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Figure 3.11: (a) Typical hologram of theBPMsample in logarithmic pseudo-color inten-sity scale and(b)difference hologram from holograms taken with left and right circularly polarized light in linear gray scale.
In order to gain the maximum magnetic contrast in the images, the signed magnitude of the signal was calculated as described in Sec. 2.5. In particular the phase of the reconstructed exit wave is manipulated referring to Eq. 2.57, i.e. the reconstructed complex value in all pixels is rotated in the complex plane by a constant angle α in a way that the magnetic contrast is maximized in the real part and vanishes in the imaginary part.
The angleα was individually determined for every image by visual inspection. In theory one would expect, that for a photon energy calibration to maximum XMCDcontrast, the initially reconstructed phases would already equal zero and magnetic contrast is found only in the real part. The deviation of the phases from zero is mainly explained by an improper centering of the hologram. If the hologram is miscentered by an offset ∆q= (∆qx,∆qy), the reconstruction is superimposed by a phase gradient exp(i∆qr) [SN09]. In the present case, already a subpixel offset of half a pixel would induce a phase shift of 10° at the position of the images in the reconstruction matrix and the center position is known with a precision of at best one pixel. Unfortunately, finding the right offset ∆q is a complicated task and cannot easily be automated. For this reason the phase shift over the small area of the reconstructed images is considered to be constant and is corrected as described above.
Examples of optimized reconstructions can be found in Fig. 3.12(b)–(e). The magnetic contrast is shown in gray scale with the magnetization in white and black areas pointing in opposite out-of-plane directions. An absolute magnetization value cannot be determined
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Figure 3.12: (a) Complete reconstruction matrix of a typical hologram (Fig. 3.11). In the center the auto-correlation of every individual object is located. The residual fringing is the result of the missing data in the center of the hologram due to the beamstop. Around the center the images of the four object holes and their twin images become visible. In the corners, weak object–object cross-correlations emerge. (b–e) Magnification of the image reconstructions. The magnetization is encoded as gray scale with white and black regions pointing into opposite directions. The images show the pattern ensembles with pitches: (b) 240 nm,(c)200 nm,(d)160 nm, and(e) 120 nm. TheFOVhas a diameter of 1.5 µm.
Figure 3.13: Magnetic trench material pinned at the pat-terned substrate. TheFOVhas a diameter of 1.5 µm, the pitch size is 240 nm.
as the intensity information at low momentum transfer is lost. All magnetic state images shown in this thesis are scaled to the minimum intensity value represented as black and the maximum intensity as white, i.e. the images are scaled to ±Ms.
Since the aim of the experiment was the analysis of the switching behavior of the magnetic islands, the sample was investigated under different externally applied magnetic fields. The usual procedure was to first magnetically saturate the sample at a field ofHmax=±7 kOe and then image the sample after certain field steps. Images taken during such a field sweep are presented in Figs. 3.14 and 3.15. As already pointed out, all four patterned areas are imaged simultaneously at the same external field values. After saturation at −7 kOe the first image is taken before remanence at −1.2 kOe still showing completely saturated areas. When approaching remanence the magnetic film in the trenches partially reverses its magnetization in the case of the 240 nm and 200 nm pitch samples while the samples with smaller pitch length stay saturated. The domain pattern is similar to the worm domain patterns known from continuous film Co/Pd or Co/Pt multilayer samples [Hel06; Hel07b].
In the 160 nm and 120 nm pitch samples, the coercive field of the magnetic film in the trenches is increased since the missing material at the island positions acts as defects and pinning centers [Alb09]. This pinning becomes also visible for the patterns with higher pitch when applying a field of 1.2 kOe and 2.3 kOe. At these fields values, the islands that have not switched appear on the background of the nearly completely reversed film in the trenches. But in addition, between the islands, bridges of non-reversed, pinned magnetic material in the trenches remains visible (Fig. 3.13). Between 2.3 kOe and 3.4 kOe the first islands start to reverse their magnetization. At 4.5 kOe slightly more than half of the islands has switched. The last islands switch between 4.5 kOe and 5.4 kOe and at 6.7 kOe the sample is completely saturated in the reverse direction compared to the situation at the beginning.
The difference of the coercive field of the magnetic island versus the continuous magnetic film is explained by the different reversal mechanism. Whereas a continuous film reverses via nucleation and rapid domain wall motion, the switching of an island is commonly described as a quasi-coherent rotation of the magnetization in the island volume. This mechanism is also known as Stoner–Wohlfarth behavior [Alb09; Hu05a; Sto06].
The majority of the holograms in this study was taken in applied field. However, for the field sweep presented in Figs. 3.14 and 3.15 also images in remanence have been recorded.
In the figures, the remanent images after a certain field step are presented on the right side next to the in-field images. These images prove that although the film in the trenches partially switches back, the islands always retain their magnetization. This result does not play a role for the FTH study, but is important forMFM studies that can be performed in remanence only and for data storage applications where the information is stored and read out under remanent conditions.
In order to perform a statistical analysis of the switching behavior of the magnetic islands, the islands were labeled in a square matrix as shown in Fig. 3.5 using the positions known from the SEM image. A few labeled islands are not visible in the FOV and were ignored in the analysis. The magnetic state of every individual island was recorded for
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Figure 3.14: FTHreconstructions of theBPMsample in a magnetic reversal. Each double-column belongs to one BPMensemble and each row is assigned to a certain field step. At the beginning of the image series the sample was saturated at −7 kOe. Then the field was swept in the indicated field steps. At each field step (except for the first two ones for ob-vious reasons) images in applied field (left side of each double-column) and in remanence (right side) were recorded. TheFOVhas a diameter of 1.5 µm.
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Figure 3.15: Continuation of Fig. 3.14.
every image. In total, N(p= 240 nm) = 29, N(p= 200 nm) = 42, N(p= 160 nm) = 64, andN(p= 120 nm) = 112 islands are visible in the fourFOVs and have been investigated.