J. Phys. D: Appl. Phys. 31 (1998) 649–655. Printed in the UK
PII: S0022-3727(98)88436-2
Imaging of magnetic domains by
transmission x-ray microscopy
P Fischer†, T Eimüller†, G Schütz‡, P Guttmann§, G Schmahl§,
K Prueglk and G Bayreutherk
† Universität Augsburg, EPII, Memmingerstraße 6, D 86135 Augsburg, Germany
‡ Universität Würzburg, EP IV, Am Hubland, D 97074 Würzburg, Germany
§ Forschungseinrichtung Röntgenphysik, Universität Göttingen, Geiststraße 11,
D 37073 Göttingen, Germany
k Universität Regensburg, Institut für Experimentelle und Angewandte Physik,
Universitätsstraße 31, D 93040 Regensburg, Germany
Received 14 October 1997
Abstract. The combination of the high-resolution transmission x-ray microscope
(TXM) based on the zone plate technique with the x-ray magnetic circular
dichroism (X-MCD) providing a huge magnetic contrast is a new technique to
image magnetic domain structures. It is inherently element specific and contains
information on the local spin and orbital moments of the absorbing species that can
be obtained by applying magneto-optical sum rules. A lateral spatial resolution
depending on the quality of the zone plates down to 30 nm can be achieved. We
report on first results at the Fe L3,2 edges of Fe both in amorphous and in
multilayered Gd–Fe systems. With a TXM set-up at BESSY I adapted to record
magnetic images in varying magnetic fields the evolution of magnetic domains
within a complete hysteresis loop and magnetic aftereffects have been studied.
1. Introduction
The detailed understanding of magnetism in systems of low
dimensionality such as ultra-thin magnetic films and multilayers is nowadays of great importance. Recent discoveries of novel phenomena such as the giant magnetoresistance (GMR) effect, quantum oscillations like oscillatory interlayer exchange coupling and magnetic interface
anisotropies emphasize the basic aspects concerning fundamental research into magnetism. Besides this curiosity
their technical relevance as promising candidates for magnetic sensors (GMR, spin valve structures or tunnelling
junctions), ultra-high-density magnetic and magneto-optic
recording of information, magnetic memories and logic elements for which the bit size approaches the 1–100 nm
length scale pushes these systems to the frontier of technological relevance. The process of miniaturization itself, for
example in the research and development of the MRAM
technology in which currently nanostructured systems are
of major interest, requires reliable information on the magnetic microstructure so that one is able to determine the
technical limits that can be achieved. Thereby one aspect
is the exact switching behaviour of magnetic dots within
an applied field which is still unknown. The imaging of
the magnetic domain evolution in external fields within a
nanometre scale is therefore an outstanding challenge.
Modern techniques to study both static and dynamic
properties of magnetic domains with high spatial resolution
down to several nanometres, such as Bitter pattern imaging
c 1998 IOP Publishing Ltd
0022-3727/98/060649+07$19.50 [1], scanning electron microscopy with polarization
analysis (SEMPA) [2], Lorentz microscopy [3], magnetic
force microscopy (MFM) [4], scanning near-field optical
microscopy (SNOM) [5], spin-polarized low-energy
electron microscopy (SPLEEM) [6], electron holography
[7] and scanning Hall [8] and SQUID microscopies [9]
are established. Each of these methods exhibits specific
virtues but has also inherent drawbacks, described in
[10]. One important aspect is the possibility of recording
magnetic images in a varying applied magnetic field, which
poses severe problems to electron detection techniques.
Furthermore, for technical applications a quantitative
analysis of the strengths and the directions of magnetic
moments is mandatory. The scanning techniques can be
time consuming in particular for obtaining reproducible
imaging of areas extending to several micrometres. The
study of the dynamics of magnetic domains with the
powerful Kerr microscopy [11] can be applied in magnetic
fields; its spatial resolution, however, is diffraction limited
by the wavelength of visible light.
Closely related to the magneto-optical Kerr effect
(MOKE) is the occurence of x-ray magnetic circular
dichroism (X-MCD) in the x-ray range corresponding to
wavelengths down to the sub-nanometre regime, namely
two orders of magnitude smaller than visible light. The
dichroic effect, which occurs in the vicinity of elementspecific inner-core absorption edges, exhibits a dependence
of the absorption of circular polarized x-rays on the
projection of the magnetization onto the photon propagation
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P Fischer et al
direction in ferromagnetic samples. At L edges in 3d
transition metals relative changes in the absorption cross
section by up to 50% occur. It can therefore serve as a
huge magnetic contrast in imaging techniques using the
absorption mode. The X-MCD can be detected both in the
primary absorption process and in the succeeding emission
of secondary electrons.
First attempts to image magnetic structures with the
help of the X-MCD used a photoemission microscope
(PEEM). A spatial resolution of a few micrometres could
be obtained while observing remanent magnetized samples
[12].
Further developments of this surface-sensitive
technique obtain nowadays resolutions down to 300 nm
[13]. Basic features of these experiments are the element
specificity and the surface sensitivity. However, this
method is restricted to studies in zero magnetic field.
A different approach to image magnetic domains even
on the nanometre length scale by the combination of the
transmission x-ray microscope (TXM) at BESSY I and
the X-MCD effect used in the complementary transmission
mode could be realized recently [14]. In this short paper
the outstanding features of this new concept in imaging
techniques which should make remarkable contributions
even to the technological challenges mentioned above will
be exemplified by some selected results on layered Gd–Fe
systems.
2. Magnetic imaging via X-MCD
The physical origin of X-MCD in the x-ray absorption is
based on angular momentum conservation and spin–orbit
interaction basically in the initial state. If the energy
of the absorbed photon equals the binding energy of a
particular inner-core level (e.g. p3/2 ) the photoelectron is
excited into an unoccupied state of d symmetry above
the Fermi level obeying dipolar selection rules.
In
the case of a circularly polarized absorbed photon the
outgoing photoelectron acquires both an expectation value
of the spin and the orbital momentum projected onto the
direction of propagation of the incoming photon due to the
constraint that 1ml = ±1. The spin hσz i and orbital hlz i
polarizations can be calculated on the basis of Clebsch–
Gordan coefficients to amount to hσz i = −50% and +25%
at the L2 and L3 edges, whereas hlz i = +75% at both
L2 and L3 edges. According to the Pauli principle the
photoelectron can be considered as a local probe for the
spin and orbital polarization of the absorbing atom. Just
like in a spin ferromagnet, the final density of states exhibits
a spin polarization due to the exchange interaction and
the transition probability of the absorption process depends
on the polarization of the final d states, which is directly
related to the magnetization of the absorbing atom. In the
ideal case of a completely spin-polarized final state, that is,
one spin band is completely shifted below the Fermi level
and the magnetic moments are fully aligned, the difference
between the absorption coefficients for the direction of the
magnetization parallel µ+ and antiparallel µ− to the photon
propagation direction (µ+ −µ− ) normalized with respect to
the unpolarized absorption (µ+ + µ− ) corresponds directly
to hσz i provided that the corresponding orbital polarization
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can be neglected. Taking into account also the orbital
contribution there would be a further increase/decrease of
the dichroic signal at the L3 /L2 edge, respectively.
Therefore the huge magnetic contrast that can be
used in imaging techniques relying on X-MCD in the
transmission mode is provided by the energy-dependent,
element-selective and symmetry-sensitive deviation of the
absorption coefficient 1µ(E) relative to the polarizationaveraged absorption coefficient µ|ii (E) which takes into
account only the photoprocess in an atomic core level |ii
σc
1µ
(E) =
(E)(m̂ · êz )Pc .
µ|ii
σ|ii
(1)
Thereby m̂ · êz denotes the projection of the normalized
magnetic moment m̂ = m/|m| onto the propagation
direction with unit vector êz of the photons with a degree of
circular polarization Pc . The value of µ|ii (E) is specific and
can be taken from spectroscopic data tables. Background
extinction due to absorption into higher levels contributes
for example at the Fe L3 edge on a 10% level relative to the
absorption occurring within the resonantly enhanced white
line profile for a pure Fe substrate layer. The magnetic
contrast at the corresponding L2 edge is much weaker
insofar as its signal-to-background ratio contributes on a
50% level. However, this is partly compensated due to the
higher value of hσz i.
The magnetic absorption cross section normalized
with respect to the polarization-averaged atomic cross
section σc /σ|ii has been determined by X-MCD studies
to reach, for example, at the maximum of the Fe metal
L3 edge σc /σ|2p3/2 i (E = 706 eV) ≈ 23%.
From
equation (1) it can be seen that, provided that Pc is known,
the observable experimental quantity (1µ(E)) allows a
quantitative determination of the absolute projection of the
magnetic moment of Fe.
The main interest in X-MCD experiments, however,
is based on the fact that a correlation of data from
corresponding spin–orbit split initial states, such as L3 and
L2 edges, allows one to extract separately the spin and the
orbital moments directly by applying the sum rules [15, 16].
This is a unique feature of X-MCD spectroscopy and has
led to a spectacular revival of interest in the role of the
orbital moment in many unsolved problems such as the
origin of the magnetocrystalline anisotropy energy which
determines predominantly the macroscopic behaviour in
thin films. Thus in principle the comparison of the magnetic
contrast taken at the L3 and the L2 edge contains directly
the information on the lateral spin and orbital contributions
separately.
3. Experimental aspects
The x-ray optical set-up of the TXM, which is described in
more detail in [17, 18] is shown in figure 1, including the
modifications needed in order to perform magnetic imaging.
The x-ray source of the synchrotron is imaged into the
object plane with the object field limited by a pinhole with
a diameter chosen in the range 10–20 µm. Circularly
polarized light could be selected by partly masking the
Imaging of magnetic domains by transmission x-ray microscopy
Polychromatic X-Radiation
Monochromator
Pinhole d=20µm
Mask
Experimental set-up at BESSY I
e.g. L3 (Fe): λ=1.76nm (Eγ=706eV)
B-Field <80mT
Object
Image
Image CCD
Camera
Field
≈17µm
Micro Zone Plate
drn=40nm, Eff. 9.1%
Circular Polarized Light
Pc≈60%
Condensor Zone Plate
D=9mm
Monochromaticity λ/∆λ = D/2d =225
Figure 1. The experimental set-up of the TXM extended for magnetic imaging at BESSY I. Circularly polarized light is
obtained by masking part of the condensor; a solenoid allows one to align the magnetic moments in the sample.
synchrotron beam so that only the lower segment of the
condensor with a height of 2 mm was illuminated. The
degree of circular polarization (Pc ) can be estimated on the
basis of beam parameters to amount to ≈60% [19]. The
condensor optics serves as a linear monochromator due to
the wavelength-dependent focal length of the condensor
zone plate (CZP). This allows one easily to tune the
photon energy to a value at which the dichroic effect is
maximum by moving the condensor along the optical axis
of the microscope. The monochromaticity which is given
by λ/1λ = D/(2d), with D = 9 mm the diameter of
the CZP and d = 20 µm the diameter of the pinhole,
amounts to λ/1λ = 225. This is sufficient to separate
in particular the L3 and the L2 edges which are separated
by 13 eV. The microzone plate used as a high-resolution
x-ray objective generates a magnified image of the object
in the image field with a spatial resolution of about 30 nm.
The spatial resolution is basically determined by the width
of the outermost zone. Special microstructures produced by
means of electron lithography could be used as a gauging
device and demonstrated that we had obtained a resolution
of 30 nm. A slow-scan CCD camera with a thinned,
back-side-illuminated CCD chip with a detective quantum
efficiency (DQE) of about 70% is used to record the x-ray
images. A small solenoid placed close to the sample allows
one to apply small magnetic fields up to 80 mT onto the
sample with its field direction pointing parallel/antiparallel
to the photon beam propagation direction.
The results presented in this paper had been obtained
with two different Gd–Fe systems. An amorphous system
(Gd27.7 Fe72.3 ) has been prepared by co-evaporation from
two electron-gun sources, whereas the second one was
a multilayered system prepared by magnetron sputtering
composed of 75 double layers, each consisting of 4 Å Gd
and 4 Å Fe single layer thicknesses. For both specimens we
used a 325 nm thin polyimide substrate and for chemical
protection they were topped with a thin layer of Al.
The macroscopic magnetization had been determined from
MOKE and VSM measurements and the results verified that
there was a strong anisotropy perpendicular to the surface.
4. Results
Figure 2 shows the magnetic x-ray microscope images of
the Gd/Fe layered systems ((4 Å Gd/4 Å Fe) × 75). They
were obtained by tuning the x-ray energy to the Fe L3 (a)
and L2 (b) edges. The dark/light areas in figures 2(a)
and (b) indicate the direction of projection of the local Fe
magnetization in/out of the plane of the paper. According
to (1) m̂ · êz is directly related to 1µ because the other
quantities µ|ii (E), σc /σ|ii (E) and Pc are known. Thus it
can be concluded that, within the magnetic domain, the full
bulk-like Fe moment of 2.1 µB is established in accordance
with macroscopic magnetic measurements. It can also be
seen from figures 2(c) and (d) that the dichroic scan profiles
change their signs with the different edges (as expected for
the different values of hσz i) and the magnetic contrast is
weaker at the L2 edge by a factor of two.
On following the scan profiles (figures 2(c) and (d)),
it is obvious that the expected width of the domain
wall w ' (A/Ku )1/2 of the order of 20 nm is below
the spatial resolution limit in our images. However,
further experimental improvements will provide valuable
information on that issue and thus on the basic anisotropy
(Ku ) and exchange constants (A).
An interesting aspect is the question of whether this
technique will provide information even on the orbital
651
P Fischer et al
(a)
(b)
L3
L2
1µm
1µm
5.0
5.0
2.5
µc/µS (%)
(c)
L3
2.5
0.0
0.0
-2.5
-2.5
-5.0
0
10
20
30
40
50
60
-5.0
(d)
L2
0
10
20
Pixel (a.#)
5.0
combined L3,L2 signal
µc/µS (%)
2.5
30
40
50
60
Pixel (a.#)
(e)
0.0
-2.5
-5.0
1 Pixel = 13.76 nm
0
10
20
30
40
50
60
Pixel (a.#)
Figure 2. Images taken at the L3 (a) and L2 (b) edges of Fe in a layered 4 Å Gd/4 Å Fe system. The diameter of the field of
view is 10.8 µm. Line scans (one pixel is 13.76 nm) of the dichroic intensity (µc /µS ) across the magnetic domain are
marked by the arrows at the L3 (c) and L2 edges (d). Combination of the L3 and L2 images to estimate the orbital contribution
is shown in (e). The shaded areas mark the domain wall region.
652
Imaging of magnetic domains by transmission x-ray microscopy
1.0
(N)
(S)
0.5
(W)
M/MS
(C)
1 µm
0.0
(W)
(C)
-0.5
(S)
1 Pixel = 13.76 nm
-1.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
H (kOe)
Figure 3. A sequence of magnetic images at the Fe L3 edge of the layered Gd–Fe system in a varying applied magnetic
field covering the complete hysteresis loop. The different stages saturation (S), nucleation (N) and worm-like domains (W)
are marked. The hysteresis loop (M /Ms versus H (kOe)) (——) was determined from MOKE measurements.
contributions. One expects a variation of the orbital
moment mainly in the domain walls compared with the
inner domain region. In order to extract this feature we
normalized the L2 data such that the combination of the
L3 and the L2 data cancels outside the wall region (see
figure 2(e)). The occurrence of an orbital contribution
would be manifested by a deviation from zero. It can be
seen in figure 2(e) that, within the shaded areas, which
coincide with the domain wall region, there might be
evidence for the development of an orbital moment exactly
at this location within the statistical in accuracy of less
than 10%. However, a reliable proof that the dispersive
feature observed in the data presented here originates
from lateral variation of the orbital momentum will need
further improvements of the experimental conditions. In
particular, diffraction patterns which could mask the orbital
profile have to be taken seriously into account. The exact
application of the sum rules to extract spin and orbital
moments requires spectroscopic information, which is in
principle also possible with our set-up. However, even scan
profiles taken at a single energy would allow an estimate
of the contribution of the orbital moment.
Another feature of great practical importance is the
capability of recording images in arbitrary applied magnetic
fields, which allows one to study the magnetization
reversal process on a nanometre scale. Figure 3 shows
selected magnetic images of the multilayered Gd–Fe system
recorded at the Fe L3 edge. Starting at a fully oriented
sample (M = Ms ) represented by a homogeneous either
dark or light image (S), an abrupt nucleation of magnetic
domains occurs within a few times 0.1 mT (N), thereby
forming irregular complex structures. With increasing
applied field the domain evolution occurs by the starting
structures expanding and this being accompanied by the
formation of additional domains. Approaching the reversed
saturated magnetic state (light or dark, respectively) small
relatively hard magnetic regions now exhibiting a wormlike shape (W) persist. Their width distribution could
be observed to extend down to the resolution limit. The
observed behaviour of the evolution of the magnetic
domains is reflected by the shape of the hysteresis loop
which approaches the saturation value smoothly; that is,
the saturation field is ≈10Hc . Although the global pattern
of the domain structures that occur on the second half
of the hysteresis loop is identical for repeated passages
around the loop, the actual local domain structures change
irreversible with repeated cycles of magnetization. Though
the magnetization curve shown in figure 3 had been
measured with a standard MOKE apparatus, it can in
principle also be deduced by an integration of the intensity
of the magnetic images which indicates that the microscopic
field of view (≈10–20 µm) is already representative of the
macroscopic behaviour.
A typical image acquisition cycle consists of illumination of the CCD for less than 10 s and a relatively slow
read-out process, which takes about 30 s. The first time
scale depends on the flux available from the x-ray source,
whereas the latter is a characteristic of the CCD detector in
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P Fischer et al
(a)
1 µm
(b)
The unique feature of being able to acquire information
on the orbital moment via combined images taken for
spin–orbit split initial states and applying the sum rules
will be crucial for the understanding of the microscopic
and macroscopic magnetic properties of any ferromagnetic
solid.
The experimental perspectives are further improvements in the zone plate technique which will provide a
lateral spatial resolution as great as 20 nm. The image acquisition rate will increase both due to an increase in flux
available at the next generation high-brilliance synchrotron
radiation sources and because of current developments in
x-ray CCD detectors approaching the microsecond read-out
range.
Samples with in-plane anisotropy can be investigated by
tilting the sample with respect to the photon propagation
direction. The improvement of the sample preparation
can benefit from standard techniques established for TEM
experiments. Owing to the huge potential, in particular
of being able to support technological research and
development, inherent to this new technique, a dedicated
XTM set-up in which several external parameters (such as
a high magnetic field and temperature) can be applied to
the sample is being constructed for BESSY II in Berlin.
Acknowledgments
This work has been supported by the German Federal
Minister of Research (BMBF) projects 05 621 WAA and
05 644 WGA.
References
Figure 4. Magnetic images taken at the Fe L3 edge in the
amorphous Gd–Fe system with a constant applied
magnetic field of 18 mT at t = 0 s (a) and t = 60 s (b). A
magnetic aftereffect is indicated by the arrow.
use. Therefore the temporal evolution of magnetic domain
structures can be rastered only within a 1 min cycle. Nevertheless magnetic after effects on that time scale could be
observed and a typical example is shown in figure 4. Two
magnetic images of the amorphous Gd–Fe system which
were recorded within 1 min with the applied magnetic field
kept constant demonstrate that wall propagation occurs on
a length scale of ≈0.5 µm within this time interval.
5. Conclusion and outlook
The combination of X-MCD with the XTM allows one
to image magnetic structures on a nanometre scale with
a huge contrast, thereby exhibiting outstanding features.
The element specificity of X-MCD can be utilized to study
technologically relevant multi-component systems and the
available x-ray energy range provided at synchrotron
radiation sources covers the L edges of 3d transition metals
and the M edges of rare earths, which are basic elements
in technological applications.
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[19] We used a code based on the Lippmann–Schwinger
equation. The input parameters are the electron and
photon energies, radius of curvature, distance to source
point, source size, mask geometry and position. Insofar
as these parameters are only estimates, especially the
actual source size, the value given in the text is only an
estimate.
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