Magnetic circular dichroism in electron energy loss spectrometry

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Ultramicroscopy 108 (2008) 277–284 www.elsevier.com/locate/ultramic

Magnetic circular dichroism in electron energy loss spectrometry C. He´berta,b,, P. Schattschneidera,e, S. Rubinoa, P. Novakc, J. Ruszc,d, M. Sto¨ger-Pollache a

CIME–SB, MXC132, Station 12, EPLF, 1015 Lausanne, Switzerland Institut fu¨r Festko¨rper Physik, Technische Universita¨t Wien, A-1040 Wien, Austria c Institute of Physics, Academy of Sciences, Prague, Czech Republic d Department of Physics, Uppsala University, Box 530, S-751 21 Uppsala, Sweden e USTEM, Technische Universita¨t Wien, A-1040 Wien, Austria

b

Abstract The measurement of circular dichroism in the electron microscope is a new, emerging method and, as such, it is subject to constant refinement and improvement. Different ways can be envisaged to record the signal. We present an overview of the key steps in the energyloss magnetic chiral dichroism (EMCD) experiment as well as a detailed review of the methods used in the intrinsic way where the specimen is used as a beam splitter. Lateral resolution up to 20–30 nm can be achieved, and the use of convergent beam techniques leads to an improved S=N ratio. Dichroic effects are shown for Ni and Co single crystal; as a counterexample, measurements were carried also for a non-magnetic (Ti) sample, where no dichroic effect was found. r 2007 Elsevier B.V. All rights reserved. PACS: 78.20 Bh; 78.20 Ls; 79.20 Uv; 32.80 Cy Keywords: Electron energy loss spectrometry; Transmission electron microscopy; Circular dichroism; Coherence

1. Introduction A medium is dichroic when its colour depends on the polarization direction of the impinging light. In other words, the absorptive behaviour in the optical window depends on the polarization. Linear dichroism is the dependence of the absorption spectrum on the orientation of the polarization vector of a linearly polarized probing photon whereas in circular dichroism the dependence is on the helicity (right- or left-handedness) of the incident photon. Both types of dichroism are caused by the natural or magnetically induced anisotropic electronic structure of the material. Since circular dichroism translates into a change of the magnetic quantum number by Dm ¼ 1 in an electronic transition, it always signifies preferential availability of particular final jl m si-states, which in turn is intimately related to the presence of magnetism. In passing we note that a medium is birefringent when the Corresponding author. CIME-SB, MXC132, Station 12, EPLF, 1015 Lausanne, Switzerland. E-mail address: cecile.hebert@epfl.ch (C. He´bert).

0304-3991/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2007.07.011

(anisotropic) absorption bands lie outside the optical window. When polarized X-rays became popular in X-ray absorption spectrometry (XAS) for the investigation of anisotropic materials the term dichroism was adopted to describe the polarization dependence of X-ray absorption near edge structure (XANES). In the late seventies it became clear that dichroism can be induced by magnetic fields. X-ray magnetic circular dichroism (XMCD) was predicted as early as 1975 [1] and first observed 1987 in XAS of the Fe K edge by Schu¨tz et al. [2]. X-ray magnetic linear dichroism (XMLD) was predicted in 1985 [3] and observed shortly thereafter [4]. The much fainter natural circular dichroism occurs when local magnetic moments break the crystal symmetry [5,6]. In the first XMCD experiment reported in 1987 [2] the circular dichroic effect on the Fe K edge was found to be o1%. The method gained tremendous power a few years later when the importance of the spin–orbit splitting of core electrons for XMCD was realized [7]. It can amplify the dichroic signal to several 10% in many L23 and M45 edges.

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The progress in synchrotron technology led to an increased interest in dichroic experiments for the understanding of magnetism, especially in highly correlated electron systems. Nowadays, important information on orbital and spin magnetization, magnetic ordering and strong electronic correlation in a variety of ferro- and ferrimagnetic compounds is being deduced from XMLD and XMCD with the aid of modern synchrotrons providing highly polarized beams with a brilliance of up to 1019 photons per ðs mm2 mrad2 Þ and 0.1% bandwidth (e.g. Ref. [8]). These techniques have led to considerable progress in the understanding of magnetism in the solid state, and they become increasingly important for the rapidly expanding field of spintronics. The demand for extremely high spatial resolution arises precisely in this context. At present several lines of technical improvement are under way: (a) X-ray microscopes with Fresnel lenses, with resolution of the order of 30 nm. (b) A combination of XMLD or XMCD with photoelectron emission microscopes XMCD-PEEM [9,10] was first demonstrated in 1988 [11]. This method is restricted to ultrathin surface layers and has been used at several synchrotron beam lines such as PEEM2 at ALS, U2 at Bessy, IS-PEEM at SPring-8 for the imaging of magnetic domains [12,13]. Many instruments in the world achieve 0:3 mm lateral resolution, and few of them have 50 nm in magnetic contrast. Next-generation machines will have improved resolution (PEEM3 at ALS, XM-1, or the SMART project) but are unlikely to approach the nm range very soon. (c) X-ray holography has delivered first promising results as a lensless imaging technique with synchrotron radiation, and can evidently be used with polarized radiation [14]. Here the main difficulty lies in the preparation of a suitable reference beam for obtaining the hologram. This paper is arranged as follows: we repeat briefly the theoretical basis of EMCD [15,16]; in Section 3 we discuss the various geometric set-ups which can be used to obtain dichroic signal; in Section 4 we compare the respective experimental set-ups with emphasis on signal strength and spatial resolution.

are the initial and final states of the target electron with energies E i and E f , respectively. For XANES the absorption cross-section is X ~ 2 dðE þ E i  E f Þ, s/o jhf j~ e  Rjiij (2) i;f

where o is the photon radial frequency and~ e the polarization vector. From Eqs. (1) and (2) it is clear that within the dipole approximation the polarization vector ~ e in X-ray absorption spectroscopy is formally equivalent to the direction of the momentum transfer e~q in inelastic electron scattering. It is then evident that XANES spectra closely resemble ELNES spectra. This equivalence in the formalism can be understood when one realizes that in both cases the driving agent for ~ (Fig. 1). This oscillating field transitions is an electric field E of the photon or of the closely passing electron acts directly onto the electrons of the absorbing atom and changes the charge distribution in the direction of the field. Linear dichroism can be measured in angle resolved electron energy loss spectrometry (EELS): the loss spectrum depends on the direction of the selected wave vector transfer ~ q. Such measurements have been performed on many single crystals; traditionally the effect has come to be known as EELS anisotropy rather than linear dichroism although it is exactly the same. The details have been described elsewhere [18,19]. EELS experiments were done, e.g. in h-BN [19–21], in AlB2 [22] and in V2O5 [23]. Linear magnetic dichroism experiments in the TEM were reported for hematite [24,25]. The physics of the XMCD effect can be understood when we consider the electric field corresponding to the polarization vector ~ ei~ e0 with ~ e?~ e0 of a circularly polarized photon. Here the imaginary unit i signifies a phase shift of p=2 between the two perpendicular polarizations. This field will rotate clockwise or counterclockwise. At resonance the frequency will be exactly that for forcing an electron from an atomic ground state into an excited state (for convenience we can imagine a transition from an s to a p state) that rotates in phase with the electric field; quantum mechanically, the final p state is jl ¼ 1; m ¼ 1i, i.e. the angular part of the wave function will have Y 1 symmetry, obeying the selection rule 1

2. Photons and electrons The similarities between XANES and energy loss near edge structures (ELNES) have long been recognised [17]. The equations describing the double differential crosssection in ELNES and the absorption cross-section in XANES within the dipole approximation are remarkably similar [15]: In ELNES, the double differential scattering crosssection reads: X1 q2 s ~ 2 dðE i  E f þ EÞ, / jhf j~ eq  Rjiij qE qO q2 i;f

(1)

~0 is the wave vector transfer, R ~K ~ is with e~q ¼ ~ q=q, ~ q¼K the quantum mechanical position operator and jii and jf i

~ is parallel to the polarization vector ~ Fig. 1. In photon absorption E e ~ is antiparallel to the momentum whereas in inelastic electron scattering E transfer _~ q (since the interaction is largely Coulombic, the field is longitudinal). Since the charges are polarized in the direction of the electric field an s ! p transition will select a final orbital whit its main axis parallel to ~ q. This is a particular case of the (electric) dipole selection rule for optical transitions.

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Fig. 2. The equivalence between photons and electrons can be understood by invoking the electric field which is the driving agent for chiral transitions: in photon absorption, the circular polarization creates a rotating electric field at the atom position. This rotating field increases (or decreases, depending on the polarization) the magnetic quantum number by 1. Additionally to the selection rule dl ¼ 1 (in the figure realized by a transition s ! p), the selection rule Dm ¼ 1 for the magnetic quantum number applies.

Dm ¼ 1. That this orbital corresponds to a rotating final state can be seen if we introduce time dependence: the wave function is now c / eiot ef ¼ eiðotfÞ with f the azimuthal angle in a spherical coordinate system. This corresponds to a propagating wave in the angle f quite similar to a propagating plane wave eiðotkxÞ (Fig. 2). The analogy of EMCD to this experiment is seen when comparing the polarization vector ~ eþi~ e0 with ~ e?~ e0 and 0 0 ~ ~ the momentum transfer ~ q þ i  q with ~ q ? q for electrons. Also for the electron, the imaginary unit describes a phase shift of p=2 between the vertical and horizontal electric field components; in other words, the two incident electron plane waves must be shifted relative to each other by l=4, which makes a phase difference of exactly kl=4 ¼ p=2. The chiral transitions that give rise to the XMCD effect have their counterpart in the mixed dynamic form factor (MDFF) for inelastic electron scattering. Since this quantity can be measured in the TEM under particular scattering conditions we predicted [15] that the counterpart of XMCD experiments should be possible in the electron microscope. We called the predicted effect energy-loss magnetic chiral dichroism (EMCD). The MDFF is defined as [26,27]: X ~ ~ i dðE i  E f þ EÞ Sð~ q; q~0 ; EÞ:¼ hf j~ q  Rjiihij q~0  Rjf (3)

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It can be seen that only the last term in the parentheses depends on the helicity of the excitation. This term arises from the interference between the two electron waves which would produce only the DFF terms when taken separately. The dichroic signal is defined as the spectral difference observable when the helicity is reversed. To record it, two measurements are needed where the sign in front of the MDFF in Eq. (5) is reversed. When calculating the difference of the two spectra, the direct terms cancel and only the interference term remains. The dichroic signal is usually given as a percentage of the average signal by  Ds sþ  s :¼2  . (6) s Dich sþ þ s For non-magnetic materials Sð~ q; q~0 ; EÞ is real, and the dichroic signal vanishes. 3. Scattering geometries for EMCD First of all we need a superposition of two plane waves at the target atom (Fig. 3a). This can be done either by using a biprism to split the beam [28] or by using the crystal itself as a beamsplitter as already proposed by Nelhiebel [29] (the so called intrinsic way). At first sight, the biprism method would seem simpler but technical problems still limit the signal to an insufficient level of intensity. The second method is more difficult to interpret as the phase shift depends in a non-linear way on the crystal orientation and the thickness of the specimen by dynamical diffraction. Nevertheless it has been shown to work and all the results presented in this paper were obtained with this method. The necessary phase shift of p=2 between the two incident plane waves (Fig. 3b) is controlled by the exact

i;f

and is a generalization of the dynamic form factor (DFF) X ~ 2 dðE i  E f þ EÞ, jhf j~ q  Rjiij (4) Sð~ q; EÞ:¼ i;f

to which the MDFF reduces when ~ q ¼ q~0 . It can be shown that for a momentum transfer ~ q  i  q~0 [15,16] 0 s :¼

q2 s 1 B1 / @ 4 Sð~ q; EÞ þ 0 4 Sðq~0 ; EÞ qE qO q q 1 

1 C 2I½Sð~ q; q~0 ; EÞA. q2 q0 2 |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} /~ qq~0

ð5Þ

Fig. 3. The four main steps for the set-up of an EMCD experiment: (a) superposition of two incident plane waves, (b) with phase shift p=2, (c) selection of the momentum transfers ~ q ? q~0 , (d) second measurement with ~ q and q~0 . The difference of the two measurements gives the dichroic signal.

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orientation of the specimen (given by the Laue circle centre, LCC) and by the specimen thickness. In this case, the only reliable method to predict the expected dichroic effect is to perform ab initio calculations [30]. The following step is to select two perpendicular momentum transfers (Fig. 3c). This is done in the diffraction plane, either by using a contrast aperture and working in image mode, or by using the spectrometer entrance aperture (SEA) and working in diffraction mode or by working in a large angle convergence diffraction (LACDIF) geometry [31,32]; in the latter case the specimen is shifted upward from the eucentric height, causing a diffraction pattern to appear in the image plane of the objective lens. The proper momentum transfer is then selected with the SEA. All these methods will be discussed further in this paper. Another possible technique is to record a range of momentum transfers at once in an ðE; ~ qÞ diagram. The last step consists in reversing the helicity of the excitation with respect to the specimen magnetization, i.e. changing the sign of the interference term in Eq. (5). This can be done: (i) by inverting the current in the objective lens, which in turn reverses the magnetic field at the specimen position [28]; (ii) by carefully changing the orientation and/or thickness of the investigated area (so that the phase shift changes sign); (iii) by switching the sign of the vector product ~ q  q~0 which can be done by 00 ~ ~0 with respect to selecting K on the position opposite to K the line connecting the Bragg spots (Fig. 3d). Only the latter method will be discussed in this paper. In order to be able to compare results obtained in different sessions, it is necessary to give an unambiguous label to the two chiral positions. We define a right-handed orthogonal reference system in the diffraction plane having the direct beam (0 0 0) as origin. The line connecting 000 to the G-reflection is the x-axis, oriented positively from 000 to G. We call A (above) the position situated in the y40 half-plane and B (below) the position in the yo0 half-plane (Fig. 4). Of course results are comparable between different microscopes only if the magnetic field in the objective lens has the same orientation.

4. Experimental results All EELS spectra were taken on an FEI Tecnai F20-FEGTEM S-Twin equipped with a Gatan Imaging Filter. We used the intrinsic way, where the crystal itself is used to split the beam and set up the phase shift. The pair of dichroic spectra is collected by measuring at two different positions in the diffraction plane. In the following, we will describe and compare different ways of selecting the momentum transfer in the diffraction plane. 4.1. OA-Shift method In this method, the microscope is operated in image mode and the selection of ~ q ? q~0 in the diffraction pattern is made by the objective aperture (OA); the investigated area in the specimen is selected by the projected SEA and thus depends on the magnification used. The theoretical spatial resolution that can be obtained is in the nanometer range, however the intensity of the signal decreases rapidly as the investigated area becomes smaller and smaller. Another drawback is that the positioning of the OA is done by eye and is therefore not very accurate; moreover, it requires switching back to diffraction mode after the first measurement to shift the aperture between positions A and B. This is a source of instabilities in the system. It is not possible to use the dark-field (DF) mode to preselect the positions of the diffraction pattern over the OA, because in DF mode it is the tilt of the beam that is changed and this would affect the phase shift (as the LCC is changed). Furthermore, in image mode the accurate positioning of the appropriate sample area over the SEA is very difficult. Any error in the position of the specimen may influence the phase if the specimen is bent or the thickness changes. The achievable spatial resolution is still an advantage; the intensity limitation could be improved by use of a more convergent beam and maybe by the use of a nanoprobe mode instead of a microprobe mode. As the spots in the diffraction pattern become disks when increasing the convergence angle, care must be taken that they do not overlap with themselves or with the OA. The use of preprogrammed motorised apertures may help the selection of the momentum transfer. Fig. 5 shows the Ni L2,3 edge in the OA-Shift method. 4.2. Detector-shift

Fig. 4. Definition of the positions A and B as used in this paper. The positions A and B correspond to the cross-sections sþ and s , respectively.

The detector-shift method was the first experimental approach to verify the predicted effect on iron [33]. Working in diffraction mode, the specimen area is selected by an appropriate selected area aperture (SAA). The momentum transfer is selected by the camera length and the SEA. The positioning of the diffraction pattern over the SEA is made by using the diffraction shift coils situated after the specimen, which does not affect the illumination of the sample and is easy to control. In this method the LCC is easier to control, since one does not

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related to the fact that the sign of the dichroic signal remains the same in a relatively large interval of LCC. The relative dichroic signal integrated over this interval is smaller, but the total signal and therefore the total dichroic signal increases because more electrons now pass through the SA aperture. Fig. 6 compares two set-ups of the detector-shift method: left with nearly parallel illumination and right with increased convergent illumination. The total intensity is increased with a slightly convergent beam, without loosing the dichroic signal. As already stated the dichroic signal depends in a nonlinear way on the LCC position and on the specimen thickness. This is essentially related to the Pendello¨sung variations of the strength and relative phase of the 0 and g beam as a function of these parameters. As an example we show the measured signal as a function of specimen thickness compared to a 10-beam calculation within systematic row approximation for Co [30]. Considering the relatively large error bars, there is a good agreement between theory and experiment. The plots also show that it is of paramount importance to choose the best specimen thickness in order to get a strong dichroic signal (Fig. 7).

1000

4.3. LACDIF method

need to shift to diffraction mode. The main limitation is the spatial resolution which is given by the smallest SAA. In our case, this represents a field of view of about 200 nm. Similarly to what was described above, the main problem is the low intensity because the electron beam illuminates an area much larger than the SAA, especially when working with parallel illumination, and therefore a large fraction of the electrons do not contribute to the signal. Converging the beam to a limited extent increases the signal. It was suspected that the higher convergence angle then would reduce the dichroic effect, even below detectability since the LCC position would vary within the illumination cone and the angular resolution is reduced by the convolution of the illumination and collection cone. Nevertheless, the experiment yielded a detectable dichroic signal up to a relatively strongly convergent beam. This is 2500 Position A Position B

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Energy loss [eV] Fig. 5. Ni L edge in a monocrystalline region of a polycrystalline Ni ~0 . The sample. G ¼ 200, LCC ¼ 000 acquired using an OA to select K change in intensity is roughly of 10% at the L3 edge. The sampled area had a thickness of  50 nm and a radius of  75 nm.

Encouraged by the success of using a moderately converged beam in the detector-shift method, we decided to try a completely converged beam, using the specimen z-shift to separate the diffraction spots [31,32]: an LACDIF method. In this geometry, the beam is first completely converged on the specimen in eucentric position (in the image plane one sees one sharp spot). The sample is then shifted upward, causing more spots to appear because of Bragg scattering. The image plane (which now contains a series of sharp spots similar to a diffraction pattern with parallel

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Fig. 6. Ni L2;3 with the detector-shift method. Left: Ni ½1 1 0 g ¼ ð0 0 2Þ, LCC ¼ ð0 0 1Þ, 200 nm lateral resolution, parallel illumination, 60 s acquisition time; right: Ni ½1 1 1 g ¼ ð2 2 0Þ, LCC ¼ ð1 1 0Þ, 200 nm lateral resolution, optimized beam convergence, 60 s acquisition time.

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incident beam) is then projected on the SEA. As the illumination is a cone with its apex in the image plane, the area of the (thin) specimen that interacts with the electron beam is a circle with radius proportional to the z-shift and the convergence angle a. For appropriate values of these two parameters, the investigated area can be reduced to a few tens of nanometers, which is smaller than what could be obtained with an SAA. The advantage of this configuration is that no intensity is cut off by the SAA, so the signal is very strong. On the other hand, it remained to be seen if the EMCD signature achieved a detectable percentage of the signal after being averaged over a large range of LCC positions induced by the convergent illumination. In this geometry the angular

5 Experiment

Dichroic signal [%]

4

resolution is only given by the collection angle since the detector is situated in the image plane, where the ‘‘diffraction’’ spots are sharp. The collection angle can be changed by changing the magnification. The drawbacks of the method is that it is more difficult to set the right orientation of the sample as the z-shift interplays with the illuminated area and therefore the LCC as well as with the distance of Bragg spots. To move the ‘‘diffraction pattern’’ the beam shift is used, but then one has to move the specimen back with the stage movement to illuminate the same area. Fig. 8 compares the same specimen area with the detector-shift method and the LACDIF method on Co. The intensity (counts) per unit of time is improved by a factor of more than 40, and the energy resolution is also improved. In the same time, the lateral resolution is improved from 200 to 30 nm. 4.4. Cross check with a non-magnetic material

Simulation

In order to ensure that the faint effects measured are really the TEM equivalent of the XMCD and not an artefact, EMCD measurements have been performed on non-magnetic materials such as metallic titanium, rutile or copper oxide (CuO). Several different methods have been tested, with different tilt angles and specimen thicknesses. One example is reported in Fig. 9. All measurements evidenced no difference in the ELNES of the spectra after variation of the chirality of the excitation.

3 2 1 0 0

20

40

60 80 Thickness [nm]

100

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5. Conclusion and outlook

Fig. 7. Thickness profile of the EMCD at the Co L3 edge, obtained with the detector-shift method in a Cobalt [0 0 1] hcp single crystal specimen, tilted to the g ¼ ð1; 0; 0Þ systematic row and with LCC ¼ ð0:5; 0; 0Þ. The illuminated area is approx. 200 nm in diameter. The experiment is compared with DFT based band structure calculation for the same dynamical diffraction conditions.

We have shown an overview of methods to make EMCD experiments in the conventional spectroscopic set-up and for the intrinsic way, where the crystal itself is used as a beam splitter. The following table summarizes the comparison of the three methods with the key parameters that

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Fig. 8. L2;3 edges in a [0 0 1] Co hcp single crystal. Orientation: g ¼ ð1; 0; 0Þ, LCC ¼ ð0:5; 0; 0Þ. Left: detector-shift method, 200 nm lateral resolution, 40 s acquisition time; right: LACDIF method, 30 nm lateral resolution, 10 s acquisition time.

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Counts

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465

470

475

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Energy Loss [eV] Fig. 9. Ti L2,3 edges in metallic titanium taken with the detector-shift technique. As expected, there is no significant difference in the intensity ratio of the edges. This excludes the possibility that detected dichroic measurements could have been artefacts.

define the momentum transfer selection and the lateral resolution. Method

Specimen area selection

Momentum transfer selection

Spatial resolution

OA-Shift Detectorshift LACDIF

SEA+Mag SAA

Obj aperture SEA + Cam length SEA + Mag + z-shift

Some nm 200 nm

z-Shift + C2 aperture

30 nm achieved, 10 nm expected

All methods have advantages and disadvantages such that it is not possible to dismiss a priori one or the other. The detector-shift method is easy to set up but has a limited lateral resolution and part of the signal is lost due to the SAA. The OA-Shift method has a better lateral resolution but again part of the signal is lost and the momentum transfer selection lacks precision. The LACDIF method has a better collection efficiency as none of the electrons which hit the sample are filtered out in the image plane, but the set-up is much more difficult. Nice dichroic signals have been shown on nickel and cobalt single crystals, and a metallic Ti sample was used as a counterexample to show that the dichroic signal is not an artefact. Other methods can be envisaged and remain to be explored for the detection of the dichroic signal:



The recording of an ðE; qÞ diagram on the GIF CCD, using the axis perpendicular to the energy axis to record the momentum transfer. The advantage of this method is that the two measurements at the chiral plus and



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minus positions can be done in a single acquisition, the disadvantage is the lack of flexibility for the position and size of the aperture, and therefore in the S/N optimization. It would be interesting to use the energy filtering technique to record a 3D data cube. First attempts to record a 3D data cube in the diffraction plane show promising results [34]. The advantage of the method lies in the possibility of recording all the information and post processing it to obtain the best S/N ratio. This makes it easy to use even non-circular apertures to integrate the dichroic signal since the integration is made numerically in post processing. Non-isochromaticity and drift may be problematic components, and as this method disperses the available signal over many more pixels than the spectroscopic method, it requires a detector with low noise and low and stable dark count rates. Filtered imaging can be envisaged in image mode, using an objective aperture (similarly to the OA-Shift method) to select the correct momentum transfer in the diffraction pattern and obtaining a chirally active illumination. Again, drift, detector background and non-isochromaticity makes this method difficult to set up, but the possible attainable lateral resolution is promising.

Acknowledgement This work was supported by the European Union under contract no. 508971 (FP6-2003-NEST-A) ‘‘CHIRALTEM’’. References [1] J.L. Erskine, E.A. Stern, Phys. Rev. B 12 (11) (1975) 5016. [2] G. Schu¨tz, W. Wagner, W. Wilhelm, P. Kienle, R. Zeller, R. Frahm, G. Materlik, Phys. Rev. Lett. 58 (7) (1987) 737. [3] B.T. Thole, G. van der Laan, G.A. Sawatzky, Phys. Rev. Lett. 55 (19) (1985) 2086. [4] G. van der Laan, B.T. Thole, G.A. Sawatzky, J.B. Goedkoop, J.C. Fuggle, J.-M. Esteva, R. Karnatak, J.P. Remeika, H.A. Dabkovska, Phys. Rev. B 34 (9) (1986) 6529. [5] J. Goulon, C. Goulon-Ginet, A. Rogalev, V. Gotte, C. Malgrange, C. Brouder, C. Natoli, J. Chem. Phys. 108 (15) (1998) 6394. [6] J. Goulon, C. Goulon-Ginet, A. Rogalev, G. Benayoun, C. Brouder, C. Natoli, J. Synchrotron Radiat. 7 (3) (2000) 182. [7] C.T. Chen, Y.U. Idzerda, H.-J. Lin, N.V. Smith, G. Meigs, E. Chaban, G.H. Ho, E. Pellegrin, F. Sette, Phys. Rev. Lett. 75 (1995) 152. [8] G. Rossi, F. Sirotti, G. Panaccione, Atom specific surface magnetometry with linear magnetic dichroism in directional photoemission, in: Magnetic Ultrathin Films, Multilayers and Surfaces Symposium, vol. 384, 1995, pp. 447–456. [9] J. Stohr, Y. Wu, B.D. Hermsmeier, M.G. Samant, G.R. Harp, S. Koranda, D. Dunham, B.P. Tonner, Science 259 (1993) 658. [10] J. Stohr, H. Padmore, S. Anders, T. Stammler, M. Scheinfein, Surf. Rev. Lett. 5 (6) (1998) 1297. [11] B. Tonner, G. Harp, Rev. Sci. Instrum. 59 (6) (1988) 853. [12] H. Ohldag, T. Regan, J. Stohr, et al., Phys. Rev. Lett. 87 (24) (2001) 24720.

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