1. Introduction

Since the first demonstration [1] in 1992 and its first application to magnetic materials [2] in 2004, Fourier transform holography (FTH) has now developed into a mature magnetic imaging technique. It features nanometer spatial resolution, magnetic and element contrast via the x-ray magnetic circular dichroism (XMCD), sensitivity to buried layers, and a straightforward image reconstruction with the possibility of multiplexing [3]. In addition, images can be recorded at variable sample temperatures [4] and in external magnetic fields [5–7]. FTH is also expected to be a key imaging technique at free-electron laser sources where phase contrast imaging could be an option to cope with the high photon flux and radiation-sensitive samples [8].

In the field of magnetic imaging, FTH has solely been applied to systems with out-of-plane magnetization, either based on [Co/Pd] or on [Co/Pt] multilayers. This limitation is owing to the special sample-mask structure and the angular dependence of the XMCD effect. FTH samples are prepared on the back side of a Si₃N₄ membrane while the front side carries the mask for the object and reference beams. This common sample-mask design has a fixed field-of-view. Recently we have demonstrated that imaging with a movable field-of-view can be realized by separating mask and sample [9, 10].

In this paper we report on imaging the in-plane magnetization. This is achieved by adapting the mask and scattering geometry to the directional sensitivity of the XMCD effect. Holograms were recorded from a Co square at off-normal incidence. For this geometry the reference beam was defined by an inclined reference hole.

2. Results and discussion

Magnetic contrast in FTH using the XMCD effect is proportional to the projection of the magnetization on the beam direction. Hence, in-plane magnetized samples have to be imaged at a tilt angle α. Fig. 1 illustrates the sample-mask assembly in the tilted geometry (a), and shows a scanning electron microscope (SEM) image of the sample (b). The mask was prepared on the etched side and the cobalt sample on the flat side of a silicon nitride substrate. Focused ion beam (FIB) structuring was used to mill a perpendicular reference hole at 0° and an inclined reference hole at 20° with respect to the surface normal into the opaque mask and the membrane of [Au₂₂₀nm/Pd₁₀₀nm]₄/Au₁₀₀nm/Si₃N₄(200nm). The reference holes, having an exit diameter of about 65 nm, were placed at 8 μm from the center of the 2 × 2 μm² object hole. For simplicity, the square object hole was milled at normal incidence. The sample, a 2 × 2μm² Co square with 20 nm thickness, was placed on the back side of the membrane right behind the object hole. The Co film was prepared by sputter deposition on a 5 nm Pt seed layer and capped by a 2 nm Pt protection layer [11]. FIB milling was employed to cut out the square from the continuous film. In order to compensate for x-ray shadowing by the object hole’s upper edge upon sample rotation, the position of the Co square was shifted downwards by 0.3μm, leading to an L-shaped area of bare membrane in the object hole. Next to the upper right corner of the Co square the milling process left an unintended elliptical hole (black) in the bare membrane. The Co square is rotated by 18° in the plane parallel to the tilt axis. This ensures different magnetic contrasts for all four magnetization orientations parallel to the edges of the square. The experiments were performed at beamline ID08 at the ESRF. We have used circularly polarized x-rays tuned to the Co L₃ absorption edge at 778 eV. Details of the setup can be found elsewhere [6].

 

Fig. 1 Cross section (a) of the sample-mask assembly with an inclined and conically shaped reference hole for imaging at off-normal incidence in order to obtain sensitivity to the in-plane magnetization. SEM image (b) recorded from the side supporting the Co element (light gray). The square object hole (dark) is indicated by yellow corners. Note the downward shift of the Co element with respect to the object hole.

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In Fig. 2 we show the holograms recorded at the tilt angles α of 0°, 15°, and 30°. The tilt axis for the measurements is the same as for milling the reference holes. Images a–c) correspond to the difference between the holograms recorded with opposite photon helicity. In e) we show the sum of both helicity images at α = 15°. The total exposure time for each helicity image was 20 s for α = 0°, and 50 s for 15° and 30°. For better comparison, we have normalized the 0°-image by multiplying it with a factor of 5/2. The figures show only the center of the holograms. For the reconstruction we used the full data covering a wave vector range of 0.23 nm⁻¹. Due to the limited dynamical range of the CCD chip, a beam stop of 0.7 mm diameter was used to block the direct beam. In the sum hologram the four prominent streaks reflect the square shape of the object hole and its 18°-azimuthal orientation. The size of the object hole projected on the detector plane can be deduced from the period of the streaks. From the horizontal streaks we obtain 2π/3μm⁻¹ = 2.1μm, which changes only little upon tilting while the projected vertical size shrinks as cosα. The reconstruction of the sample from the sum hologram using the 20°-reference hole, i.e. the real part of the FFT image [6], is given in f). Note the agreement with the SEM image in Fig. 1(b) although here the bottom edge of the Co square is hidden behind the opaque mask.

 

Fig. 2 Holograms from a 2 × 2μm² Co square measured at tilt angles α of 0° (a), 15° (b, e), and 30° (c). Images a)–c) show difference holograms for opposite photon helicities and the pattern in e) gives the sum of both helicities. The line scans in d) show that the intensity in the difference hologram scales with the projection of the magnetization on the incoming beam direction. The reconstruction of the sample using e) is given in f).

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In general, the XMCD effect is proportional to M · k_i, i.e. to the projection of the magnetization M on the incident wave vector k_i. Applied to our geometry, where M lies in the sample plane and k_i is perpendicular to the tilt axis, we obtain a sinα-dependence for the magnetic contrast. The increase of the signal with larger tilt can bee seen in Fig. 2(a–c). For better comparison, we show for each α the line scan along the black line indicated in Fig. 2(a). The sinα-dependence is reflected by the approximately two-fold increase of the signal upon changing α from 15° to 30°. The tiny, non-vanishing intensity at 0° can be explained by a small misalignment of about 1°.

From the difference holograms, in which the magnetic real-space structure is encoded, we have reconstructed by FFT the images displayed in Fig. 3. Here we show the region of the FFT image containing the reconstruction from the 20°-reference hole. Our cross-section analysis of the conically shaped reference channels [5] with the exit hole on the downstream side has shown opening angles of about ±6°. We found that this milling-induced opening angle is an advantageous feature since it allows FFT imaging with good contrast at various tilt angles within a range of ±15° relative to the milling direction. In addition, it relaxes the angular precision requirement of the milling process for high-resolution imaging with very narrow holes. It follows that a 20°-reference hole is well suited for α = 15° and 30° while the perpendicular reference hole can be employed for imaging at 0°. The position of the object hole is indicated by the square drawn in white. As mentioned above, tilting leads to a projection of the sample onto the plane normal to the beam. This causes a contraction of the real-space images along the vertical direction. Simultaneously, the magnetic contrast increases as sinα due to the increasing projection of the in-plane magnetization along the beam direction. Note that this tilt geometry does not yield sensitivity to the magnetization parallel to the tilt axis (M · k_i = 0), i.e. along the horizontal direction. Thus the contrast reflects different magnetization components parallel to the vertical direction in the image. With the 30°-geometry we obtain half of the maximal magnetic contrast at a moderate contraction of only 14%. Regions in black and white correspond to opposite in-plane magnetization orientations along the vertical direction while in the gray regions the magnetization is oriented predominantly along a horizontal direction.

 

Fig. 3 Reconstructed magnetic structure in the Co square from the difference holograms in Fig. 2. The image series show the reconstructions obtained from the 20°-reference hole. The contrast, which increases with tilt angle, corresponds to the magnetization component along the beam direction. A complex magnetic structure with two vortices with identical circulation is present in the Co element. The rectangle indicates the boundaries of the object hole. Note the contraction along the vertical direction as a result of the sample tilt.

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As expected for an in-plane magnetized system, no magnetic contrast is found in the reconstructions from the perpendicular reference hole at normal incidence (α = 0°). At zero tilt the reference beam of the perpendicular hole has its maximum intensity but the FFT image (not shown) is as featureless as Fig. 3(a). Magnetic contrast is also not found with the perpendicular reference hole at α = 15° where the higher but still small magnetic sensitivity does not counter balance the large reduction of the reference beam intensity.

The magnetic domain structure, best seen in Fig. 3(c), differs from the simple Landau ground state that is expected for this symmetry and dimension [12]. Instead of a flux-closure pattern with a single vortex, a complex domain structure with two vortices is found. Due to the offset between Co element and object hole, the lower vortex is partly hidden behind the mask. The second feature of this domain state is the large triangular domain in black at the lower right corner. Such a magnetic structure is most probably defined by magnetic defects [12, 13].

We have also studied the sample in different magnetic states. In Fig. 4 we present the reconstructed and compression-corrected images in saturation and in remanence. The images in (a) and (b) were recorded at α = 30° while applying a field of ± 140 mT along the beam direction. The field component in the sample plane of ±70 mT was sufficient to saturate and reverse the sample magnetization in the plane, as can be deduced from the inverted gray scale value. Here, the arrows indicate the magnetization direction. The low signal-to-noise ratio in (a) and (b) is due to the short total exposure time of only 10 s per helicity image. Imaging after applying a field pulse of +350 mT along the sample normal gives rise to the remanent state shown in Fig. 4(c) (exposure time of 200 s). As before, the Co element does not exhibit a Landau ground state. Instead, we find a single asymmetric vortex state with domains of different sizes. In fact there is only little contrast between the large domains which are presumably aligned along the edges. However, the position of the domain walls can easily be identified. This is a consequence of the missing data in the center of the hologram blocked by the beam stop. It is this part of the hologram that contains the information of extended areas in the reconstruction. This explains also why this effect was less obvious in the case of the smaller domains in Fig. 3(c). Finally, we have determined the spatial resolution in the magnetic images. Applying the 20%–80% resolution criterion to a profile through the central vortex core in Fig. 3(c) yields a value of 50 nm.

 

Fig. 4 Various magnetic states of the Co element imaged at 30° tilt angle: in the saturating fields of μ₀H = −140 mT (a), +140 mT (b), and in remanence (c). Note the inversion of the gray scale value from a) to b), corresponding to an opposite in-plane magnetization.

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3. Conclusion

In summary, we have reported on the application of FTH for imaging magnetic systems with in-plane magnetization. This was achieved by using an inclined reference hole which allows imaging at off-normal incidence in order to obtain magnetic contrast via the XMCD effect. We could show that the conical shape of the reference holes allows imaging at tilt angles that differ from its milling direction. This scheme was used to map the magnetic structure of a 2μm × 2μm × 20nm Co element by using a reference hole milled at 20° and a tilt angle of 30°. We found complex vortex structures deviating from the ground state which indicates the presence of imperfections.