Applied
Crystallography
ISSN 0021-8898
Received 19 December 2006 Accepted 19 March 2007
#2007 International Union of Crystallography Printed in Singapore – all rights reserved
Contrast variation by anomalous X-ray scattering applied to investigation of the interface morphology in a giant magnetoresistance Fe/Cr/Fe trilayer
Mikhail Feygenson,a* Emmanuel Kentzinger,aNicole Ziegenhagen,a Ulrich Ru¨cker,aGu¨nter Goerigk,aYingang Wangband Thomas Bru¨ckela
aInstitut fu¨r Festko¨rperforschung, Forschungszentrum Ju¨lich GmbH, D-52425 Ju¨lich, Germany, and
bCollege of Material Science and Technology, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing 210016, People’s Republic of China. Correspondence e-mail:
m.feygenson@fz-juelich.de
The structural properties of an epitaxically grown Fe/Cr/Fe trilayer were studied with anomalous X-ray scattering. Two different X-ray energies have been used:
(i)E1= 5985 eV to match the maximum contrast of the Fe/Cr interface close to the Cr absorptionKedge; (ii)E2= 6940 eV where the Fe/Cr interface displays the lowest contrast. The specular reflectivity and longitudinal diffuse scans together with!scans for both energies were measured. The simulations within the frame of the distorted-wave Born approximation allowed a quantitative description of the morphology of each interface. The roughness, Hurst parameter and the thickness of every layer, as well as an oxidation effect at the surface of the sample, are derived. The strength and limitations of the method are discussed.
1. Introduction
In recent years, systems displaying the giant magnetoresis- tance effect (GMR) (Binashet al., 1989, 1988) have been the focus of many research activities. Besides the fundamental interest in the magnetic and transport properties of thin film and nanostructured systems, GMR systems are attractive for many applications (Zhuet al., 2000; Milleret al., 2001; Parkin, 1998). There are aspects concerning the GMR effect which are still far from being understood. For instance, the dependence of the strength of the GMR effect on interfacial roughnesses is still under debate (Thomsonet al., 1994; Olligset al., 2002). It was shown that in an Fe/Cr superlattice the GMR effect decreases with increasing roughness of the substrate (Paulet al., 2001), while it may be enhanced by the presence of Fe/Cr interfacial roughness (Fullerton et al., 1992). In order to confirm some theoretical predictions about the GMR effect (Levy et al., 1990; Inoue et al., 1991), exact structural infor- mation about every layer and every interface is required.
Surface-sensitivity techniques, such as scanning tunneling microscopy (STM), are extremely powerful methods to determine morphology of surfaces in situ during film preparation. This has been demonstrated for the Fe/Ag interface and for Cr/Fe superlattices by Bu¨rgleret al.(1997) and Schmidt et al. (2001). However, as the next layer is deposited, the resulting interface morphology might be different from the morphology of the exposed surface.
Moreover, STM probes only smaller sample regions and thus gives access only to shorter lateral correlations lengths. To gain access to a larger range of correlation length and to a
buried layer, scattering techniques are the method of choice.
X-ray and neutron scattering are non-destructive methods which are able to characterize quantitatively the properties of buried layers in superlattices. In previous publications (Nitzet al., 1996; Zimmermannet al., 1998; Stettneret al., 1996), the analysis of measured X-ray reflectivity combined with off- specular scattering was introduced. This technique has to be extended for typical GMR multilayers, which consist of tran- sition metal layers with nearly identical scattering length densities. For example, in Fe/Cr/Fe GMR trilayers, Fe and Cr have nearly the same electron density and thus the interface between Fe and Cr is nearly invisible to conventional X-ray reflectometry. To overcome this problem, we used the advantages offered by anomalous X-ray scattering. We were able to achieve the maximum contrast between Fe and Cr as well as the lowest one using two different photon energies.
In what follows, we will briefly outline the theoretical model used for the simulations, describe the fitting procedure to the measured data, and discuss the quantitative description of the trilayer. The application of the outlined method will enable one to obtain a better understanding of the relation between morphology and functionality in similar spintronic devices.
2. Sample preparation
The sample under investigation is a typical GMR system: two ferromagnetic iron layers separated by a non-ferromagnetic chromium spacer layer. The nominal thickness of the Cr spacer layer is 11 A˚ , which is appropriate to give rise to antiferromagnetic coupling between two Fe layers. The sample
was produced in a ultra-high-vacuum molecular beam epitaxy (MBE) machine (Ru¨cker, 1994). We followed the growing procedure of Fe/Cr/Fe layers on a GaAs (001) single-crystal substrate with Ag buffer given by Bu¨rgler et al. (1997). An overview of the sample preparation parameters is given in Table 1. It is important that the roughness of the epitaxically grown layer depends on the deposition temperature (Bu¨rgler et al., 1997; Schmidtet al., 1999).
The nominal thicknesses were obtained with a quartz microbalance, with uncertainties in the range 5–10%.
After deposition of each layer, low-energy electron diffraction patterns were recorded, in order to prove the single-crystalline nature of every layer. While the morphology of a surface can be changed as it becomes an interface during deposition of the next layer, we expect the layers to remain single-crystalline. Therefore, we applied the scattering method to study the interface morphology of the buried layers.
3. Experiment
The geometry of the scattering experiment is shown in Fig. 1.
The scattering vectorq= kfkidepends on wavevectors of incident and scattered waves ki and kf, respectively. The projections of theqvector on thexandzdirections are
qx¼2
ðcosfcosiÞ; ð1Þ qz¼2
ðsinfþsiniÞ; ð2Þ whereis the X-ray wavelength andiandfare the angles of the incident and scattered photons, respectively. The scan conditions are shown in Fig. 2.
The anomalous X-ray scattering measurements were performed at the beamline C1 in HASYLAB at two photon energies:E1= 5985 eV andE2= 6940 eV. AtE2= 6940 eV iron and chromium display no contrast (see Fig. 3b). The experi- mental details are as follows: sample size = 10 mm10 mm;
sample-to-detector distance = 1400 mm; beam size at the sample position = 0.47 mm; opening of the slit in front of the NaI scintillation detector = 1 mm. This resulted in aqreso- lution for different energies. For the energyE1, the resolution was: qz ’ 1.53 103A˚1, qx ’ 1.53–4.6 103A˚1 (depending on incident angle). For the energyE2,qz’1.78 103A˚1,qx’1.78–5.35103A˚1.
Close to theK-absorption edge of Cr (EKCr = 5989 eV), the low electron density contrast between Fe and Cr is enhanced due to anomalous scattering (Fig. 3a). For both energies, a set of different measurements was performed. First, we measured the reflectivity (i = f) and longitudinal diffuse (i = f + 0.05) scans (Fig. 4), then a number of!scans (i+f = 2, 2= const) were performed (Fig. 5).
An overview of the diffuse scattering measurements is presented in Fig. 6, where the intensity of the scattered photons is plotted as a function of incident and outgoing angles of the photons.
Figure 1
The scattering geometry of the experiment.
Figure 2
Scans inðqx;qzÞspace for the energyE1= 5985 eV. The vertical solid line is the reflectivity scan (i=f), the dashed line is the longitudinal diffuse scan (i=f+ 0.05) and the solid horizontal lines are!scans (i+f= 2) at 2values listed in Fig. 5(a). The regions below the solid curved lines are not assessable with the experimental set-up we used.
Table 1
Sample preparation parameters.
The layers are in the order of the deposition.dis the nominal thickness,Tis the deposition temperature,ris the growth rate, LS is the lattice structure (b.c.c. = body-centred cubic; f.c.c. = face-centred cubic).
Layers d(A˚ ) T(K) r(A˚ s1) LS
GaAs Bulk Annealed at 913 K – –
Fe 10 393 0.1 b.c.c.
Ag 1500 393 1.6 f.c.c.
Fe 150 293 0.2 b.c.c.
Cr 11 293 0.1 b.c.c.
Fe 150 293 0.2 b.c.c.
Figure 3
The dispersionat (a)E1= 5985 eV, CrK-absorption edge, (b)E2= 6940 eV (http://www.cxro.lbl.gov).
4. Simulations
The fitting routine is based on the distorted-wave Born approximation (DWBA) introduced for scattering from interface roughnesses by Sinhaet al.(1988) for one layer and extended by Holy´et al. (1993) for multilayers. For the simu- lations of the specular reflectivity, the well known Parratt (1954) formalism has been used. To calculate the diffuse intensity, we used the equation for the differential scattering cross section as presented by Stettneret al.(1996, 1995),
d d
diff
¼Ak21 82
XN
j;k¼1
ðn2j n2jþ1Þðn2kn2kþ1Þ
X3
m;n¼0
G~
GmjGG~mk exp 1
2ðqmz;jjÞ2þ ðqnz;kkÞ2
Sjkmnðqx;qmz;j;qnz;kÞ; ð3Þ with the structure factor
Sjkmnðqx;qmz;j;qnz;kÞ
¼ 4 qmz;jqnz;k
Z1
0
dX expqmz;jqnz;kCjkðXÞ 1
cosðqxXÞ; ð4Þ where k1 is the wavevector in a vacuum, j and k denote different interfaces,Ais the illuminated area of the sample,nj
is the refractive index of the layerjjust above interfacej,qmj = ðqx;qmz;jÞT is the momentum transfer within each layer. qmj
decomposes itself into qx, the in-plane component of the momentum transfer, andqmz;jis the perpendicular component of the wavevector within this layer.
The terms GG~mj exp½ð1=2Þðqmz;jjÞ2 appearing on the right- hand side of equation (3) have a clear physical meaning. For instance, the term Tjþ1i Tjþ1f exp½ð1=2Þðq0z;jjÞ2 expresses the scattering from the transmitted wave with amplitudeTjþ1i into the wave with amplitudeTjþ1f . The change of the wavevector corresponding to this process is q0z;j = kiz;jþ1þkiz;jþ1. The exponential term represents a damping with a ‘Debye–Waller’
type factor due to interfacial roughnesses (Debye, 1913).
The quantityGG~mj is defined through G~
Gmj ¼Gmj expðiqmz;jzjÞ; ð5Þ Figure 4
Intensity measured at the specular position and longitudinal diffuse scans at (a)E1= 5898 eV, (b)E2= 6940 eV. Open symbols are data points; the solid lines show the best fit obtained from a simultaneous refinement of all data. The calculated values for the specular intensity are the sum of the diffuse scattering forqx= 0 calculated within the DWBA, and the true specular reflectivity calculated within a Parratt formalism. The effect of the contrast variation is clearly visible from the different intensity modulations at the two energies. For visualization, the experimental data were displaced by a factor of 25 for specular reflectivity and by a factor of 1/25 for the longitudinal diffuse scan, with corresponding fitting curves.
The crossing solid lines in the centre of every plot are the fits of the original data with no displacement.
Figure 5
!scans for different 2=i+fvalues at (a)E1= 5898 eV, (b)E2= 6940 eV. Open circles are data points; the solid lines show the simulation for the parameters obtained from the best fit. For visualization, all scans are displaced with respect to each other by one order of magnitude in intensity scale.
whereGmj are the coefficients describing the dynamical effects (see Table 2) andzjis the vertical position of interfacej(layer thicknessdj=zjþ1zj; see Fig. 1).
CjkðXÞin equation (4) denote the auto-correlation (j¼k) and cross-correlation (j6¼k) functions between interface j andk. Here we assume that the interface heights are Gaussian variables of the lateral coordinate and that the interface j fluctuates with a root-mean-square (r.m.s.) roughness value that saturates to a valuej above an effective cut-off length denoted as j. Owing to the horizontally focusing of our experimental set-up, we integrate over the corresponding intensity distribution alongqy.
Assuming self-affine rough interfaces at length scales well below j, the height–height auto-correlation function of interfacejcan be written as
CjjðXÞ ¼j2exphX=j2hji
: ð6Þ The exponent (‘Hurst parameter’) hj(0<hj<1) determines how smooth or jagged such an interface is. Small values ofhj
correspond to extremely jagged interfaces, while a value ofhj
approaching 1 corresponds to smooth hills and valleys.
Therefore, in a statistical description using the model described by Sinha et al.(1988) and Holy´et al.(1993), each interface and layerjis characterized by six parameters:dj, the thickness of the layerj;nj= 1jþij, the refractive index of layer j, which is energy-dependent; j, the r.m.s. roughness amplitude for interfacej; j, the lateral correlation length of roughness for interfacej;hj, the Hurst parameter for interface j. To calculate the cross-correlation function Cjk, the auto- correlation function is first Fourier transformed. The Fourier transform of the cross-correlation function is then defined through
C~
CjkðqxÞ ¼CC~jjðqxÞCC~kkðqxÞ1=2
exp jzjzkj=?jk
; ð7Þ
where ?jk is a quantity of dimension ‘length’ denoting how strong the height fluctuations of interfacejandkare corre- lated (‘vertical correlation length’).
If?jk= 0, interfacesjandkare not correlated andCC~jkðqxÞ= 0. Ifjk? jzjzkj, the two interfaces are fully correlated.
The cross-correlation function in real spaceCjkðXÞis then obtained by inverse Fourier transformation ofCC~jkðqxÞ.
For our fits we assumedjk?to be independent of the pair (j,k) of interfaces considered.
Owing to the large number of parameters, an independent refinement without prior knowledge leading to good estima- tions of starting values will not be successful. Some estima- tions can be obtained from the preparation conditions and some from inspection of the raw data (see argumentations for vertical correlation length above).
From the qz period qz of the Kiessig fringes in the reflectivity, a layer thickness can be estimated byD= 2=qz. For the energy E1 = 5985 eV with maximal contrast, the oscillations steam mainly from the thickness of the Fe layer, while forE2= 6940 eV at vanishing contrast the total Fe/Cr/Fe trilayer thickness becomes visible.
From the data in Fig. 4 we obtained thicknesses of Fe layers and of the spacer Cr layer, which are close to those obtained by the quartz microbalance during the sample preparation (see Table 1). In the model we assumed an infinite thickness of the Ag buffer layer and ignored the GaAs substrate.
Tabulated values were taken forjandjfor both energies (http://www.cxro.lbl.gov). This approximation is good enough owing to the match of the critical angle of total reflection ci ’ ð2E2iÞ1=2for both energies. Whilejwas a free parameter, the absorption coefficients j were kept fixed during the refinement since they are one order of magnitude smaller then the dispersion. To adjust the refractive indices and thicknesses of every layer we performed simulations. For the simulations of diffuse scattering intensity we have found first the initial values of the lateral correlation lengthj = 3000 A˚ and the Hurst parameterhj= 0.8 for each layer (j= 1–5). They were adjusted by the widths of the ! scans and were also constrained to be equal at all interfaces during the simulations and the following fits.
On top of the trilayer we introduced an oxide layer with reduced refractive index. The initial values of the thicknessd1
and refractive index n1 of this layer were adjusted by the simulations of the reflectivity scans.
Table 2
The expression for Gjm in equation (5) with respective momentum transfers according to Schlomkaet al.(1995) and Stettner (1995).
Tjþ1i ,Rjþ1i andTjþ1f ,Rjþ1f are the amplitudes of the transmitted and reflected incoming and outgoing beams, respectively, in layerjas obtained from the Parratt formalism for sharp interfaces.kði;fÞz;j =k1½n2jcos2ði;fÞ1=2 is the z component of the incoming (i) or outgoing (f) wavevector in layerj.
Gj0¼Tjþ1i Tjþ1f q0z;j¼kiz;jþ1þkfz;jþ1
Gj1¼Tjiþ1Rjfþ1 q1z;j¼kiz;jþ1kfz;jþ1
Gj2¼Rjþ1i Tjþ1f q2z;j¼ q1z;j Gj3¼Rjþ1i Rjþ1f q3z;j¼ q0z;j
Figure 6
The intensity distribution for diffuse scattering as a function of incidenti and scatteringfangles: (a) the data; (b) the simulations. The intensity from specular reflection is not shown.
The correction of the measured data due to the illumination effect, which is related to the sample size and the projection of the incoming beam onto the sample surface, and the instru- mental resolution effect have been taken into account during simulations and fits, as described by Holy´et al.(1999).
At higher incident angles, the specular reflected intensity in our experiment became comparable with, or even less than, the diffuse scattering photon intensity owing to the scattering from ‘in-plane’ roughness. There are methods (Kaendleret al., 2000) to separate the diffuse scattering from the specular reflectivity resulting in a ‘true specular reflectivity’ but, as already discussed (Prokertet al., 2003; Schlomkaet al., 1995), the fitting of the ‘true specular reflectivity’ alone can give misleading results, especially in cases where the intensity due to diffuse scattering is comparable with the intensity due to specular reflectivity. This is the reason why we fitted simulta- neously the diffuse and specularly scattering intensities.
In a first step we performed the fits at the second energyE2= 6940 eV. Owing to the low Fe/Cr contrast, a significant number of parameters, namely all those describing the interfaces between Fe and Cr layers, become irrelevant for the fit and can be fixed to tabulated values. Thus the free parameters during this fit were the thickness of the oxide layerd1, the refractive index E12 and the r.m.s. roughnesses of the air/Fe-oxide, Fe- oxide/Fe and Fe/Ag interfaces, as well as the Hurst parameter hjand lateral correlation lengthsj(j= 1, 2, 5).
While this is still a large number of parameters, one has to keep in mind that we have good estimations from prior knowledge of the system and that we used all data from specular as well as off-specular scattering for a simultaneous refinement.
Keeping these parameters constant, we have performed the fits for photon energyE1usingdj,jandj(j= 3, 4) as free parameters for the Fe/Cr and Cr/Fe interfaces.
The results of the simultaneous fits of the specular reflec- tivity, longitudinal diffuse and!scans are shown in Figs. 4 and 5. The structural parameters obtained from the fits are presented in Table 3.
5. Results and discussion
Here we will first examine the quality of refinement and point out the limitations of the applied method. Then we will discuss the morphology of the multilayer system, comparing para- meters expected from the preparation procedure with the
actual structure of our sample. Finally, we will discuss the strength and limitations of the method.
At both energies, diffuse scattering can be observed extending for certainqzvalues along theqxdirection (constant i+f). These ‘Bragg sheets’ are characteristic for vertically correlated roughnesses between interfaces. However, theqz
period is quite different for both energies. Since for both energies the biggest contrast comes from the interfaces of the trilayer with the substrate and with vacuum, the oscillations due to the total trilayer system are present at both energies.
For the data at high contrast, the Fe/Cr interfaces also become visible, as may be seen in the data presented in Fig. 6. The beating effect between the many spatial frequencies present in Fig. 4(a) amplifies the oscillations due to the Fe layer thickness in theQrange from 0.2 to 0.4 A˚1, while the oscillations due to the total trilayer thickness are visible at low Q values.
Corresponding to the larger thickness in real space, the oscillation period is small in Fourier space atE2. Based on the parameters obtained, it was possible to reproduce the dispersion profile in thezdirection at both energies with the given roughnesses (Fig. 7). Fig. 8 shows one of the possible realizations of the sample structure in real space consistent with parameters given in Table 3.
The refinements of the intensities at the specular position (see Figs. 4aand 4b) deviate for both energies from the data at higher qz values. As discussed by Sinha et al. (1988), the DWBA is a good approximation for calculating the diffuse scattering forqz< 1 (see Sinhaet al., 1988, before equation 4.38 therein). In our case, we see deviations starting at qz
larger than 0.35 A˚1 where, depending on the interface considered, we have values ofqzbetween 1.5 and 3.5.
Table 3
The structural parameters obtained from the simultaneous fit of reflectivity, longitudinal diffuse scan and seven!scans at both energies.
We assumed fully vertical correlated roughness and thus fixed the corresponding correlation length?= 10000 A˚ (infinite in practice). Thejvalues were kept fixed to the tabulated values (http://www.cxro.lbl.gov) during refinement. The values marked with * were constrained to be equal during the fitting. The values in square brackets are tabulated/nominal values used as starting values in the simulations, deduced from the data and sample preparation details.
j Layers dj(A˚ ) Ej1106 Ej2106 j(A˚ ) j(A˚ ) hj
1 Fe oxide 17 (1) 21 (2) 15 (1) 5 (1) 2000* (1000) 0.79* (0.1)
2 Fe 150 (1) [150] 38* (2) [39.8] 27* (3) [27.5] 10 (1) 2000* 0.79*
3 Cr 7 (2) [11] 18 (3) [21.5] 27* [27.5] 5 (1) 2000* 0.79*
4 Fe 164 (2) [150] 38* [39.8] 27* [27.5] 7 (1) 2000* 0.79*
5 Ag Semi-infinite 50 (3) [52.8] 39 (2) [39.5] 6 (1) 2000* 0.79*
Figure 7
The dispersion profile for both energies (http://www.hmi.de). Note that the tanh profile at the interfaces results in a smearing out and the plateau for the oxide layer and the Cr layer vanishes.
The fit of the reflectivity is not perfect in theqzrange from 0.12 to 0.2 A˚1for both energies. These deviations are due to the top Fe oxide layer, which is not well described within the interface model used by Sinha et al.(1988) and Holy´ et al.
(1993). These deviations can be reduced by varying the fitting parameter for this layer, which mainly affects the fit in the corresponding region. The oxide layer is due to the intense X-ray beam from the synchrotron storage ring which causes a break up of the gas molecules in air and produces strongly reactive O3and HNO3, even from rest gas in a vacuum reci- pient. This causes a chemical reaction with the exposed metal surface and is visible in a beam-footprint on the sample. It is likely that the assumption of a self-affine rough interface does not hold for such an oxide layer. Since we were mainly interested in the interfaces between Fe and Cr, we accepted the deviations in the reflectivity curve of Fig. 4(a) after we had convinced ourselves that they were caused by limitation in the model description of the oxide layer only.
The thickness of the Cr layer evaluated from the fits (7.3 A˚ ) is smaller than that obtained by the quartz microbalance of the MBE machine (11 A˚ ). At the same time, the thickness of the bottom-most Fe layer is larger than the one obtained by the microbalance (see Table 3). This can be an indication for interdiffusion at the Cr/Fe interface. As was shown (Guptaet al., 2004; Schmidt et al., 2001), interdiffusion at a Cr/Fe interface is stronger compared with interdiffusion at an Fe/Cr interface. The explanation was given in terms of a higher melting point of Cr compared with Fe leading to different solubilities. In our case, an introduction of interdiffusion layers between Cr/Fe and Fe/Cr interfaces with an averaged electron density did not improve the quality of the specular and longitudinal diffuse scans.
Introducing such additional layers increases the number of refined parameters significantly. Clearly, with our limited data set, these additional parameters cannot be determined. Here we approach the limits of our method, as we already have to determine the parameters describing the morphology of four layers plus buffer. Nevertheless, we interpret the refined layer thicknesses as an indication of dilution of Cr within the bottom Fe layer.
Apart from this observation, the statistical parameters describing the interfaces are rather similar. In particular, owing to the MBE preparation at moderate temperature,
vertically strong correlated roughness appears as the main features of an exposed surface are reproduced during the deposition of the next layer. This explains why a continuous Cr interlayer exists despite the fact that its averaged layer thickness is comparable with the interfacial width character- ized by the r.m.s. roughness. This is consistent with the observation of antiparallel coupling between the Fe layers, while pinholes in the Cr layer would lead to an enhanced parallel coupling.
In summary, we successfully applied the contrast variation method by means of anomalous X-ray scattering in order to achieve a description of the interface morphology of an Fe/Cr/
Fe trilayer system on an Ag buffer.
Using two different energiesE1= 5985 eV andE2= 6940 eV, we achieved the maximum contrast between Fe and Cr layers and vanishing contrast, respectively. Simulations and fits in the frame of the DWBA allowed us to describe quantitatively the structure of the sample, including the information about buried layers and a top-most oxide layer.
It is a pleasure to thank Dmitri Novikov and Wolfgang Caliebe (HASYLAB) for their efficient support on the CEMO beamline. We also wish to acknowledge Oliver Seeck (HASYLAB) for his help in the development of the off- specular analysis software.
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