Detection of magnetic circular dichroism on the two-nanometer scale
Peter Schattschneider
*
and Michael Stöger-Pollach
University Service Center for Transmission Electron Microscopy, Vienna University of Technology, Wiedner Hauptstrasse 8-10/052,
A-1040 Vienna, Austria
Stefano Rubino
†
Institute for Solid State Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/138, A-1040 Vienna, Austria
Matthias Sperl, Christian Hurm, and Josef Zweck
Institut für Experimentelle und Angewandte Physik, University of Regensburg, D-93047 Regensburg, Germany
Ján Rusz
‡
Department of Physics, Uppsala University, P.O. Box 530, S-751 21 Uppsala, Sweden
共Received 17 July 2008; revised manuscript received 18 August 2008; published 18 September 2008
兲
Magnetic circular dichroism 共MCD兲 is a standard technique for the study of magnetic properties of materials
in synchrotron beamlines. We present here a scattering geometry in the transmission electron microscope
through which MCD can be observed with unprecedented spatial resolution. A convergent electron beam is
used to scan a cross sectional preparation of a Fe/Au multilayer sample. Differences in the energy-loss spectra
induced by the magnetic moments of the Fe atoms can be resolved with a resolution of better than 2 nm. This
is a breakthrough achievement when compared both to the previous energy-loss MCD resolution 共200 nm兲 or
the best x-ray MCD experiments 共approximately 20 nm兲.
DOI: 10.1103/PhysRevB.78.104413 PACS number共s兲: 75.30.Gw, 78.20.Ls, 68.37.Lp, 79.20.Uv
I. INTRODUCTION
Detection of magnetic circular dichroism 共MCD兲 in the
electron microscope was first reported in 2006,
1
providing an
alternative to x-ray magnetic circular dichroism 共XMCD兲,
the standard technique for investigation of spin and orbital
magnetic moments in the synchrotron. The fact that spin-
related properties can now be studied with a commercial
transmission electron microscope equipped with an energy
spectrometer or an energy filter explains the attraction of this
technique, named energy-loss magnetic chiral dichroism
共EMCD兲. Contrary to XMCD that measures polarization de-
pendent x-ray absorption cross sections,
2–5
EMCD exploits
faint differences in the double-differential scattering cross
section 共DDSCS兲 of fast electrons in the diffraction plane of
an electron microscope.
When the method was introduced two years ago,
1
the spa-
tial resolution was intrinsically limited to 200 nm by the size
of the selected area aperture. To improve that limit, one
would have to improve the machinability of transmission
electron microscopy 共TEM兲 apertures or develop new scat-
tering geometries. Since then, several laboratories have
adopted EMCD,
6–8
and it has become clear that at least two
more experimental geometries can be used. The spatial res-
olution was improved to 30 nm with the large angle conver-
gent diffraction 共LACDIF兲 method;
9
here we report a sub-
stantial improvement that allows a spatial resolution of 2 nm
to be attained by using convergent electron-beam diffraction
in the scanning mode of the TEM. In these geometries, the
limiting factors are the aberrations of the microscope and the
low count rate resulting from EMCD being essentially an
interference effect.
The standard technique for the study of magnetic dichro-
ism on a submicrometer scale is XMCD microscopy 共typi-
cally with resolutions of about 25–50 nm兲 based on obtaining
a circular dichroic signal in combination with imaging optics
in a synchrotron. This can be achieved either with electron-
optical lenses to form images with photoemitted electrons
共XMCD photoemission electron microscopy兲 or with diffrac-
tive x-ray optics
4,10–14
where a resolution of 15 nm has been
reported.
15
Also lensless imaging techniques appear to be
very promising, in particular, for time-resolved
experiments.
16
For the study of dynamical magnetic proper-
ties, EMCD is not suited. Developments of pulsed electron
emitters in the TEM may change this situation in the long
run.
These techniques have led to considerable progress in the
understanding of magnetism in the solid state, and they be-
come increasingly important for the rapidly expanding field
of spintronics. The demand for extremely high spatial reso-
lution that arises in this context is met by the intrinsic sub-
nanometer resolution of the TEM.
Here we present a geometry that allows the detection of
EMCD in the TEM on the nanometer scale. The method is
applied to an epitaxial multilayer of Fe/Au, demonstrating a
spatially resolved MCD signal ona3nmwide Fe layer. An
analysis of the signal-to-noise ratio 共SNR兲 shows that the
spatial resolution for the detection of MCD is 2 nm with the
chosen setup. This value is likely to be better in a C
S
cor-
rected microscope.
II. PRINCIPLES OF THE METHOD
The DDSCS in the dipole approximation for a geometry
with two coherent incident plane waves k
ជ
0
, k
ជ
0
⬘
phase shifted
by ⫾
/ 2 关Fig. 1共A兲兴 is
17,18
PHYSICAL REVIEW B 78, 104413 共2008兲
1098-0121/2008/78共10兲/104413共5兲 ©2008 The American Physical Society104413-1
2
E
⍀
=
4
␥
2
a
0
2
k
f
k
0
冉
S共q
ជ
,q
ជ
,E兲
q
4
+
S共q
⬘
ជ
,q
⬘
ជ
,E兲
q
⬘
4
⫿ 2
I关S共q
ជ
,q
⬘
ជ
,E兲兴
q
2
q
⬘
2
冊
,
共1兲
where
S共q
ជ
,q
⬘
ជ
,E兲 ª
兺
i,f
具f兩q
ជ
· R
ជ
兩i典具i兩q
⬘
ជ
· R
ជ
兩f典
␦
共E
i
− E
f
+ E兲共2兲
is the mixed dynamic form factor,
19,20
k
ជ
f
is the final scatter-
ing wave vector 共defined by the detector position兲, q
ជ
=k
ជ
f
−k
ជ
0
and q
ជ
⬘
=k
ជ
f
−k
ជ
0
⬘
are the wave vector transfers,
␥
is the
relativistic factor, a
0
is the Bohr radius, and E is the energy
lost by the fast electron. Using the crystal lattice as a beam
splitter the coherent incident waves k
ជ
0
,k
ជ
0
⬘
are replaced by
k
ជ
0
,k
ជ
g
=k
ជ
0
+g
ជ
with a reciprocal-lattice vector g
ជ
, as drawn in
Fig. 1共B兲.
For an atom at the origin the quantity S possesses an
imaginary part if the atom has a net magnetic moment M
ជ
,
which in the present case is forced to be out of the specimen
plane and parallel to the optical axis of the TEM by the
strong magnetic field 共⬇2T兲 of the objective lens,
21
I关S共q
ជ
,q
⬘
ជ
,E兲兴 ⬀ 共q
ជ
⫻ q
⬘
ជ
兲 · M
ជ
. 共3兲
The dichroic signal is the difference of two spectra 关Eq. 共1兲兴
obtained by reversing the sign of the third 共interference兲
term. In the difference spectrum the first two terms cancel;
only the third one remains. The triple product is nonzero
because the wave vector transfers q
ជ
and q
⬘
ជ
are nearly per-
pendicular to the optical axis, as their z component 共due to
the energy lost in the ionization兲 is considerably smaller than
the x, y components set by positioning the detector in the
diffraction plane.
The helicity of the excitation is changed by placing the
detector in the two positions in the diffraction plane 关Fig.
1共C兲兴 thus selecting two scattering vectors q ⬜ q
⬘
of equal
length. Shifting the detector from the “+” to the “−” position
in Fig. 1共B兲 changes the sign 共but not the magnitude兲 of the
vector product q
ជ
⫻q
ជ
⬘
and thus of the interference term in Eq.
共1兲.
The equivalence with XMCD can be understood when
considering that the inelastic interaction with a given target
atom is Coulombic. The perturbation, leading to an elec-
tronic transition for an atom at the origin, is an electric field
F⬀qe
i共
t+
兲
共and similarly for q
⬘
兲, with ប
=E, the energy
lost by the probe electron in the transition. By forcing the
two coherent plane waves 共0 and g in Fig. 1兲 to exhibit a
phase difference
␦
=
−
⬘
=
/ 2, the electric perturbation
vector F
ជ
+F
ជ
⬘
at the atomic site rotates clockwise in a plane
with surface normal q
ជ
⫻q
ជ
⬘
, thereby forcing a chiral transition
obeying the selection rule ⌬m=+1共equivalent to the absorp-
tion of a photon with positive helicity兲. When shifting the
detector from position + to − in Fig. 1共C兲, the vector q
ជ
⫻q
ជ
⬘
changes sign, the perturbation field rotates counter-
clockwise, and the chirality of the transition is reversed. As
with XMCD, the measured difference spectrum is the di-
chroic signal.
This ideal situation is never met in practice because it
assumes a pointlike detector in the diffraction plane measur-
ing a signal from two monochromatic plane waves ionizing
an atom at the origin, without any other interaction. Dynami-
cal electron diffraction from the crystal lattice causes a varia-
tion of the phase difference
␦
along the electron trajectory
with a periodicity given by the extinction distance
22
共which
appears as a beating effect in the intensity known as
Pendellösung in electron microscopy兲. Therefore, even using
two nearly monochromatic plane waves, the EMCD signal
would always be reduced with respect to XMCD. The favor-
able phase relation can be approximately maintained over a
thickness range of half an extinction distance 共20 nm in Fe
for the 200 reflection; however, differences up to 5% are
expected for samples as thick as 75 nm兲. Specimens should
therefore be prepared for electron microscopy with appropri-
ate thickness. Integration over convergence and collection
angles in the microscope and/or detector system induces ad-
ditional variations in the phase shift between the coherent
partial waves, and the presence of secondary Bragg spots
other than 0 and g has a complex influence on the dichroic
component of the signal.
Diffraction on the crystal lattice, at first view detrimental
to the dichroic signal, can be turned to advantage when one
realizes that the phase shift between the 0 and the g wave can
be tuned by varying the excitation error. Moreover, the lattice
periodicity automatically serves as a phase-lock amplifier,
creating equal-phase shifts in each elementary cell.
When we extend this formalism to the realistic case of
many Bragg scattered waves, Eq. 共1兲 is replaced by
detector positions
+
scan direction
e beam
t=20nm
Au
Fe
5nm
A
B
C
k
0
k
0
q’
q
/2
phase shift
0
k
k’
f
g
0
FF’
g
k
FIG. 1. 共Color online兲 Principle of EMCD. 共A兲 Two coherent
incident plane waves, dephased by
/ 2, produce a rotating electric
perturbation F
ជ
during the atomic excitation. 共B兲 When crystal dif-
fraction is used, the detector position with respect to the 0 and g
beam determines the final scattering direction k
ជ
f
and thus q
ជ
and q
ជ
⬘
.
共C兲 A convergent electron beam is scanned across the Au/Fe
multilayer sample. The detector is alternatively placed at positions
+ and − in the diffraction plane selecting two scattering vectors
q⬜ q
⬘
. The specimen image is a high-angle annular dark field
共HAADF兲 map of the multilayer taken with the 1.7 nm electron
probe.
SCHATTSCHNEIDER et al. PHYSICAL REVIEW B 78, 104413 共2008兲
104413-2
2
E
⍀
=
4
␥
2
a
0
2
k
f
k
0
兺
iⱕj
2R
冋
A
ij
S共q
ជ
i
,q
ជ
j
,E兲
q
i
2
q
j
2
册
, 共4兲
where the scattering vectors are enumerated according to the
Bragg scattered plane waves in the elastic diffraction pattern.
The coefficients A
ij
are calculated in the framework of dy-
namical electron-diffraction theory.
22
Figure 2 shows the
simulated Fe L
3
signal and the relative dichroic signal in the
diffraction plane in the symmetric three-beam case 关g
=共200兲, t=22 nm兴 for parallel illumination. The detector po-
sitions are marked with circles.
III. EXPERIMENTAL PROCEDURE
It is found that the dichroic signal is rather robust with
respect to variations in detection angle, with only the prefac-
tor varying in magnitude.
9
Since the incident and the outgo-
ing beams appear symmetrically in the expressions for the
prefactors,
22
the same robustness must hold for the incident
electron. We had therefore reason to hope that a converged
beam with a convergence angle of the same magnitude as the
collector angle would perform almost as well as an incident
plane wave. It was therefore tempting to replace the LACDIF
共Ref. 23兲 by a convergent beam diffraction geometry 关Fig.
1共C兲兴; here, the specimen remains in eucentric position, and
the signal is taken in the diffraction plane. Differently from
previously reported geometries
1,9
the crystal is tilted to a
three-beam case 共i.e., exciting equally the +g and −g beams兲.
This setup has a symmetry plane perpendicular to g
ជ
passing
through the 0 beam 共Fig. 2兲. The diffraction pattern, consist-
ing now of broad Bragg disks instead of sharp pointlike
spots, is then electronically shifted such that the detector is
placed at symmetric positions, labeled − and + relative to a
line perpendicular to the g vector and passing through 共000兲.
As opposed to the two-beam case this geometry has the ad-
vantage that one avoids any spectral difference not related to
dichroism. The EMCD signal has a spatial resolution given
by the beam diameter which cannot be reduced below a cer-
tain limit because spectra obtained with smaller electron
probes have a lower spectral intensity and low SNR. Experi-
mentally it was found that a nominal spot size of 1.7 nm
yielded a signal strong enough for detection of EMCD in Fe.
In order to reliably determine the spatial resolution, a test
specimen was produced by means of molecular-beam epi-
taxy. First a 0.8 nm Fe thin film was grown on a 共001兲-GaAs
substrate followed by 25 nm of Au. Then successive Fe and
Au layers were stacked as the following: 3 nm Fe, 5 nm Au,
6 nm Fe, 10 nm Au, 10 nm Fe, 21 nm Au, and 31 nm Fe
covered with a 25 nm Au protection layer.
The sample was then prepared in cross section by me-
chanical grinding and ion polishing. In order to avoid con-
tamination of the sample in the 200 keV electron beam, the
sample was plasma cleaned in 5N Ar atmosphere directly
before inserting it into the microscope. No oxygen was de-
tected during the electron-energy-loss spectroscopy 共EELS兲
characterization.
The specimen was first oriented in zone axis conditions,
with the Au/Fe interfaces projecting in the TEM image. Then
a symmetric three-beam case was set up, tilting the specimen
by roughly 5° off the zone axis such that the interfaces were
still projecting, resulting in the excitation of the 共⫾200兲
spots. The specimen was characterized with Z-contrast imag-
ing and high-resolution TEM shown in Figs. 1共C兲 and 3共A兲.
The EMCD measurements were performed in the scan-
ning mode of the TEM using the focused probe for two sub-
sequent line scans of the same region, one for each detector
position 共+ and −兲. Each line scan, consisting of 20 spectra
with a nominal separation of 0.9 nm for a total of 17 nm scan
length, started in the first 25 nm Au layer and proceeded on
FIG. 2. 共Color online兲共A兲 Fe L
3
signal in the diffraction plane.
Symmetric three-beam case g = 共200兲, t =22 nm, for parallel illumi-
nation, which is similar to the LACDIF condition described in the
text. The three diffraction spots −g, 共000兲, and g are marked by
small circles 共blue兲. The detector positions are marked with large
circles. 共B兲 The dichroic signal in the diffraction plane is obtained
by subtracting the signal at a point in the left half plane from the
signal at the mirror point in the right half plane. Maximum values
are ⫾15% relative. The dashed vertical line in both panels is a
mirror plane for the cubic crystal, yet the symmetry across the plane
is broken by the presence of magnetism.
scan direction
Fe
Au
Fe
Au
0
0.2
0.4
0.6
0.8
1
1.2
B
700 710 720 730 740 75
0
normalized intensity
ener
gy
loss
[
eV
]
plus
minus
difference
A
A
FIG. 3. 共Color online兲共A兲 High-resolution TEM image of the investigated area; the shape and position of the beam during the scan are
indicated by the superimposed circles. 共B兲 Spectra from the middle of the 3 nm Fe layer. The difference is the dichroic signal.
DETECTION OF MAGNETIC CIRCULAR DICHROISM ON… PHYSICAL REVIEW B 78, 104413 共2008兲
104413-3
a straight line perpendicular to the Au/Fe interfaces across
the first 3 nm Fe layer, the 5 nm Au, the 6 nm Fe, and ended
close to the interface with the 10 nm Au layer 关Fig. 3共A兲兴.At
each point an energy-loss spectrum at the Fe L
2,3
edge was
acquired, with 10 s acquisition time. These values were cho-
sen to have the highest signal intensity allowed by the speci-
men and beam drift. The + and − spectra for the point in the
middle of the first Fe layer are shown with their difference,
representing the dichroic signal 关Fig. 3共B兲兴.
IV. RESULTS AND DISCUSSION
In Fig. 4 the spectral intensity 共A兲 and the dichroic signal
共B兲, integrated over the L
3
edge from 707.9 to 713.9 eV, are
shown. The Fe and Au layers are clearly resolved, thus dem-
onstrating a spatial resolution of at least 3 nm.
For the determination of the effective resolution of the
EMCD experiment a Gaussian spot profile sweeping across
the Au/Fe multilayer is assumed. A least-squares fit to the
experimental values yields a variance of
2
=1.0 nm
2
which
translates into a Gaussian full width at half maximum
共FWHM兲 of 1.66 nm. This proves that the factor limiting the
resolution is indeed the spot size; delocalization
24
or non-
projecting interfaces are negligible in the present case. The
deviations from the fit function in the leftmost slope in the
figure are caused by inconstant drift of the specimen during
the scan; variations on the plateau to the right stem from
faint thickness variation resulting in changes in the peak
height.
We conclude that the Fe signal can be detected with a
resolution limit of ⱕ1.7 nm in the present experiment. Since
the EMCD is a difference of Fe signals, its theoretical geo-
metric resolution must be the same. But this is only true for
the same SNR. The smaller SNR in the EMCD signal re-
duces this limit. Nonetheless, the EMCD signal is clearly
visible across the 3 nm Fe layer in Fig. 4共B兲. The dichroic
signal at the L
2
edge is spread over a larger energy range due
to its shorter core-hole lifetime, corresponding to a larger
Lorentzian broadening of the L
2
compared to L
3
edge. More-
over, the orbital to spin moment ratio is expected to be small
but positive for Fe atoms; according to the sum rules
21
this
means that the integrated area under the L
2
peak is smaller
than the one under the L
3
peak. The theoretical peak of the
dichroic signal at the L
2
edge is thus expected to be between
800 and 1200 counts, which is statistically insignificant con-
sidering the given 3
interval. We note in passing that the
statistics of background subtraction can enhance the L
3
sig-
nal at the expenses of the L
2
signal or vice versa.
The advantage of the geometry presented here lies in the
improved use of symmetry and in the optimization of the
illumination and acquisition process that enabled the exten-
sion to the scanning mode of the TEM. The outcome is atom-
specific magnetic characterization with unprecedented spatial
resolution. More in detail, the three-beam geometry allows
us to acquire two spectra at detector positions connected by a
mirror plane, which 共unlike the two-beam case used previ-
ously兲 is a true symmetry operation of the whole measure-
ment system. Not only detector positions are symmetric but
also the incoming beam lies on the mirror-symmetry plane
and the crystal lattice is symmetric with respect to the same
plane. This leads to equal dynamical effects at both detector
positions 共dephasing of wave fronts兲 and to the same back-
ground signals.
It should be noted that cubic crystals such as the one used
in the experiment are not expected to show any difference in
spectra acquired at those detector positions because of their
high symmetry. It is only because of the pseudovectorial na-
ture of the sample’s magnetization that a spectral difference
arises. In this geometry, spectral differences are caused only
by magnetic effects 共and noise or inaccuracies
25
兲.
Sum rules
21
have shown that spectra can be acquired at
any position in diffraction plane when the symmetry require-
ments 共see above兲 are fulfilled. Therefore large collection
angles are not an obstacle, as a simple calculation of the
diffraction patterns and dichroic maps have shown. It is true
that the spread in k
f
can reduce the EMCD percentage of the
spectra, but this reduction in percentage is traded for a sig-
nificant increase in total signal and results in better EMCD
SNR overall.
Similarly, a symmetrical spread of incoming beam wave
vectors 共k
0
兲 is also allowed. In the past it was shown that the
improved SNR could lead to better spatial resolution and this
was used here in combination with theoretical results to ex-
tend the EMCD technique to scanning transmission electron
microscopy 共STEM兲 mode, where the electron beam is fo-
cused on a small spot and scanned across the sample.
Smaller spot sizes or high beam intensities require more con-
vergent beams. This in turn would reduce the relative varia-
tion of the spectral signal due to dichroism. For example, an
electron beam with 1 mrad convergent angle could give 100
counts at the L
3
peak with 10% dichroism 共variation兲,
whereas a 5 mrad convergent beam could give 10 000 counts
at the L
3
peak with 5% dichroism. Assuming Poissonian
noise, the EMCD SNR in the first case is 1 and in the second
case is 5. It can be seen that as we need to detect differences
in EELS spectra, the demand on the SNR is more stringent.
This means that, in some cases, it would be possible to detect
an element but not its EMCD signature 共or lack thereof兲.
Apart from these physical developments, the technique
itself will have considerable consequences in near future—
for high-resolution atom-specific magnetic studies. We pro-
FIG. 4. 共A兲 Profile of the line scanned in Fig. 3. The experimen-
tal points are the integrated Fe signal 共sum of the + and − spectra兲
at the L
3
edge 共707.9–713.9 eV兲. The best fit with a Gaussian spot
shape gives a FWHM of 1.66 nm for the spot. The error bars are
3
=855 counts. 共B兲 Corresponding line profile of the dichroic sig-
nal 共difference of the + and − spectra兲 integrated at the L
3
edge.
SCHATTSCHNEIDER et al. PHYSICAL REVIEW B 78, 104413 共2008兲
104413-4
vide a method to approach a whole new class of physical
problems to be studied. In all previous works published on
EMCD, spectra were acquired from a single region in the
specimen. The only possibility to study different features in
the specimen was to repeat it on another part of the sample.
With the STEM mode, line scans are possible, which means
that magnetic properties of multilayers can be investigated in
a matter of minutes and directly related to high-resolution
images. This brings us a step closer to the realization of
EMCD imaging capable of revealing magnetic contrast.
Moreover, it is an experiment with a cross sectional magnetic
multilayer specimen, thus approaching real problems of na-
nomagnetism.
V. CONCLUSIONS
In summary, we have measured an EMCD signal in the
STEM mode of the electron microscope. As compared to the
original EMCD setup this opens the exciting possibility to
map magnetic moments with a lateral resolution of better
than 2 nm. This constitutes a breakthrough for the study of
nanomagnetism at interfaces and boundaries. The main lim-
iting factors in this experiment are specimen drift and beam
instability, which set upper bounds on the collection time of
the spectra. If drift can be reduced the dwell time could be
increased, thereby lowering the noise level and allowing
smaller spots. With the new generation of C
S
corrected 共scan-
ning兲 TEMs it is likely to achieve subnanometer resolution in
EMCD spectrometry.
ACKNOWLEDGMENTS
The authors acknowledge N. J. Zaluzec, C. Hébert, and J.
Verbeeck for programming the script for the electronic shift
of the diffraction pattern and E. Carlino, L. Felisari, F. Mac-
cherozzi, and P. Fischer for fruitful discussions. P.S. and S.R.
acknowledge funding from the European Union under Con-
tract No. 508971 共FP6-2003-NEST-A兲 “CHIRALTEM.”
*
Also at Institute for Solid State Physics, Vienna University of
Technology, Wiedner Hauptstrasse 8-10/138, A-1040 Vienna,
Austria.
†
Also at Department of Engineering, Uppsala University, P.O. Box
534, S-751 21, Uppsala, Sweden; stefanorubino@yahoo.it
‡
Also at Institute of Physics, Academy of Sciences of the Czech
Republic, Na Slovance 2, CZ-182 21 Prague, Czech Republic.
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The delocalization via the long-range Coulomb interaction is
given by the modified Bessel function K
0
共q
E
x兲, where q
E
=k
0
E/ 2E
0
is the characteristic wave number, i.e., for the Fe L
edge and 200 keV primary electron energy q
E
=4.4/ nm. The
FWHM of the delocalization function is 0.08 nm, and the 10%
level is at 0.6 nm 共Ref. 20兲.
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E. Coronel, O. Eriksson, and K. Leifer, arXiv:0807.1805 共un-
published兲.
DETECTION OF MAGNETIC CIRCULAR DICHROISM ON… PHYSICAL REVIEW B 78, 104413 共2008兲
104413-5
