PHYSICAL REVIEW B VOLUME 57, NUMBER 21 1 JUNE 1998-I

Quantitative study of the interdependence of interface structure and giant magnetoresistance
in polycrystalline Fe/Cr superlattices

R. Schad*
Laboratorium voor Vast-Stoffysika en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium
and Research Institute for Materials, KU Nijmegen, NL-6525 ED Nijmegen, The Netherlands

P. Belie¨n, G. Verbanck, and C. D. Potter
Laboratorium voor Vast-Stoffysika en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium

H. Fischer
Institute Laue Langevin, 38042 Grenoble Cedex 9, France

S. Lefebvre and M. Bessiere
LURE, Universite´ de Paris-Sud, 91405 Orsay Cedex, France

V. V. Moshchalkov and Y. Bruynseraede
Laboratorium voor Vast-Stoffysika en Magnetisme, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium
Received 15 September 1997
We present a quantitative characterization of the interface roughness of Fe/Cr superlattices based on specular
and off-specular x-ray diffraction using anomalous scattering. We discuss the dependence of the amplitude of
the giant magnetoresistance GMR effect, including changes in the interlayer magnetic coupling, on the
interface structure. We observe a reduction of the GMR effect with increasing amplitude of the interface
roughness having constant lateral correlation length. However, the physical interpretation of this clear result in
terms of spin-dependent interface scattering remains unclear because of the unknown bulk contribution.
S0163-1829 98 03918-6

INTRODUCTION configuration changes from fully antiparallel to parallel
alignment. The latter will be easily achieved only if the ex-
The discovery of giant magnetoresistance1 GMR in ternal magnetic field is strong enough to saturate the magne-
Fe/Cr superlattices opened a new field of possible applica- tization. The antiferromagnetic alignment at zero field, how-
tions for artificially tailored materials. The effect is explained ever, depends in the case of an exchange coupled
by spin-dependent scattering of the electrons at impurities or superlattice on the kind of the exchange coupling and on
interfaces.24 This spin dependence results from spin- superlattice imperfections in the form of pinholes. Instead of
dependent electron states and from the spin dependence of a simple antiferromagnetic alignment, the magnetization di-
the scattering potential. For instance, the majority electrons rections can form 90° angles between adjacent magnetic
of Fe are much stronger scattered at Cr impurities than are layers.8 This will reduce the observed GMR by a factor of 2.9
the minority electrons.5 This leads to different resistivities The strength of the 90° coupling is mediated by roughness of
for the parallel and the antiparallel alignment of the magne- the interfaces10 or loose spins inside the spacer layers.11 So,
tization directions of the magnetic layers. The antiparallel in both cases the 90° coupling indirectly links the size of the
configuration at zero strength of the external field is provided GMR effect to the superlattice quality. Magnetic pinholes
by antiferromagnetic exchange coupling for an appropriate will cause ferromagnetic alignment of parts of the sample
thickness of the Cr spacer layer. This configuration can be which consequently do not contribute to the GMR effect,
forced into parallel alignment by an external field, thus re- thus diminishing its amplitude. Not only pinholes but also
sulting in a change of the resistance. However, antiferromag- precursors of these in the form of larger spacer layer thick-
netic exchange coupling is not a prerequisite for the obser- ness fluctuations might lead to partially ferromagnetic align-
vation of the GMR effect since the antiparallel alignment can ment because of local changes of the exchange coupling.
be obtained also by other methods.6,7 These magnetic contributions can be separated experimen-
The burning question was and still is, how the size of the tally from the pure electronic contributions by magnetization
GMR effect is related to the structural properties of the su- measurements which give directly the fraction of the sample
perlattice. Here one has to distinguish between several con- which is antiferromagnetically ordered AFF and the part
tributions to the GMR which are directly or indirectly linked which does not contribute local ferromagnetic alignment,
to the structural properties. These are contributions of i the pinholes or which contributes only partially to the GMR
magnetic structure, ii the spin-dependent electronic struc- angle between magnetization directions of adjacent mag-
ture, and iii the spin-dependent electron scattering. netic layers between 0° and 180° .
The magnetic structure is of importance because the full The second contribution to the GMR effect, the electronic
size of the GMR effect is only observed when the magnetic structure, can generate a GMR effect even in defect-free

57 QUANTITATIVE STUDY OF THE INTERDEPENDENCE . . . 13 693

point contacts with ballistic transport12 or in the limit of di- independent ones. We present XRD spectra of high quality
luted scatterers.13,14 This contribution comes mostly from the Fe/Cr superlattices together with simulations which deter-
asymmetry of the Fermi velocities of the two spin channels. mine the values of parameters for the interface structure both
These band-structure effects are to some extent related to the perpendicular to and in the plane of the interfaces.
third contribution to the GMR effect, the spin-dependent
electron scattering. On one hand, the minigaps in the band EXPERIMENTAL
structure caused by the periodicity of the superlattice will be
influenced by the defects which cause the scattering. On the The superlattices were prepared in a Riber molecular-
other hand, the spin dependence of the scattering process is beam epitaxy deposition system 2 10 11 mbar base pres-
caused by the asymmetry of the band structure, first via the sure using electron-beam evaporation hearths, which were
density of states at the Fermi level, and second via the spin- rate stabilized to within 1% by a homemade feedback control
dependent scattering potential at impurities or interfaces. The system32 using Balzers quadrupole mass spectrometers
first contribution makes any scattering event spin dependent, QMS . Additionally, integration of the QMS signal was
even scattering at phonons.15 Experimentally, the contribu- used for automatic control of the shutters of the individual
tions of the electronic structure and the spin-dependent scat- evaporation sources. In this way, a reproducible bilayer
tering cannot yet be separated since scattering is dominant in thickness throughout the whole superlattice was ensured, as
all reported samples so far. It is this spin-dependent scatter- well as a constant Cr thickness over all superlattices. The Fe
ing that generally receives the most attention in the literature, and Cr layers starting material of 99.996% purity were
experimentally and theoretically. electron-beam evaporated in a pressure of 4 10 10 mbar at
Here two contributions have to be considered separately, a rate of 1 Å/s on polycrystalline yttrium stabilized zirco-
the spin-dependent scattering at impurities inside the mag- nium oxide YSZ substrates typically 5 5 mm2 . In order
netic layers referred to as bulk scattering and the scattering to minimize thickness inhomogeneities, the substrate was ro-
at the interfaces. Both can in principle cause a GMR tated at 60 rpm during the whole growth process. The surface
effect.1622 In combination they can even cancel each other roughness of the YSZ substrates was evaluated ex situ by
provided that their spin asymmetry is opposite. The ideally atomic-force microscopy AFM . Typical rms values of the
pure cases, samples with only bulk or only interface scatter- YSZ surface roughness were 5 Å on a 1 m2 area. After
ing, are difficult to achieve experimentally. This would re- rinsing in isopropyl alcohol and drying in a dry N2 flow, the
quire the growth of samples with either ideally flat interfaces substrate was annealed for 15 min at 600 °C in UHV.
or defect-free layers. However, recent experiments on Co/Cu The superlattices consisted of ten bilayers with 22 Å of Fe
superlattices indicate that spin-dependent interface scattering and 13 Å of Cr starting the growth with a Fe layer. The
dominates the GMR effect.23 interface roughness was varied by growing the samples ei-
We therefore have a strong motivation to investigate ther directly onto the YSZ substrates sample numbers 5,7,9
quantitatively the effects of interface structure e.g., rough- or onto a 20 Å thick Cr buffer sample numbers
ness on GMR. A detailed comparison with theory requires a 6,8,10,12,14,16 using substrate temperatures TG increas-
comprehensive and quantitative analysis of the interface ing from 0 to 400 °C in steps of 50 °C increasing sample
structure. The most powerful technique for this purpose is numbers . In this way, we obtained a series of 18 Fe/Cr
x-ray diffraction24 XRD because, first, it is a nondestructive superlattices of which nine have been selected for this analy-
technique applied after the completion of the growth of the sis because of their magnetic properties see below .
sample, second it probes the whole superlattice structure as it The structural characterization of the superlattices was
is seen by the electrons in the transport measurements and, obtained through small angle SA XRD measurements using
third, it uses waves with a wavelength similar to the one of either a synchrotron source with wavelength of 2.0753 Å 15
the electrons at the Fermi level of usual metals. Unfortu- eV below the Cr absorption edge or a Rigaku rotating anode
nately, ordinary XRD provides only low contrast for Fe/Cr diffractometer at 4 kW power and with an x-ray wavelength
superlattices, because of the comparable electron densities of of 1.542 Å (Cu K ). The following experimental XRD set-
Fe and Cr. This effect has impeded until now the quantitative ups were used: i specular reflectivity measurements or
evaluation of the XRD spectra. However, synchrotron radia- symmetrical -2 scans at SA were used to determine the
tion allows the use of anomalous diffraction by choosing the interface roughness in perpendicular direction; ii rocking
wavelength close to the absorption edge of one of the atomic curve or -scan measurements at SA providing information
species, resulting in an enhanced contrast. Additionally, re- about the lateral correlation length x of the interface rough-
cent developments of theoretical models describing specular ness and the Hurst parameter h. The lateral correlation
and diffuse x-ray scattering from superlattices2531 allow length is a measure for the spatial decay of the height-height
simulations of XRD spectra which are characterized by a correlation function whereas h describes the fractality of the
high degree of agreement with the measured spectra and ac- interface structure; iii offset ( ) 2 scans to study the
cordingly deliver very reliable values for the interface struc- correlation of the interface roughness in perpendicular direc-
ture of the superlattices. tion expressed by the correlation length z . The measured
In this paper we present the interpretation of the transport spectra were simulated applying recently developed theories
properties of polycrystalline Fe/Cr superlattices based on a describing specular as well as diffuse x-ray scattering at su-
quantitative analysis of their XRD data. The transport prop- perlattices. In this model the scattered intensity is calculated
erties are characterized by high values of the GMR effect up by dynamical scattering in the distorted-wave Born approxi-
to 80% for samples with 10 bilayers indicating the domi- mation as a function of the vertical and lateral scattering
nance of spin-dependent scattering processes above spin- vectors qz and qx . Further details can be found in the origi-

13 694 R. SCHAD et al. 57

nal literature.2531 Large-angle XRD which usually can be
employed for quantitative analysis of the interface structure
of superlattices24 cannot be used in this case because the
samples are polycrystalline with only poor texture.20 But also
in the case of high-quality epitaxial Fe/Cr superlattices33,34
the similar lattice constants of Fe and Cr are responsible for
the much less pronounced large-angle spectra compared to
the SA XRD scans. Therefore, the analysis of the SA data
generally delivers more robust values of .
The electrical measurements were performed in an Ox-
ford cryostat 1.5 up to 300 K equipped with a 15 T magnet.
Resistivities were determined using a standard four-probe
Van der Pauw method. The magnetoresistance is defined as
/ s ( 0 s)/ s , where 0 is the resistivity in zero field
and s the saturation resistivity in a magnetic field Hs paral-
lel to the interfaces. All quoted resistivity values were mea-
sured at 4.2 K.
The magnetization measurements were performed in an
alternating gradient magnetometer. The antiferromagnetic
fraction of the samples is defined as AFF 1 (Mr /Ms)
with Mr and Ms being, respectively, the remnant and the
saturation magnetization. This AFF was used to correct the FIG. 1. Specular SA XRD spectra of one sample measured with
magnetoresistance for small variations in the magnetic order x-ray wavelengths of, respectively, 1.542 Å Cu K laboratory
of the samples by dividing by AFF.35 This way the mag- source and 2.0753 Å synchrotron source . Shown are the mea-
netoresistance data become independent of this contribution. sured data points and the simulations lines . The two simulations
are obtained using identical input parameters except for the differ-
ent optical constants which were taken from literature. All curves
RESULTS AND DISCUSSION are vertically offset for clarity.

As a function of the sample growth temperature TG we oxide. Then the simulation was optimized by adjusting the
found the best layering quality and a maximum of the GMR vertical interface roughness Fig. 1 lower curve . The cri-
amplitude around TG 250 °C.20 However, the reduction of teria for assessing the quality of a simulation was the match-
the GMR towards higher TG is only caused by a decrease of ing of the superlattice Bragg peak intensities and shapes. The
the AFF Ref. 35 and is thus a magnetic contribution. uncertainty of the obtained roughness value depends on the
Therefore our analysis is restricted to nine samples grown at distinctness of the superlattice structure in the spectrum. This
lower TG where the changes of the GMR are of spin- varies with the roughness itself and the x-ray wavelength
dependent origin. used. Careful estimates of these uncertainties were obtained
First, we will discuss the structural properties of the su- by studies of the influence of on the quality of the simu-
perlattices measured with XRD. In Ref. 20 we assessed the lations and are used as error bars in Fig. 4.
interface quality by the peak to background intensity ratio of Simulations taking into account possible variations of the
SA XRD rocking curves. This was, however, revealing no interface roughness throughout the stacking of the superlat-
information over the lateral roughness length scale and addi- tice cumulative roughness24 or inequality of Fe/Cr and
tionally, the intuitive interpretation of the diffuse intensity Cr/Fe interfaces were not successful so that we can con-
can be misleading.30,31 Here we are able to present a quanti- clude that this effect must be small or absent. In order to
tative simulation of the specular and diffuse XRD spectra keep the number of simulation parameters limited we used
giving a comprehensive overview over the relevant interface identical roughness for all superlattice interfaces. Addition-
structure parameters. Since not all samples could be mea- ally, it should be noted that the obtained values of were not
sured at the synchrotron source we first will compare simu- influenced by a later fine adjustment of the substrate rough-
lations of the specular SA XRD data obtained using, respec- ness s which only determines the inter-Bragg peak intensity
tively, the synchrotron source and the laboratory source. This and the damping of the finite-size peak oscillations. We find
is demonstrated for the sample with the most pronounced values of s about 3 Å being slightly smaller than
superlattice structure since here any deviations between the ones measured by AFM about 5 Å . This small differ-
simulation and measurement will become most obvious, but ence might be caused by the different lateral length scale
of course, similar agreement is found also for the other over which the two methods are sensitive38 and by the fact
samples Fig. 1 . The specular data show a rich structure that the AFM data were taken in air.
being the pronounced superlattice Bragg peaks and the As next step, all parameters of this simulation had served
higher frequent finite-size peaks. We produced the best simu- as input parameters for the simulation of the spectrum mea-
lation for the spectrum measured at the synchrotron using as sured with the Cu K wavelength. Only the optical con-
input parameters the thicknesses of all layers Fe, Cr, and a stants had, of course, to be changed according to the different
top oxide layer ,36 the number of bilayers, the optical param- wavelength used.37 Although the two measured spectra look
eters of Fe, Cr, YSZ, top oxide,37 and the roughnesses of, very different because of the enhanced material contrast in
respectively, the substrate determined by AFM and the top the case of the synchrotron data for which the wavelength

57 QUANTITATIVE STUDY OF THE INTERDEPENDENCE . . . 13 695

FIG. 3. SA XRD rocking curves of samples 6 and 16 with qz at
the position of the second-order superlattice Bragg peak. Shown are
the measured data crosses and the simulations lines . All curves
are vertically offset for clarity.

substrate. The values we obtain are in qualitative agree-
ment with the peak-to-background intensity ratios derived in
FIG. 2. Specular SA XRD spectra of all samples measured ei- Ref. 20. However, the quantitative structure analysis by
ther with a wavelength of 1.542 Å Cu K laboratory source; simulation provides values of well-defined structure param-
samples 7, 8, 10, 12, 14 or 2.0753 Å synchrotron source; samples eters and additionally, allows us to estimate the lateral
5, 6, 9, 16 . Shown are the measured data crosses and the simu- roughness components.
lations lines . All curves are vertically offset for clarity. The lateral correlation of the interface roughness was
measured by scans at qz , the vertical wave vector, set to
was chosen close to the absorption edge of Cr, both simula- the position of the second superlattice Bragg peak. These
tions are in excellent agreement with the data Fig. 1 . This measurements were done at the synchrotron, so data are
degree of agreement proves that spectra from superlattices available for samples 5, 6, 9, and 16 which are samples
with such low material contrast as Fe/Cr can be successfully grown at, respectively, low and high TG and with or without
simulated and quantitative roughness data can be obtained. a Cr buffer. Two examples of measured data together with
Furthermore, it gives confidence in the structure analysis ob- their respective simulation are shown in Fig. 3. The relevant
tained through simulations of spectra measured with the parameters of the simulation are the lateral correlation length
laboratory source. x and the Hurst parameter h which describe the decay of the
The specular data with their respective simulations of all height-height correlation function. In simple terms h can be
samples are shown in Fig. 2. Deviations between simulation taken as a measure for the jaggedness of the interfaces.28
and measurement can be observed at very small angles for all Both parameters will be relevant for the transport properties
samples measured with the laboratory source sample num- since, for a given value of the roughness amplitude, they will
bers 7,8,10,12,14 . This is caused by the nonlinearity of the determine the density of steps at the interfaces which form
x-ray detector at high intensities. The other samples had been finally the deviations from a perfect interface, i.e., the scat-
measured at the synchrotron. Deviations in intensity between tering centers.39 The interdependence of x and h results in
measurement and simulation at wave vectors in-between su- some uncertainty of their estimated values with h 0.5
perlattice Bragg peaks most pronounced in the spectrum of 0.2. In order to limit the number of free simulation param-
sample 6 are likely caused by surface contamination. In eters we kept h fixed at h 0.5. The lateral correlation length
principle, these long-wavelength deviations can be repro- is about 90 Å for all samples. The roughness correlation in
duced in the simulation by introducing an extra surface layer the z direction, expressed by z , is likely of less direct im-
of several nm thickness and adjusting its optical parameters. portance for the electron scattering, but it might have an
However, this does not influence the intensities of the super- influence on the interlayer exchange coupling via thickness
lattice Bragg peaks and hence the values obtained for the variations of the Cr layer. Variations of the exchange cou-
relevant interface roughness parameter . Furthermore, this pling are taken into account by the antiferromagnetic frac-
contamination layer is also unlikely to influence the electri- tion. The samples discussed here have a constant value of
cal transport data. Therefore, we decided to keep the simu- z 130 Å, obtained from simulations of the asymmetric
lations as simple as possible, only including the relevant lay- ( ) 2 scans.
ers. In general, the films grown on the Cr buffer are smoother In summary, the SA XRD analysis reveals that the struc-
than without buffer. Obviously, this Cr seed layer provides a tural parameters of the samples discussed here vary mostly in
better template for the superlattice growth than the bare YSZ the amplitude of the interface roughness (2.2 Å 5 Å),

13 696 R. SCHAD et al. 57

taxial samples . The scattering at such big steps could be less
spin selective than at monoatomic ones.
ii Since these polycrystalline samples have a high de-
gree of bulk defects it is doubtful whether their contribution
can be neglected. Including in the discussion bulk scattering
which might have a spin asymmetry in the electron scattering
there would exist a GMR effect already without any interface
contribution. In order to explain now the observed roughness
dependence of the GMR amplitude, the spin asymmetry of
the electron scattering at the interfaces would have to be
opposite to the bulk contribution. Then increasing scattering
at the interfaces increasingly compensates the GMR effect
stemming from the bulk scattering. The electrons which are
less scattered at the bulk impurities would be scattered at the
interfaces and vice versa.4
For both scenarios increasing values of would increase
s and, at the same time, decrease . However, the inter-
face roughness dependence of the spin asymmetry of the
interface scattering would be exactly opposite. This dilemma
in the interpretation of the experimental data is an inherent
problem for all samples with a non-negligible amount of
bulk defects, in particular polycrystalline samples. A clear
interpretation is impeded not only by the presence of such
bulk defects but also their undefined contribution to the spin
FIG. 4. Saturation resistivity S a and magnetoresistance, cor- asymmetry of the electron scattering and their unknown
rected for variations of the antiferromagnetic fraction, changes in concentration and influence when varying the in-
/AFFT b as a function of the interface roughness amplitude . terface quality. These undefined and variable bulk contribu-
Shown are the measured data crosses and linear best fits lines . tions might also account for the scatter of the transport data
S increases with increasing whereas decreases. in Fig. 4.
with little variation in the lateral roughness parameters. This
structural information is now used to understand the trans- SUMMARY
port properties. Since the interface roughness amplitude is We presented the interpretation of the transport properties
the structure parameter varying mostly we focus on the dis- of Fe/Cr superlattices based on their structural properties.
cussion of s and as a function of Fig. 4 . First, it has The GMR effect reaches very high values compared to other
to be noted that the GMR / s is rather high up to 80% polycrystalline samples of up to 80% for ten bilayers indi-
compared to values usually reported for nonepitaxial cating the importance of spin-dependent scattering processes.
samples.1619 This indicates, in our case, that the spin- We analyzed the structure of the high-quality Fe/Cr superlat-
dependent electron scattering dominates the spin- tices by quantitative simulation of the XRD spectra revealing
independent ( s) events. Therefore our analysis is rather in- the relevant structural interface parameters perpendicular to
dependent of uncharacterized changes in structural defects and in the plane of the interfaces. We found a decrease of the
affecting the spin-independent background resistivity. In ad- magnetoresistance and /
dition, the transport properties show a strong variation with s with increasing roughness
amplitude. The theoretical understanding is not clear. The
indicating a strong link between interface roughness and decrease of the magnetoresistance could be either caused by
magnetoresistance. We observe an increase of s and a de- enhanced roughness increasingly scattering electrons of both
crease of or / s with increasing Fig. 4 . The expla- spin orientations with similar strength or by a compensation
nation of this might be one of the following scenarios: of a bulk contribution by the interface scattering having op-
i Neglecting any spin-dependent bulk scattering, the ob- posite spin asymmetry to the electron scattering. Therefore, a
served roughness dependence of the magnetoresistance has clear experimental result about the influence of the interface
to be ascribed to the changes in the interface properties in the structure on the GMR amplitude will have to be based on
following way. The increasing interface roughness amplitude samples with negligible bulk scattering.
reduces the spin asymmetry of the interface scattering. This
is expected for higher values of when the minority elec-
trons are also increasingly scattered, thus reducing the spin ACKNOWLEDGMENTS
asymmetry of the interface scattering.4 On the other hand, This work was financially supported by the Belgian Con-
the pronounced superlattice Bragg peaks in the SA XRD certed Action GOA and Interuniversity Attraction Poles
spectra indicate rather smooth interfaces, certainly for the IUAP programs. R.S., C.D.P., and G.V. acknowledge sup-
best samples. However, the exact value of the roughness am- port by, respectively, the European Community Marie Cu-
plitude above which the GMR amplitude should decrease rie , the Research Council of the Katholieke Universiteit
with increasing is not known. An alternative explanation Leuven, and the Belgium Iteruniversity Institute for Nuclear
could be the possible occurrence of bigger steps at the inter- Sciences. We are indebted to J. Barnas for helpful discussion
faces of these polycrystalline superlattices contrary to epi- and carefully reading the manuscript.

57 QUANTITATIVE STUDY OF THE INTERDEPENDENCE . . . 13 697

*Author to whom correspondence should be addressed: Research 20 P. Belie¨n, R. Schad, C. D. Potter, G. Verbanck, V. V. Mosh-
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