46] already proposed that
composites of magnetostrictive and piezoelectric components
can exhibit a stress-mediated electromagnetic inter-constit-
uent coupling forming an articial multiferroic composite.
This has been an important approach to tailored multiferroic
composites, especially as the number of single-phase mate-
rials exhibiting multiferroic order is limited. The two-phase
composites can be grown in a layered lm geometry, so-called
(2,2) structures, or vertically aligned as pillars in a host matrix,
so-called (1,3) structures. The latter geometry has the advan-
tage that clamping effects to a substrate are minimised result-
ing in a large ferroelectricferromagnetic coupling [48]. As
an example, we discuss CoFe
2
O
4
nanopillars embedded in a
BaTiO
3
matrix as introduced by Zheng et al [49].
BaTiO
3
(BTO) is ferroelectric at room temperature and
exhibits a signicant piezoelectric effect. If the electric eld
is applied along the long axis of the tetragonal unit cell (z
axis), the macroscopic piezoelectric coefcients are p
z
150
pm V
1
along the z axis and p
z
80 pm V
1
along x and y
axis, respectively [50]. On a microscopic scale, the spontane-
ous electric polarisation of BTO along the crystallographic z
axis is connected to an off-centre displacement of the Ti
4+
ion
as sketched in gure5. Due to hybridisation of the 3d states
of the Ti cation with the 2p states of the surrounding O ani-
ons, the off-centre displacement is connected to a substantial
charge rearrangement changing the occupation of the
d
z
2
, d
xz
and d
yz
orbitals of Ti cation to slightly higher values at the
expense of electron occupation of the d
xy
orbital of Ti and p
orbitals of the oxygen ions located on the z axis. This leads to
a destabilisation of the centrosymmetric conguration [51].
The piezoelectric response of the BTO to a voltage applied
can be used to modify the magnetisation of a magnetostric-
tive compound if the coupling between the two constituents
is strong enough. In 2004 Zheng et al presented a study on
the stress-mediated coupling between a BTO host matrix
and embedded CoFe
2
O
4
(CFO) nanopillars [49]. This gives
the possibility to tune the electric polarisation of the hosting
BTO by magnetic elds and to tune the magnetisation of the
CFO nanopillars by an electric eld. Thus, this composite is
a prototype system for electrically addressable magnetic data
storage devices. In order to achieve complete regularity of
the nanopillar pattern a recently experienced stencil-derived
direct epitaxy technique [52] might eventually be chosen for
pertinent applications.
As presented in section 5.5, the x-ray absorption spectros-
copy gives the possibility to study the response to an applied
external magnetic eld of the ferrimagnetic component on the
one hand and the ferroelectric component on the other hand [53].
3.4. High-moment materials
Now we turn to the discussion of conventional magnetic data
storage, i.e. writing magnetic information by local magnetic
elds. For the write heads (gure4) used, a high stray eld
can be obtained by using materials with a high magnetic satu-
ration moment at room temperature. Its magnetisation direc-
tion can be switched by an electric current through a tiny coil
around the magnetic material. Nowadays, the reading process
is done by utilising the giant magnetoresistance effect [55,
56]. One suitable material for a write head is Fe
0.7
Co
0.3
that
has a maximum magnetic moment among the ferromagnetic
alloys, μ
tot
2.45 μ
B
, according to the SlaterPauling curve
[57]. Some materials have been suggested to overcome this
magnetic moment, like Mn multilayers with Fe or FeCo
[58], other Mn compounds [59], some Fe nitrides [60, 61] or
densely packed Fe clusters in a Co matrix [62, 63], but no
denite evidence has been presented for reaching a higher
Rep. Prog. Phys. 78 (2015) 062501
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8
averaged magnetic saturation moment at room temperature
than the one at the SlaterPauling maximum.
Rare earth elements have a much larger magnetic moment,
but they are not ferromagnetic at room temperature. One sim-
ple idea is to combine rare earth metals with Fe, Ni or Co to
obtain a Curie temperature that is increased with respect to
the one of the pure rare earth metal due to the coupling to the
3d ferromagnet. But heavy rare earth metals and 3d transition
metals have a strong antiferromagnetic coupling reducing the
net magnetic moment of the alloy or compound [64, 65]. A
parallel alignment can be forced by introducing an interlayer
of a layerwise antiferromagnet like Cr between an Fe and a
rare earth lm as sketched in gure6. The parallel alignment
between Fe and the rare earth is possible since it is known
that Cr couples antiferromagnetically to both Fe [67] and rare
earth metals [68, 69]. Due to the layerwise antiferromagnetic
structure of Cr, an odd number of atomic Cr interlayers will
consequently yield a parallel alignment of Fe and rare earth
moments whereas for even numbers of atomic Cr interlayers
the alignment is antiparallel.
The validity of this simple approach was evidenced by den-
sity functional theory calculations by two different methods.
The Vienna ab-initio simulation package (VASP) [7073] was
used with the all-electron projector augmented wave method
[74, 75] and the generalised gradient approximation to obtain
the equilibrium interlayer separations along the stacking direc-
tion by minimizing the HellmanFeynman forces as explained
in [76]. After structural relaxation the distance between the
rare earth metal and Cr is larger while the distance between
Fe and Cr is smaller than the atomic distances in bulk Fe or
Cr. Magnetic moments and exchange energies were calculated
by means of a fully relativistic implementation of the full-
potential linear mufn tin orbitals (FP-LMTO) method [77,
78] treating the 4f states of the rare earth metal atoms as core
states with the spin moments constrained to the values derived
from Hunds rules. Indeed, for the case of a single Cr layer in
between Fe and rare earth metal, Fe and rare earth metal mag-
netic moments are aligned parallel to each other whereas the
smaller Cr magnetic moment is aligned antiparallel to the Fe
and rare earth atoms, conrming the coupling scheme sketched
in gure6. The corresponding experimental study is presented
in section5.4. It shows that the Slater–Pauling limit has not yet
been beaten at room-temperature.
4. X-ray absorption spectroscopy
X-ray absorption spectroscopy (XAS) is a powerful tool to
characterise nanoparticles element-specically regarding
their electronic structure, magnetic properties, crystal struc-
ture, chemical environment and lattice dynamics as will be
shortly described in this subsection. In XAS, core-level elec-
trons with their element-specic binding energies are excited
by incident x-rays. It is the generic term for the spectroscopic
measurement of the:
x-ray absorption near edge structure (XANES) that con-
tains information about the unoccupied electronic states
and the chemical environment;
extended x-ray absorption ne structure (EXAFS) for
determination of type and distance of atoms in the local
environment of the absorbing atom as well as local dis-
order and lattice dynamics.
A polarisation dependent absorption behaviour is called
dichroism. In a microscopic picture, it is caused by an anisot-
ropy of charge and/or spin distribution. If the dichroism is due
to a charge anisotropy only, it is called natural dichroism such
as x-ray natural linear dichroism (XNLD) and natural circular
dichroism (XNCD). In the case of an anisotropic spin distribu-
tion, it is called magnetic dichroism such as x-ray magnetic
linear dichroism (XMLD) and magnetic circular dichroism
(XMCD). Recently, more complicated origins of different types
of dichroic effects have been discussed: x-ray non-reciprocal
Figure 4. Conventional hard-disk drive for magnetic data storage.
Figure 5. Sketch of the BaTiO
3
unit cell in the high-temperature
para-electric cubic phase (a) and the room-temperature tetragonally
distorted phase (b). The displacement of the Ti
4+
ion yields a non-
vanishing electric polarisation in the latter case.
Figure 6. Coupling scheme for a parallel alignment of Fe and rare
earth magnetic moments by a Cr interlayer.
Rep. Prog. Phys. 78 (2015) 062501
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9
linear dichroism caused by breaking inversion symmetry by
magnetoelectric ordering and x-ray magnetochiral dichroism
(XMχD) due to a chiral charge distribution and an axial spin
alignment. Both x-ray non-reciprocal linear dichroism and
XMχD have been experimentally proven [79, 80].
In this work, it is focussed on XANES to monitor changes
in the electronic structure and XMCD and XNLD effects to
analyse spin and charge anisotropies. There are several review
articles and textbooks dealing with these techniques (e.g. [81,
106]), therefore we restrict ourselves to a brief survey of this
topic. The presentation of the common EXAFS analysis will
be complemented by the new method of using wavelet trans-
forms. The different facets related to the x-ray absorption
spectroscopy will be discussed in this subsection after an intro-
duction to x-rays from synchrotron radiation.
4.1. Synchrotron radiation
In general, after pre-acceleration in a microtron or linear accel-
erator, electrons are accelerated in the synchrotron to a veloc-
ity close to the speed of light. Afterwards, the electrons are
injected into a storage ring and kept at constant energy by radio
frequency cavities on a circular trajectory by magnetic elds.
Following the laws of classical electrodynamics, the electrons
as accelerated charged particles emit electromagnetic radia-
tion, the so-called synchrotron radiation. The mathematical
background for this radiation was established already around
1900 by Liénard and Wiechert who obtained a relation between
electromagnetic elds at the observation point (in space and
time) and charges and currents at the time of emission by
retarded potentials [82, 83]. The derivation of the radiation
characteristics starting from the Maxwell equationsand using
retarded potentials can be found e.g. in [84]. Here, some of the
most important approaches and results are presented.
On a circular orbit with radius R, the radiation eld of a
non-relativistic electron corresponds to an isotropic Hertzian
dipole. For ultrarelativistic electrons, the radiation eld is
distorted towards an extremely forward-pointing cone of
radiation with a vertical opening angle ψ 1/γ where γ is the
Lorentzian factor depending on electron velocity v and speed
of light c according to γ β=−
=−
vc1/ 1
22 2
. This sharp
collimation to the forward direction makes synchrotron radia-
tion the brightest articial source of x-rays. It covers a broad
energy range from the far infrared up to hard x-rays and the
radiation is polarised. The spectral and spatial intensity emit-
ted in a frequency interval dω and solid angle dΩ is propor-
tional to
ωγ
θξ
ψ
γψ
ξ∝+ +
+
I
KK
d
ddΩ
1
()
(1/)
()
2
2
2
2
2/3
2
2
22
1/3
2
(15)
with the modied Bessel functions K
2/3
(ξ), K
1/3
(ξ) and
ξ
ω
γ
ψ
=+
R
c3
1
.
2
2
3/2
(16)
The formalism to describe the synchrotron radiation was intro-
duced by Ivaneko and Sokolov [85] and independently by
Schwinger [86]. In equation(15) the rst term, i.e. the K
2/3
(ξ)
term, describes the fraction of horizontally polarised radiation
parallel to the plane of the electron orbit, while the second term
in square brackets describes the vertically polarised fraction
perpendicular to this plane. It can easily be seen that in the
plane of the electron orbit (ψ = 0) the second term vanishes due
to the prefactor ψ
2
and thus, the radiation is purely polarised
in the horizontal plane. With increasing vertical angle ψ, the
fraction of horizontally polarised radiation decreases and the
fraction of vertically polarised radiation increases approach-
ing the ratio of 1 : 1 for circular polarisation with a phase
shift of ± π/2. Whether the circular polarisation is described
as right- or left-handed depends on whether the vertical angle
is positive (above the plane of the electron orbit) or negative
(below the plane of the electron orbit), of the orientation of
the electron trajectory and unfortunately, which convention is
used: from the point of view of the source or the receiver. Here,
we use the convention from the point of view of the source.
In that case, left- and right handedness for the description of
the rotation of the electric eld vector means that by pointing
ones left (right) thumb in the direction of radiation propaga-
tion, i.e. away from the source along the wave vector k, the
curling of ones ngers sketch the direction of the temporal
rotation of the electric eld vector at a given point in space. If
the electron is moving clockwise on its circular orbit, i.e. it is
moving from the right to the left for an observer in the plane
of the electron orbit, the circularly polarised emitted radiation
is left-handed (photons with negative helicity) above the plane
and right-handed (photons with positive helicity) below the
plane. In gures7(a) and (b), horizontally polarised, vertically
polarised and total radiation intensity are plotted as a func-
tion of normalised vertical angle ψγ and normalised energy
E/E
c
= ω/ω
c
where E
c
and ω
c
denote the critical energy and
critical frequency, respectively. The critical frequency is the
frequency for ψ = 0 when ξ = 1/2:
ωγ
=
R
c
3
2
c
3
(17)
The total power emitted by the storage ring with frequencies
ω < ω
c
is identical to that with ω > ω
c
. Note that the denition
in [84] is slightly different from equation(17), which is the
conventional one. For ω ω
c
the intensity of emitted radiation
is negligible. The same holds for angles ψ ψ
c
with the criti-
cal angle
ψ
ωωγ
= //
c
c
at which the intensity is only 1/e of the
value at ψ = 0. That means, for higher frequencies, the major
intensity is collimated in a smaller angular range as can be seen
in gure7(b). Figure7(c) shows the degree of horizontal linear
polarisation and circular polarisation, respectively. The former
can be calculated according to P
lin
= (I
hor
I
ver
)/(I
hor
+ I
ver
),
the latter according to
=−PP
(1 )
circ
lin
2
. As already men-
tioned before in the discussion of equation(15), the emitted
radiation is purely polarised in the horizontal plane for ψ = 0.
The larger the vertical angle ψ is, the higher the degree of circu-
lar polarisation is. Additionally it can be seen in this gurethat
at a constant vertical angle, the degree of circular polarisation
is decreasing for smaller energies. However, as the degree of
circular polarisation is highest at the edge of the radiation cone
Rep. Prog. Phys. 78 (2015) 062501
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10
where the total intensity is vanishing, in experiments one has
to nd a compromise between high intensity and high degree
of polarisation. This is represented by the gureof meritthe
product of the total intensity and
P
circ
2
plotted in gure7(d).
In particular in the projection it is clearly visible that for lower
energies, the vertical angle should be larger to optimise the
gureof merit. Note that for the use of synchrotron radiation
in experiments, the beam has to pass several optical elements.
Each optical element changes the radiation eld, i.e. the direc-
tion, intensity and phase of horizontally and vertically polar-
ised components. In principle the polarisation can be changed
by reection at each optical element. In the soft x-ray regime
it is mainly conserved because the optical elements are used
under grazing incidence.
To extend the available energy range, the critical frequency
ω
c
has to be shifted to higher values. As can be deduced from
equation(17) either the Lorentzian factor γ has to be increased
or the bending radius R has to be decreased. For a given γ of
electrons in the storage ring, ω
c
can be enhanced by a stronger
bending of the electron orbit which is usually achieved by
higher magnetic elds, e.g. from a superconducting dipole
magnet, so-called superbends. To preserve the storage ring
geometry, the stronger magnet has to be shorter. If the instal-
lation of a superbend is not desirable or feasible, a so-called
wavelength shifter can be used. As the name already implies,
the main objective in wavelength shifters is to shift the avail-
able wavelengths or energies. This is achieved by using a
few short superconducting magnets in a line with alternating
directions of the magnetic eld. Usually, there are three or ve
magnets used with the rst and last one used to reduce the net
deection of the electron beam ideally to zero after passing
the whole device. The periodic acceleration is the character-
istic property of so-called insertion devices. If the number of
periods P is highly extended, the device is called a wiggler. Its
Figure 7. Radiation characteristic for synchrotron radiation emitted by ultrarelativistic electrons forced on a circular orbit by a bending
magnet. The intensity shown here is resolved by means of photon energy E/E
c
and vertical angle ψγ. Horizontally and vertically polarised
components (a), total intensity (b), degree of linear (horizontal) and circular polarisation (c) and the gureof merit for circular polarised
radiation (d) are shown.
Rep. Prog. Phys. 78 (2015) 062501
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11
main advantage is a high photon ux that is proportional to P
on the symmetry axes. The radiation cone has the same verti-
cal opening angle as a single bending magnet, but due to the
strong electron deection by the high magnetic elds, most of
the power is contained horizontally within an opening angle
of 2θ 2Kγ
1
with the deection parameter
λ
π
=K
eB
mc2
U0
(18)
containing the periodic length λ
U
and the peak magnetic eld
B
0
. A wiggler is characterised by K 1. For small magnetic
elds, the electron deection is reduced and may become
comparable or even smaller than the radiation cone open-
ing angle of a single magnetic pole of the insertion device,
i.e. K 1. In this case, interference effects between radia-
tion emitted from an electron at different essentially collinear
source points occur resulting in a spectrum with quasi-mono-
chromatic peaks given by
λ
λ
γ
γθ=++
n
K
2
1
2
n
U
2
2
22
(19)
for a sinusoidal electron path with a bandwidth of Δ
λ/λ P
1
n
1
. The positive integer n denotes the number of the
harmonic. On-axis, i.e. for ψ = 0 and θ = 0, there occur only
odd harmonics. This type of insertion device is called undula-
tor and is characterised by K 1. It provides a large photon
ux proportional to P
2
on-axis and a high brilliance. The emit-
ted radiation can be approximated by an analytical expression
following equation(19) multiplied by an interference term
πλ λθ
πλ λθ
∣∣=IF
Psin[ /()]
sin[ /()]
2
2
1
2
1
(20)
By plotting this expression for different parameters it can be
seen that
on-axis, there occur only odd harmonics (n = 1, 3, 5,...),
for lower K values, higher harmonics become less impor-
tant,
a higher number of periods P yields a smaller bandwidth
of the harmonics.
More details can be found in several textbooks and articles,
e.g. [8790]. The photon wavelength according to equa-
tion (19) for the radiation emitted by the undulator can be
tuned by changing the peak magnetic eld which is usually
done by changing the gap between facing magnets. An exam-
ple is schematically shown in gure8 for an undulator of the
so-called Advanced Planar Polarised Light Emitter (APPLE)
II type [91]. It consists of four movable rows of magnets
which can be used to provide not only horizontally polarised
radiation, but also vertically polarised radiation by shifting
two rows parallel, e.g. the upper right and lower left, by λ
U
/2.
Shifting the two rows by ±λ
U
/4 will force the electrons on spi-
ral-like paths yielding circularly polarised light. In this helical
geometry, the wavelength of the radiation is given by
λ
λ
γ
γθ=++
n
K
2
(1 ).
U
2
22
2
(21)
Relating experiments on nanoscale systems it should be men-
tioned that the intense x-rays of an undulator may also be a
disadvantage. In particular, some molecular systems may
suffer from radiation damage either directly by the incoming
x-rays or by the outgoing photoelectrons. In this case, a detun-
ing of the undulator with respect to the monochromator can be
used to overcome this problem. Usually, a gap of the undula-
tor that determines the energy of maximum radiation intensity
is chosen corresponding to lower energies than x-rays pass-
ing the monochromator. In other words, the monochromator
is set to energies above the peak maximum of the undulator
harmonic. In addition, also ferroelectric systems with low
electric conductivity may be disturbed by intense x-rays since
the outgoing photoelectrons yield a local positive charging of
the sample which may induce electric domains. However, this
effect can also be used to write domains in multiferroic mate-
rials as shown in [93].
In very long undulators the interaction between the elec-
trons and the emitted synchrotron radiation may yield a
so-called microbunching of the electrons which continue
to radiate in phase with each other emitting x-ray radiation
that amplies more and more. This self-amplied spontane-
ous emission (SASE) produces extremely short and intense
x-ray ashes with the properties of laser light. Therefore, such
devices are called free-electron lasers. The wavelength of the
light emitted can be readily tuned by adjusting the energy of
the electron beam or the magnetic eld strength of the undu-
lators. A crucial prerequisite for the free-electron laser is an
electron beam of such extremely high quality. A detailed
description of the physics of free-electron lasers is given in
several textbooks, e.g. [94].
Another on-going development is the use of electron storage
rings in new operation modes that allows to meet the diverse
requirements of different experiments, e.g. high photon-ux on
the one hand and a well-dened time structure of short x-ray
pulses on the other hand [95, 96].
4.2. Measurements of solid and liquid samples
Solid samples can be measured in transmission by detect-
ing the x-ray intensity after passing through the sample. This
is a standard method e.g. for measurements of thin lms either
free-standing or on membranes andespecially in the hard
x-ray regimepellets of diluted nanoparticles. For the case of
nanoscale systems on solid substrates, XAS is usually performed
by measuring the uorescence yield (FY) or total electron yield
(TEY). The FY can be detected e.g. by photodiodes of GaAs. In
the measurement geometry one should avoid a position of the
photo diode in the x-ray scattering plane of the sample since this
usually yields a large background signal due to diffuse elastic
scattering making the detection of the FY due to x-ray absorp-
tion difcult or even impossible. To measure the TEY, in general
two different methods exist. On the one hand, it can be detected
by measuring the sample drain current. It may be advantageous
to set the sample to a negative potential that helps to push the
electrons out of the sample. On the other hand, a plate or grid
on a positive potential may be used to extract the electrons and
detecting the TEY by measuring the source current.
Rep. Prog. Phys. 78 (2015) 062501
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12
In all cases, a normalisation to the intensity of incom-
ing x-rays is crucial for a proper analysis of the absorption
signal of the sample. In particular for measurements of light
elements like carbon or oxygen, it is important that the refer-
ence signal is measured behind the last optical element since a
contamination of optical elements with these elements cannot
be avoided and reduces the intensity of x-rays. In this case,
a clean gold mesh or thin foil can be used to measure the
intensity of incoming x-rays. In other cases, the absorption of
the last mirror in the beamline may be sufcient as reference
signal.
The x-ray absorption spectroscopy of dispersions or solu-
tions in the soft x-ray regime is more complex since the liquid
samples have to be in a high vacuum environment to avoid
absorption of incoming x-rays by residual gases. Using a spe-
cially dedicated set-up [92], x-ray absorption spectra of highly
diluted (i.e. 8 mmol l
1
) nanoparticles in dispersion could be
measured for the rst time [33]. In the set-up, the liquid is
pumped in a closed cycle through a ow-cell with a silicon
nitride membrane separating the liquid from the vacuum. The
absorption signal is detected by measuring the FY through the
same membrane by a GaAs photo diode.
Saturation effects are an issue for both, TEY and FY meas-
urements. For the description of a saturation of the measured
signal, i.e. a deviation from the proportionality between the
TEY or FY and the x-ray absorption, two important val-
ues have to be compared: The penetration depth of incom-
ing x-rays λ
x
cos θ and the escape depth for electrons in TEY
measurements λ
e
or outgoing photons in FY measurements λ
p
,
respectively. The x-ray penetration depth includes the angle
θ of the x-ray beam with respect to the sample surface nor-
mal and the penetration length λ
x
which is the inverse of the
absorption coefcient and is sometimes called x-ray attenua-
tion length. Considering the extreme case of an x-ray penetra-
tion depth that is much smaller than the electron or photon
escape depth (λ
x
cos θ λ
e, p
) helps to illustrate the effect of
saturation of the signal. All incident photons will be converted
into photoelectrons or uorescence photons that leave the
sample and will be detected. This leads to an measured sig-
nal that is proportional only to the intensity of incoming pho-
tons and does not depend on the absorption coefcient. In this
sense, the signal is saturated. A more detailed description and
quantitative treatment can be found in the work of Nakajima
et al [97] for TEY and Eisebitt et al [98] for FY. Saturation
effects become important in general when measurements are
performed under grazing x-ray incidence (reducing the pen-
etration depth through the cos θ term) or at the energies of the
absorption edges where the absorption coefcient becomes
large and consequently, the penetration length becomes small.
Saturation effects in ensembles of nanoparticles measured by
detection of TEY and how the correct absorption coefcient
can be obtained from experimental data are also discussed in
the literature [99].
However, as already implied by the electron or photon
escape depth, not all electrons and photons generated in the
absorption process will leave the sample. A fraction will be
absorbed by the sample before leaving the surface. This self-
absorption is usually described by an exponential damping
which is quite large for electrons corresponding to a small
escape length in the range of 220 nm. In this regard, a strong
self-absorption helps to reduce saturation effects, since the
condition λ
x
cos θ λ
e, p
is fullled only for a severely reduced
x-ray penetration depth. To avoid strong saturation effects in
FY detection connected to the large escape length of photons, a
measurement geometry in normal x-ray incidence (θ = 0) and
detection under grazing take-off seems to be advantageous.
4.3. X-ray absorption near-edge structure and its dichroism
In XAS, the absorption of photons excites core-level electrons
into higher unoccupied states or into the continuum. The x-ray
absorption near-edge structure (XANES) can be understood
as a convolution between the density of initial states and the
density of unoccupied nal states. Since the excited elec-
trons stem from core-levels which are very sharply localised
in energy, the spectral shape of the XANES mainly reects
the density of states (DOS) of the unoccupied nal states.
This gives the opportunity to study changes of the electronic
structure in nanoparticles compared to bulk materials [100].
Excitations into the continuum yield a step-like background
without any ne structure. For the 3d transition metals, the
interesting states that carry the major magnetic contribution
and may be strongly inuenced by hybridisation effects in
alloys or compounds are the 3d states. Therefore it is common
to measure the x-ray absorption related to core-level electron
excitations from 2p
3/2
and 2p
1/2
states into the 3d states (so-
called L
3
and L
2
absorption edges, respectively). Electronic
transitions into higher unoccupied states or even into the con-
tinuum are separated by a two-step-like function from the
Figure 8. Schematic settings of an APPLE II type undulator to
obtain either horizontally polarised (a), right circularly polarised (b)
or vertically polarised (c) x-rays by shifting two of the four rows of
magnets in parallel mode. A shift of λ
U
/4 leads to left circularly
polarised x-rays (not shown here).
Rep. Prog. Phys. 78 (2015) 062501
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13
transitions into the 3d states as shown in gure10. The height
for these two steps reects the occupation of initial states that
is two times higher for the 2p
3/2
states than for the 2p
1/2
states.
The position of the steps is usually taken as the inection
points of the absorption edges.
By measuring the x-ray absorption of linearly polarised
light for different angles of incidence, one can use the electric
eld vector of the x-rays as a search light for the maximum
and minimum unoccupied states. For instance, at the L
3,2
absorption edges the unoccupied d states are probed and the
x-ray absorption intensity vanishes if the vector of the elec-
tric eld E lies along the d orbital nodal axis. One example
of the x-ray linear dichroism (XLD) effect measured at the
Cu L
3,2
absorption edges of La
1.85
Sr
0.15
CuO
4
can be found
in [103].
As stated by Stöhr and Siegmann [81], the transition inten-
sity is directly proportional to the number of empty valence
states in the direction of E. Thus, deviations from a spheri-
cal charge density of the nal states of the absorbing atom
give rise to an absorption intensity I depending on the angle θ
between the electric eld vector and the symmetry axes of the
system which has to have a higher than three-fold symmetry
about this symmetry axis. It is [101]
θθθ
=+
∥⊥
II I() co
ss
in
22
(22)
where I
(I
) denotes the absorption intensity with the electric
eld vector of x-rays parallel (perpendicular) to the symmetry
axis and reects the charge distribution projected on a direc-
tion parallel (perpendicular) to the symmetry axis.
The linear dichroism is dened as
=−
⊥∥
III
XLD
(23)
and depends on how severely the charge distribution is dis-
torted from a spherical one. An easily interpreted picture is
given by the d orbitals in gure 9 and the p to d transition
intensities summarised in table1.
The transition intensities for the different d orbitals are
given for the electric eld vector of the x-rays along x, y and
z axis. In a cubic crystal symmetry, the
d
xy
22
and
d
z
2
orbit-
als are energetically degenerated and sum up to a spherical
shape. This leads to a transition intensity of 4/15 along each
axis and no linear dichroism can be obtained. The same holds
for the three t
2g
orbitalsd
xy
, d
yz
and d
xz
that have in total an
absorption intensity of 4/15 along each axis. For systems with
lower symmetry, e.g. a tetragonal system, the degeneracy is
lifted and a linear dichroism occurs.
The asphericity of the charge density can be mathemati-
cally described by its quadrupole moment. More precisely, the
quadrupole moment of the density of unoccupied statesor
hole densitythat are probed in an absorption experiment can
be related to the occurence of a linear dichroism. The quad-
rupole tensor behind this moment is symmetric, traceless and
the expectation values of all its elements vanish for a system
with spherical symmetry.
In ferromagnetic and antiferromagnetic systems, the
spherical charge or hole density distribution in cubic symme-
try may be distorted via spinorbit coupling by the exchange
interaction driven axial alignment of spins. This gives rise to
the x-ray magnetic linear dichroism (XMLD). For systems
with bandlike electronic structures and rather delocalized nal
states like the ferromagnets of the 3d transition elements, the
argument of a non-spherical hole density of the nal states
does not apply any more. In this case, the model of Kuneš
and Oppeneer [102] is useful that ascribes the XMLD to tran-
sitions from the localized spinorbit and exchange split 2p
states to the d states. In this sense, the asphericity of the charge
density of exchange split initial states is crucial to obtain a
linear dichroism.
For circularly polarised x-rays the excited electrons are
polarised for both orbital and spin momentum. The electron
excitations with their probabilities given by the Clebsch
Gordan coefcientswithout taking into account the num-
ber of unoccupied nal statesyield an orbital polarisation
of excited electrons that is the same for electrons from the
2p
1/2
or 2p
3/2
state. By simply summing up all possible exci-
tations weighted by their probabilities, one nds also a spin
polarisation of the excited electrons. For right circularly
polarised light (with photon helicity of +), 62.5% of excited
electrons from the 2p
3/2
state, carry a spin of m
s
= +1/2
and only 37.5% of m
s
= 1/2. From the 2p
1/2
state, 75% of
excited electrons carry a spin of m
s
= 1/2 and only 25% of
m
s
= +1/2. Note, that the sign of spin polarisation is differ-
ent for the different 2p states. This is schematically shown in
gures10(a) and (b). For simplication, one spin channel of
the 3d states is assumed to be completely occupied. If there is
no spinorbit-splitting, i.e. no energy gap between 2p
3/2
and
2p
1/2
states, the averaged spin polarisation would be zero.
In the second step of this simple model, the spin polarised
excited electrons probe the spin polarisation of unoccupied
nal states, which is reversed for opposite magnetisation of
a ferromagnet. This gives rise to a magnetisation dependent
absorption behaviour, the so-called x-ray magnetic circular
dichroism XMCD. Alternatively, the polarisation of x-rays
can be changed from right to left circular to reverse the spin
polarisation of excited electrons.
The XMCD effect was predicted in 1975 by Erskine and
Stern who performed band structure calculations for the M
3,2
absorption edges of Ni [104]. The rst experimental results
were reported in 1987 by Schütz et al who detected a sig-
nicant XMCD effect at the K absorption edge of an Fe foil
[105]. A more detailed historical overview can be found e.g. in
[106], an introduction and description of dichroisms in XAS
are given in various textbooks e.g. in [107]. From the XMCD,
spin and orbital magnetic moments can be deduced by a sum-
rule [108, 109] based analysis of the integrated spectral inten-
sities. Using p =
L3
(μ
+
μ
) dE, q =
L3+L2
(μ
+
μ
) dE and
r =
L3+L2
(μ
+
+ μ
)dE/2 where μ
+
and μ
denotes the absorp-
tion with reversed spin polarisation of either excited electrons
(by switching the polarisation of x-rays) or unoccupied nal
states (by magnetisation reversal), respectively, the spin and
orbital magnetic moments per unoccupied nal state n
h
can be
written as [110]:
μ
μ=−
n
q
r
2
3
l
h
B
(24)
Rep. Prog. Phys. 78 (2015) 062501
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14
μ
μ=
−+
n
pq
r
32
s
h
eff
B
(25)
μ
μ
⇒=
=
q
pq pq
2
96
2
9/ 6
l
s
eff
(26)
Here the effective spin magnetic moment
μ μμ=+
7
sst
eff
is
the sum of the pure spin magnetic moment μ
s
and an intra-
atomic dipole term μ
t
due to a possible asphericity of the spin
density distribution. For ensembles of nanoparticles with
randomly oriented axes it is often argued that μ
t
is averaging
out. However, if the distorted spin density distribution (partly)
follows the direction of an external magnetic eld as it is
expected for elements with a large spinorbit coupling energy,
a fraction of μ
t
may be present all the time and will not aver-
age out. In single-crystalline samples or crystallographically
well-oriented nanoscale systems, a strong spinorbit coupling
will also hinder the extraction of the correct value of μ
t
from
angular dependent measurements for the same reason. It has
been shown recently [113] that μ
t
can also be used to monitor
phase transitions in nanoparticle systems, which is in particu-
lar interesting for systems where other methods fail e.g. due
to line broadening in diffraction methods caused by the small
particle size or superparamagnetism masking changes in clas-
sical magnetometry.
The sum-rules were derived by Thole and Carra in an
atomistic picture [108, 109] and were later also derived
within the independent electron approximation [111]. A
brief summary on validation of the sum-rules and possible
draw-backs can be found e.g. in the work of van der Laan
[112]. For the case of Fe, Ni and Co metals, it has been
experimentally shown that the sum rules yield reasonable
results [110]. The error bar is assumed to be about 1020%
for
μ
s
eff
and about 510% for μ
l
. A discussion for 3d transi-
tion metal ions can be found in [114].
Beside the question of applicability of sum-rules and the
μ
t
term in the spin sum rule, the determination of spin and
orbital magnetic moments from experimental data may also be
impeded e.g. by an overlapping of absorption edges. For the
light 3d elements, this leads to a large underestimation of the
induced spin moments, e.g by a factor of about 5 for the case
of vanadium [115]. For the case of the L
3,2
absorption edges
of the rare earth elements application of the XMCD sum rules
would even lead to the wrong sign of the 5d moments due to
a strong spin-dependence of the transition matrix elements for
the electric dipolar transitions. The limits of the applicability
Figure 9. Illustration of d orbitals.
Table 1. Polarisation dependent p to d transition intensities for
different alignments of the electric eld vector of x-rays.
e
g
orbitals t
2g
orbitals
d
xy
22
d
z
2
d
xy
d
yz
d
xz
I (E x)
3/15 1/15 3/15 0 3/15
I (E y)
3/15 1/15 3/15 3/15 0
I (E z)
0 4/15 0 3/15 3/15
Note: Values are taken from [81] and denote the intensity per orbital per spin
in units of πe
2
ωR
2
/(ϵ
0
c), where R is the radial matrix element.
Figure 10.
Schematic electron excitations with right circularly
polarised x-rays from 2p
3/2
and 2p
1/2
core-level states into
unoccupied 3d states for opposite magnetisation directions. For
simplication, either spin down (a) or spin up (b) 3d states are
completely occupied. In (c) XANES of Fe in FePt bulk material for
opposite direction of saturation magnetisation, i.e. either parallel
(blue line) or antiparallel (red line) to the k vector of incident
x-rays is presented. The grey shaded area corresponds to electronic
excitations into the 3d band, which are separated by a two-step-like
function (dashed line) from excitation into higher unoccupied states
and into the continuum, respectively. The XMCD (black line) is the
difference between the blue and the red spectrum. The same XMCD
can be obtained as the difference between right and left circularly
polarised x-rays at constant saturation magnetisation.
Rep. Prog. Phys. 78 (2015) 062501
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15
of the sum rules have already been discussed in the original
presentation of these rules [108, 109].
For nanoparticles and clusters of a few atoms, XANES
and XMCD spectra may differ signicantly from the corre-
sponding bulk material. This can be related to a localisation
of electrons due to the reduced size. In XANES, the localisa-
tion manifests in an energy shift and sharper absorption lines
as discussed e.g. in the work of Reif et al [116] for the case
of small Cr clusters consisting of 113 atoms. In 3d (and
4d) transition metals this change in the electronic structure
gives rise also to a change of the magnetic properties since
the well-established Stoner criterion for itinerant ferromag-
netism relates the occurence of magnetic order to the density
of states at the Fermi level. It seems to be reasonable that
the electron localisation may switch on ferromagnetism
in compliance with the Stoner criterion in elements like
Pd, Ru or Rh. For conventional ferromagnets, an increased
density of states around the Fermi level leads to enhanced
spin magnetic moments, since the parallel alignment of elec-
tron spins happens at the expense of a smaller increase of
kinetic energy compared to more delocalised electrons. For
instance, Fe clusters (29 atoms) show an enhanced spin
magnetic moment in XMCD experiments compared to bulk
Fe [117]. In addition, the break of crystal symmetry at the
surface leads to an unquenching of orbital moments which
is even more signicant [117, 118]. In clusters of alloys like
Fe
n
Pt
m
clusters, the orbital magnetic moment is enhanced
too, compared to the bulk material and compared to Fe
x
Pt
1x
nanoparticles. The behaviour of the spin magnetic moment
when changing the number of atoms or composition is rather
complex reecting hybridisation effects between Fe 3d and
Pt 5d electrons [119].
4.4. Extended x-ray absorption ne structure
An oscillatory behaviour in the extended energy range about
1001000 eV above the absorption edge, is visible in the
absorption signal as can be seen in gure11. In a simple pic-
ture, these oscillations are caused by an interference effect
between the outgoing photoelectron as a matter wave and
backscattered waves from neighbouring atoms. Depending on
the wavelength λ of the photoelectron and the nearest-neigh-
bour distance, this gives rise to an enhanced (constructive
interference) or lowered (destructive interference) intensity.
As the wavenumber k of the photoelectron can be calculated
from the photon energy according to
=
k
m
EE
2
()
e
0
(27)
it is possible to investigate the structure in the local environ-
ment around the absorber atom by analysing the frequency
of EXAFS oscillations χ(k). Beside this microscopic picture,
the EXAFS can be related in terms of electrodynamics to the
inuence of atoms close to the absorbing atom on the tran-
sition matrix elements [120]. Since the amplitude of oscil-
lations does not depend only on the distance but alsoeven
more signicantlyon the type and number of backscatter-
ing atoms, the local chemical surrounding can be studied in
detail. In particular in nanoscale systems, the reduction of the
average coordination number of the absorbing atom at the
surface may be used to analyse size and shape of nanopar-
ticles [121] as well as a possible increase of vacancies and
defects. Analytical equations[122, 123] and approximations
[124] are used to analyse the coordination numbers for vari-
ous morphologies of nanoparticles. In combination with the
determination of the type of backscattering atoms, a possible
seggregation of one element at the surface of systems con-
taining two or more chemical elements can be obtained by
EXAFS investigations [125, 126, 140, 154]. In addition, sur-
face strain and relaxation effects can be studied and by using
linearly polarised x-rays for measuring single-crystalline
samples or oriented systems like e.g. assembled molecules,
the EXAFS analysis yielding type, distance and number of
backscattering atoms can be used for the determination of ori-
entation and bonding discrimination [127] as has been used
e.g. to study the growth of ZnO nanorods [128]. An overview
on EXAFS analysis of nanoparticles can be found e.g. in the
work of Frenkel et al [129].
For the case of backscattering atoms that carry a size-
able magnetic moment, the use of circularly polarised x-rays
give rise to the so-called magnetic EXAFS (MEXAFS) in
dichroic spectra. Usually, the amplitude of MEXAFS oscil-
lations are several orders of magnitude smaller than the
amplitudes of EXAFS oscillations. The discussion of the
Fourier transform (FT) of experimental EXAFS data as
done after the pioneering work of Sayers, Lytle and Stern
Figure 11. X-ray absorption spectrum measured at a temperature
of 300 K at the Pt L
3
absorption edge of FePt (upper panel) and
extracted EXAFS oscillations as a function of photoelectron wave
number (lower panel).
Rep. Prog. Phys. 78 (2015) 062501
Review Article
16
in 1970 [130, 131] is commonly employed for this purpose
as described e.g. in [132]. The FT of the EXAFS signal as a
function of wavenumber is related to the radial distribution
of backscattering atoms in real space χ(r). Due to possible
phase shifts in the EXAFS process and interference effects
from different scattering channels, the positions of the peaks
in the Fourier transform are not identical to the geometric
distance of the backscattering atoms to the absorbing atom.
Consequently, the FT is called in some works a pseudo radial
distribution function (pseudo-RDF). For the analysis of the
type of backscattering atoms and the coordination number
of the absorbing atom, comparison of the experimental data
with simulations using a model structure, both in k space
and real space, is advisable. Nowadays, EXAFS analysis is
usually done by the comparison of experimental data to cal-
culated ones. Its theory is implemented e.g. in FEFF [133,
134], WIEN2k [135], GNXAS [136], the Munich SPRKKR
package [137] and others [138].
As an alternative method with the potential to outper-
form the Fourier-based approach, the wavelet transform
(WT) shall be mentioned. As stated in [139, 140], the main
idea behind the wavelet transform is to replace the innitely
expanded periodic oscillations in a FT by located wavelets
as kernel for the integral transformation: A scalable mother
wavelet or analyzing wavelet Ψ(k) is used as a window
function for the transform. The bases of the transformed
signal are the so-called baby wavelets generated not only
by translation, but also by scaling of the mother wavelet.
This allows to obtain a high resolution in both k space and
real space, while for the Fourier transform magnitude the
resolution in k is lost. For the case of a short-term Fourier-
transform by using a window function, high resolution in k
space can only be achieved at the expense of good resolu-
tion in real space and vice versa. Now one may ask, why
the k resolution should be interesting at all. To answer this
question, one has to go in some more detail into the occur-
rence of EXAFS oscillations: The backscattering amplitude
from neighbouring atoms shows a signicant k depend-
ence which determines the envelope of EXAFS oscillations
χ(k). The amplitude of the EXAFS oscillations is maximum
around the k position at which the backscattering amplitude
is maximum. As a rule of thumb one may note that the larger
the atomic number of the backscatterer is, the higher the
k value of maximum backscattering amplitude will be. For
some elements, the k dependent backscattering amplitude
exhibits additional ne structures as a ngerprint for these
elements. The interested reader may be referred e.g. to the
RamsauerTownsend effect in EXAFS as one example for
such ne structures. However, the point of the matter is that
in the k-dependence of EXAFS amplitudes, important infor-
mation of the type of backscattering atom is included. In
gure12, the Fourier transform and the wavelet transform
are shown exemplarily for the EXAFS data presented in g-
ure11. However the potential to directly visualise contribu-
tions of different elemental species is not obvious here, but
becomes evident in the example presented in the following
subsection.
5. Examples of recent research
5.1. Purity of chemically synthesised Fe nanoparticles
Amine borane derivatives as mild reducing agents have
been investigated and used in a wet-chemical approach for a
cheap and reliable synthesis route not restricted to magnetic
nanoparticles, but spanning over a wide range of metallic
nanoparticles [141, 142]. Regarding the magnetic elements
Co, Fe and Niit is well-known that they exhibit a tendency
for boron incorporation when the nanoparticles are prepared
from borohydride reduction of metal salts [143]. Even FeB
nanoparticles can be prepared by the reaction of FeCl
3
with
ammonia borane [144]. Therefore, one should carefully anal-
yse the elemental contributions in magnetic nanoparticles.
Since Fe is one of the few elements exhibiting ferromagne-
tism at room temperature and one of the cheapest materials
for this purpose, it is often used for the preparation of mag-
netic nanoparticles, either pure or in an alloy or in core/shell
nanoparticles. However, impurities such as boron inclusions
may alter the magnetic properties signicantly. Therefore it
is essential to characterise the purity of synthesised nanopar-
ticles in order to achieve the desired properties. As it has
been shown recently [145] the analysis of the extended x-ray
absorption ne structure (EXAFS) can be a powerful tool to
nd even light elements like oxygen, carbon or boron. In the
following, the main results and conclusions are summarised
from the perspective of x-ray absorption. In gure 13 the
magnitudes of the FT and the WT are shown for Fe nanopar-
ticles synthesised using 2 equivalent diisopropylamine-borane
(AeB) as a reducing agent. In this reaction, the reduction of
the Fe precursor is accompanied by the reaction of AeB to
amino borane (AoB)containing a BH
2
group instead of the
BH
3
in AeBand H
2
as depicted in gure14.
Figure 12. Magnitude of Fourier transform of EXAFS measured
at the Pt L
3
absorption edge of FePt as a function of radial distance
(upper panel) and magnitude of the wavelet transform as a function
of radial distance and wave number (lower panel).
Rep. Prog. Phys. 78 (2015) 062501
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17
In the total WT (gure13(b)), three peaks are clearly vis-
ible: one at a radial distance of about 0.14 nm and a wavenum-
ber of about 20 nm
1
, the second one at the same wavenumber,
but larger radial distance (about 0.21 nm) and the third one at
a radial distance of about 0.2 nm and a signicantly higher
wavenumber of about 60 nm
1
. As a reference system, Fe
nanoparticles synthesised by hydrogenation without any fur-
ther reducing agent were measured yielding the WT shown in
gure13(c). Only one peak is obtained that can be assigned to
Fe and possible traces of other light elements like oxygen and/
or nitrogen present in the Fe precursor. After subtraction of the
reference signal, the typical ngerprint of boron is obtained in
gure13(d).
By comparison of the WT magnitude with the one of a
Fe
2
B reference sample, the amount of boron was estimated
to be about 15 ± 5 at% in reasonable agreement to the value
obtained by the analysis of Mössbauer spectroscopy data, i.e.
25 at% [145]. Using less AeB as reducing agent for the synthe-
sis of Fe nanoparticles leads to less boron incorporated. From
the reaction scheme (gure 14) it is evident that the boron
incorporation occured in the second reaction step of the AoB
byproduct connected to a further release of H
2
. To gain more
insight into the chemical reaction, pre-formed Fe nanoparti-
cles prepared by hydrogenation (without any boron) were sub-
sequently mixed with AeB at room temperature. As described
in [145], a fast H
2
evolution was observed evidencing the ef-
ciency of these Fe nanoparticles for dehydrogenation of AeB,
as depicted in gure15, step 1. However, the reactivity does
not stop with the release of AoB, as incorporation of boron
step 2 is revealed from EXAFS measurements. In a second
experiment, AoB was reacted with the preformed Fe nanopar-
ticles. Here again, H
2
evolution was observed, thus evidencing
the activity of the Fe nanoparticles towards dehydrogenation
of the AoB moiety (gure 15, step 2). The proof of boron
incorporation in Fe nanoparticles studied in this work by
EXAFS analysis opens a route for the preparation of FeB
nanoparticles and reveals the property of Fe nanoparticles to
dehydrogenate both AeB and AoB derivatives.
5.2. Ageing effects of iron oxide nanoparticles in dispersion
X-ray absorption spectroscopy has been employed recently
for the rst time to investigate nanoparticles in dispersion
which is essential for any in vivo application. As an example,
the biocompatible iron oxide system was chosen and a study
on ageing effects of dispersed nanoparticles monitored by
changes in the XANES is presented. In the as-prepared state,
the iron oxide nanoparticles consist of Fe
3
O
4
(magnetite). It is
well-known that the particles tend to further oxidise towards
γ-Fe
2
O
3
(maghaemite) after exposure to oxygen (or air), but it
was usually assumed that storing the dispersed particles in a
closed bottle is sufcient to keep a stable dispersion of Fe
3
O
4
particles. In order to avoid oxidation caused by oxygen in the
solvent, cyclohexane (C
6
H
12
) of the highest purity grade was
used. In the XANES, Fe
3
O
4
can clearly be distinguished from
γ-Fe
2
O
3
by a different spectral shape as will be explained in
the following.
Fe
3
O
4
crystallises in an inverse spinel structure that is
depicted in gure 16. For the Fe ions, there are two differ-
ent lattice sites available: either octahedrally or tetrahedrally
surrounded by oxygen anions denoted O
h
and T
d
sites, respec-
tively. Each unit cell contains 8 T
d
sites and 16 O
h
sites (and
32 oxygen atoms). In Fe
3
O
4
, the T
d
sites and half of the O
h
sites are occupied by Fe
3+
ions while the other half of the O
h
sites is occupied by Fe
2+
ions. Thus, the occupancy ratios of
Fe
2+
in O
h
symmetry to Fe
3+
in O
h
symmetry to Fe
3+
in T
d
symmetry is 1 : 1 : 1. The structure of γ-Fe
2
O
3
is closely related
to the crystal structure of Fe
3
O
4
. A distinct structural differ-
ence can only be found in the occupation of O
h
sites: while the
T
d
sites are again occupied by Fe
3+
ions, on the O
h
sites Fe
3+
ions and additional vacancies can be found. The occupancy
ratio of Fe
3+
on T
d
sites to Fe
3+
on O
h
sites is 3 : 5. Formally,
the two oxides and the off-stoichiometric oxides describing a
mixture of pure Fe
3
O
4
and γ-Fe
2
O
3
, can be written as:
δδ
δ
+
+
+
+
O
[F
e][FeF
e]
Td
Oh
3
12
3
13
2
4
2
(28)
where denotes a vacancy and 0 δ 1/3 represents the
degree of oxidation: Fe
3
O
4
is characterised by δ = 0 and γ-
Fe
2
O
3
by δ = 1/3. In the XANES, different valence states
and different oxygen surroundings are connected to differ-
ent x-ray absorption energies and intensities. An example
for a detailed analysis of the XANES for several oxidation
states can be found in the literature [146]. Here, we pres-
ent some multiplet calculation results using the CTM4XAS
programme [147] which offers the possibility to calculate
Figure 13. Magnitude of the Fourier transform (a) and wavelet
transforms (b)(d) for different elemental contributions in Fe
nanoparticles with boron incorporated.
Rep. Prog. Phys. 78 (2015) 062501
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18
the different contributions of different Fe ions to the overall
XANES signal site- and valence-specically. The contribu-
tions are shown in gure17 for Fe
3+
at either O
h
or tetrahe-
dral T
d
sites and Fe
2+
at O
h
sites. The crystal eld parameters
describing the inuence of the surrounding oxygen ions were
set to 10Dq = 1.5 eV for O
h
sites and 10Dq = 0.7 eV for T
d
sites, respectively as suggested in the literature [148, 149].
The spectra were calculated with a Lorentzian broadening of
0.25 eV and a Gaussian broadening of 0.3 eV to account for
lifetime effects and nite energy resolution in experiments. It
can clearly be seen that the spectral shape for Fe
2+
and Fe
3+
in the same O
h
environment is similar. The maximum absorp-
tion is shifted by about 3 eV to lower energies in the case of
Fe
2+
; the smaller intensity compared to the Fe
3+
contribu-
tion is due to a smaller number of unoccupied d states in the
case of Fe
2+
(3d
6
) with respect to Fe
3+
(3d
5
). Summing up
the spectra weighted by the different occupation probabilities
yields for both types of oxides basically two peaks at the Fe
L
3
absorption edge, i.e. one main peak originating from Fe
3+
and a smaller peak at lower energies. The relative intensities
of these two peaks gives the possibility to distinguish between
γ-Fe
2
O
3
and Fe
3
O
4
. As can be seen in gure17, there may be
two reasons for the occurrence of a pre-peak feature in the
XANES: Fe
2+
ions and Fe
3+
on octahedral sites. The latter
yields only a small pre-peak compared to the intensity of the
main peak, whereas Fe
2+
yields a more pronounced pre-peak.
Since Fe
2+
can be found in Fe
3
O
4
only, this type of oxide is
characterised by a larger pre-peak compared to Fe
2
O
3
. From
calculated spectra and spectra reported in the literature [146],
it can be concluded that a pre-peak intensity around 0.60.8
of the main absorption peak indicates Fe
3
O
4
, 0.30.4 indi-
cates γ-Fe
2
O
3
.
It has been shown that, indeed, the XANES of freshly
prepared Fe
3
O
4
nanoparticles with a mean diameter of 6
Figure 14. Scheme of the reaction between AeB and the precursor [Fe(N(SiMe
3
)
2
)
2
]. Adapted with permission from [145].
Figure 15. Scheme of the proposed two-step reaction for the incorporation of boron in pre-formed Fe nanoparticles. Adopted from [145].
Figure 16. Magnetite unit cell.
Rep. Prog. Phys. 78 (2015) 062501
Review Article
19
nm dispersed in cyclohexane reveals a high amount of Fe
2+
ions. But after three days stored in a sealed glass bottle,
the Fe
2+
fraction is signicantly reduced indicating a fur-
ther oxidation of Fe
3
O
4
towards γ-Fe
2
O
3
. Exposure to air
gives rise to an even faster oxidation of Fe
3
O
4
nanoparticles
in dispersion which is shown in gure18. These measure-
ments have been performed at the HZB-BESSYII synchro-
tron radiation facility using the Liquidrom endstation at the
U41-PGM beamline. In this experimental set-up the liquid
is pumped in a closed cycle through a ow-cell with a 100
nm thin window of SiN
x
. The outer environment of the
owcell is pumped to high vacuum (10
6
mbar) to minimise
losses of x-ray intensity due to unwanted absorption by
residual gas molecules. Incoming x-rays can pass through
the window and irradiate the liquid behind. The uores-
cence yield (FY) is detected through the same window by a
GaAs photodiode. In order to accelerate the ageing, air was
bubbled into the liquid cycle. Although the concentration
of nanoparticles in dispersion was quite low (about 8 mmol
l
1
), a clear signal could be detected at the Fe L
3
absorption
edge. Unfortunately, due to the low concentration, the FY
suffers from severe saturation effects, i.e. the FY is not pro-
portional to the absorption cross-subsection of the probed
material leading to a suppression of measured maxima with
respect to the off-resonance background. However, the
change in the spectral shape of the Fe L
3
absorption edge
due to further oxidation of the Fe
3
O
4
is clearly visible. After
about half an hour, this process becomes measurable and
after about two hours, the stable γ-Fe
2
O
3
is the dominat-
ing Fe-oxide. This clearly shows that Fe
3
O
4
nanoparticles in
dispersion are not stable against oxidation and special care
has to be taken to avoid ageing effects. Ideally, the disper-
sion should be stored e.g. under Ar atmosphere or should be
kept in a closed glass bottle that has been sealed under an
oxygen-free protecting atmosphere.
5.3. Tuning the magnetic properties of FePt nanoparticles by
capping
As previously discussed, FePt is one of the prime candidates
for ultrahigh density magnetic storage media. However, for
this kind of application, capping of the FePt nanoparticles is
highly desirable mainly for two reasons. Firstly, the particles
should be protected from oxidation that may alter their mag-
netic properties signicantly. Secondly, a smooth surface is
important for fast writing and reading processes and there-
fore, embedding the particles in a matrix may be advanta-
geous. However, the capping material has to be thoughtfully
chosen not to lower the anisotropy or magnetic moments via
hybridisation effects. The x-ray absorption spectroscopy has
shown to be a powerful tool to investigate changes in the
magnetic properties of Fe in FePt due to capping [45]. By
comparison to results from density functional theory cal-
culations, an atomistic model was obtained for the mutual
inuence of the FePt nanoparticle and capping layer on the
magnetic properties. Interestingly, it has been found that
depending on the capping material, the FePt nanoparticles
can be tuned from hard- to soft-magnetic with high or low
effective magnetic anisotropy and even rules for the design
of nanoscale core-shell systems were deduced from these
results [45]. In this subsection we chose as one example the
preparation and characterisation of FePt nanoparticles with
Al as a cap. One advantage of Al as a capping material is the
fact that it forms a 12 nm thin passivating Al-oxide layer
that protects the sample from further oxidation. Al is also
advantageous for XAS with soft x-rays because it is almost
transparent in this photon energy range. In addition, Al as a
light element produces only a weak background of secondary
electrons and, thus, a clear total electron yield signal from
the underlying element can be detected. Figure19 shows a
scanning electron microscopy image of FePt nanoparticles
Figure 17. Calculated XANES and XMCD for Fe
2+
and Fe
3+
in
different crystal elds which occur in magnetite.
Figure 18. Time-dependent changes of the XANES at the L
3
absorption edge of iron oxide nanoparticles in dispersion.
Rep. Prog. Phys. 78 (2015) 062501
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20
with a mean diameter of about 6 nm deposited onto a natu-
rally oxidised Si wafer using the spin-coating technique. The
particles were synthesised following the wet-chemical route
reported by Sun et al [150]. They are in the chemically disor-
dered state, dispersed in cyclohexane and are surrounded by
organic ligands in the as-prepared state. These ligands act as
spacers between the nanoparticles and avoid the formation
of agglomerates. They can be removed by a soft hydrogen
plasma treatment which reduces also iron oxides that may be
present at the surface [151, 152]. Subsequently, the chemi-
cally ordered state of the FePt alloy is achieved by annealing
the sample. As discussed above in section3.2, special care
has to be taken to exclude sintering of the nanoparticles at
elevated temperatures. In the last preparation step, the FePt
nanoparticles were covered with Al. The XANES and cor-
responding XMCD spectra at the Fe L
3,2
absorption edges of
FePt nanoparticles in the three different preparations stages
mentioned above are presented in gure20. We focus here on
the discussion of Fe magnetic moments since it has already
been shown that they are a sensitive monitor for changes
in structure and symmetry while the induced Pt magnetic
moments remain rather unchanged [153].
From equation(24) it is obvious that the orbital magnetic
moment is proportional to the integral of the XMCD signal
over the whole energy range of both L
3
and L
2
absorption
edges and beyond, which is denoted by q. Since there are only
small changes visible in the XANES, we restrict to the dis-
cussion of the integrated XMCD signals which are shown in
gure20 as well. While for the chemically disordered nano-
particles q is rather small (gure 20(a)), it is strongly increased
after annealing of the nanoparticles (gure 20(b)) indicating a
larger orbital magnetic moment. Capping with Al yields an
orbital magnetic moment that is reduced with respect to the
annealed uncapped state, but still larger than the orbital mag-
netic moment of the chemically disordered FePt nanoparticles
before annealing (gure 20(c)). The ratio of orbital-to-spin
magnetic moment can be assigned to the ratio between the
parameter q and the integral of the XMCD signal over the
energy range of the L
3
absorption edge (denoted by p) accord-
ing to equation (26). One may realise from the integrals of
the XMCD signals, that the ratio of orbital-to-spin magnetic
moment remains largely unchanged for the Al capped FePt
nanoparticles compared to the uncapped ones, while it is sig-
nicantly reduced in the case of the chemically disordered
FePt nanoparticles. In table2, the magnetic moments of Fe in
FePt are summarised. In the chemically disordered state with
an fcc lattice, the ratio of orbital-to-spin magnetic moment is
around 2% and the magnetic moments are slightly reduced
with respect to the corresponding bulk material. It has been
shown that an inhomogeneous alloying may be responsible
for the smaller moments [154, 155]. After annealingbut still
before capping the nanoparticlesthe ratio of orbital-to-spin
magnetic moment increased to about 8% which is related to
an unquenching of the orbital moment due to the tetragonal
distortion of the former cubic symmetry. Capping of the nano-
particles with Al does not affect this value within experimen-
tal errors. But interestingly, the absolute values of the effective
spin and orbital magnetic moments are signicantly reduced.
In addition, the effective magnetic anisotropy is reduced with
respect to the bulk material. This may be related to an elec-
tronic hybridisation between Fe and Al that slightly inuences
the shape of the XANES as well: for the Al capped FePt nano-
particles a small peak is visible a few eV above the maximum
absorption at the Fe L
3
absorption edge and the overshoot
of the XMCD signal between L
3
and L
2
absorption edge
vanishes.
To gain further insight into the microscopic origin of
the change in magnetic properties, density functional the-
ory calculations were performed using the Vienna ab-initio
simulation package VASP [7073]. The wavefunctions of
the valence electrons were expanded within a plane wave
basis set in combination with the projector augmented wave
(PAW) method for the interaction with nuclei and core
electrons [75]. The generalised gradient approximation
exchange correlation functional was used in the formulation
of Perdew and Wang [156] together with the spin interpola-
tion formula of Vosko, Wilk and Nusair [157]. Spinorbit
interaction can be included in the non-collinear version of
the code [158160].
For the simulations clusters of chemically ordered FePt
cuboctahedra covered by a layer of Al, Cu or Au were mod-
elled and the system was allowed to relax structurally [35].
The results are visualised in gure21. It can clearly be seen
that capping with Al has a strong inuence on the morphology
of the nanoparticle, while the structural modications for Au
or Cu capping are only moderate. It is reasonable that a differ-
ent morphology due the capping may yield different magnetic
properties. And indeed, the calculated magnetic moments
and the magnetic anisotropy are reduced in agreement to the
experimental ndings. The calculated magnetic moments for
Fe and Pt atoms of FePt nanoparticles with Fe terminated sur-
face are shown in gure 22 as a function of distance from
the centre. For the FePt nanoparticles covered by an addi-
tional Al layer, it can clearly be seen that both spin and orbital
magnetic moments of Fe are signicantly reduced at the
interface, i.e. at large distances from the centre. The reduced
magnetic moments of Fe yield a simultaneous breakdown of
the induced magnetic moments at the Pt sites. The interfacial
magnetic moments indicate a strong electronic hybridisation
Figure 19. Scanning electron microscopy image of self-assembled
FePt nanoparticles with a mean diameter of 6 nm deposited onto a
Si wafer.
Rep. Prog. Phys. 78 (2015) 062501
Review Article
21
between the Fe 3d states with additional (s,p) electrons as also
concluded from the spectral shapes of experimental XANES
and XMCD.
To minimise the inuence of the capping material on the
magnetic moments of the FePt nanoparticles, Cu or Au may
be a better choice: For the case of Cu, the calculated magnetic
moments reveal no impact on the magnetism of the Fe atoms
and only a small reduction of the Pt spin magnetic moment. In
the case of Au capping, solely the Fe orbital moment is affected.
In addition, the theoretical approach offers the unique
possibility to separate pure structural effects from elec-
tronic hybridisation effects. Therefore, the capping atoms
were removed in the next step and magnetic moments and
anisotropy were recalculated. It was found that both, struc-
tural changes and hybridisation effects strongly inuence
the magnetism of the nanoparticles. Combining theory with
experimental x-ray absorption results, design rules for the
preparation of nanoparticles with tailored magnetic properties
could be formulated and published [140], which are going to
be useful for applications:
Hard magnetic FePt nanoparticles: to maintain the large
magnetic anisotropy of uncapped FePt nanoparticles and
their magnetic moments covering with an element from
the late d series like Cu is advised.
Soft magnetic FePt nanoparticles with large saturation
magnetisation: FePt nanoparticles with Fe-terminated
surfaces should be capped with heavy elements with large
spinorbit coupling like Au, which yield largely unchanged
magnetic moments with respect to the uncapped particles,
but a signicant decrease of the MAE.
Soft magnetic FePt nanoparticles with reduced saturation
magnetisation: capping with Al leads to a signicant reduc-
tion of both magnetic anisotropy and magnetic moments.
Figure 20. XANES, XMCD and integral of XMCD at the Fe L
3,2
absorption edges of 6 nm FePt nanoparticles at about 10 K and a
magnetic eld of 2.8 T in three different preparation stages: chemically disordered (a), chemically ordered after annealing (b) and
chemically ordered after annealing and subsequently capped with Al (c).
Table 2. Magnetic moments of FePt nanoparticles at different preparation stages and with different size determined by XMCD analysis.
Sample
μ μ
/
s
eff
B
μ
l
/μ
B
μ
tot
/μ
B
μ μ
/
ls
eff
6 nm fcc, uncapped
a
2.28 ± 0.25 0.048 ± 0.010 2.33 ± 0.26 (2.1 ± 0.4)%
6 nm L1
0
, uncapped
b
2.38 ± 0.26 0.20 ± 0.02 2.58 ± 0.28 (8 ± 1)%
6 nm L1
0
, Al capped
c
2.14 ± 0.22 0.15 ± 0.02 2.29 ± 0.24 (7 ± 1)%
2 nm L1
0
, Al capped
c
1.78 ± 0.19 0.13 ± 0.02 1.91 ± 0.21 (7 ± 1)%
a
Values taken from [155].
b
Values taken from [153] and recalculated for the same number of unoccupied nal states.
c
Values taken from [140].
Rep. Prog. Phys. 78 (2015) 062501
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22
In addition it was reported that lighter elements like car-
bon show enhanced diffusion into the particle and yield to a
complete breakdown of the net magnetisation [140].
5.4. New high-moment materials for microelectronics: beat-
ing the SlaterPauling limit?
As a prototype system to achieve a high saturation magnetic
moment beyond the SlaterPauling limit, 13 monolayers
(ML) Gd on 15 ML Fe was chosen. As discussed in sec-
tion 3.4 ferromagnetic coupling between epitaxially grown
Gd and Fe thin lms was forced by a Cr interlayer with a few
monolayers thickness. The sample growth was monitored by
reection high energy electron diffraction (RHEED) patterns
revealing the epitaxial quality of the lms examined [161] as
can be seen in gure23. The spin alignment was measured by
means of x-ray magnetic circular dichroism (XMCD) at the
Fe L
3,2
and Gd M
5,4
absorption edges in magnetic remanence.
While for a Cr interlayer thickness of 4 ML an antiparallel
alignment was obtained, a Cr thickness of 5 ML yielded a
parallel alignment of Fe and Gd spins. The coupling scheme
is presented in gure 23(a). Note that an antiparallel align-
ment was also found for 3 monolayers of Cr, most probably
caused by interdiffusion at the Fe/Cr interface. However, the
ferromagnetic coupling between Gd and Fe for 5 monolay-
ers of Cr interlayer is clearly indicated by the quotient of the
x-ray absorption signals with reversed direction of magnetisa-
tion or reversed helicity of incident photons as a function of
photon energy (gure 24): The signal at the Gd M
5
absorption
edge points down (<1) and at the M
4
edge it points up (>1)
like Fe at its L
3
and L
2
edge, respectively. Note that the Fe
spectra have a low signal-to-noise ratio since all the spectra
were taken in the TEY by probing the sample drain current.
Since the electron escape depth is only a few nanometres, the
Figure 21. Calculated morphologies of capped FePt clusters after structural relaxation. Figurereprinted from [140].
Figure 22. Spatially resolved calculated spin (top) and orbital (bottom) magnetic moments for Fe and Pt atoms in FePt nanoparticles
capped with Al (left), Cu (centre) and Au (right). Blue circles denote position and moments of Fe atoms, while reddish squares depict Pt.
The intensity of the colour refers on a logarithmic scale to the number of overlapping symbols, i.e. the frequency of atoms with a given
moment and distance from centre. Figurereprinted from [140].
Rep. Prog. Phys. 78 (2015) 062501
Review Article
23
signal from the Fe layer buried under Cr, Gd and a 10 nm
thick Si/SiO
x
layer is quite hard to detect. Field-dependent
XMCD measurements at two different angles with respect to
the sample normal indicate an easy direction of magnetisation
in the sample plane and show a reversed sign for antiferro- and
ferromagnetic coupling.
In order to ensure that the Gd lm is not already decoupled
from the Fe lm by the Cr interlayer, the XMCD signal at the
Gd M
5
,
4
absorption edges was measured at different tempera-
tures between 11 K and 300 K. As suggested in the literature
[65, 66], the experimental data were simulated by a simple
model assuming an enhanced Curie temperature of Gd at the
interface due to the exchange coupling:
⎜⎟